Micromechanics and Microactuators

Micromechanics and Microactuators MECHANISMS AND MACHINE SCIENCE Volume 2 Series Editor MARCO CECCARELLI For further...

Author: Gondi Kondaiah Ananthasuresh | Burkhard Corves | Victor Petuya

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Micromechanics and Microactuators

MECHANISMS AND MACHINE SCIENCE Volume 2 Series Editor MARCO CECCARELLI

For further volumes: http://www.springer.com/series/8779

Gondi Kondaiah Ananthasuresh · Burkhard Corves · Victor Petuya Editors

Micromechanics and Microactuators Proceedings of MAMM 2010, Aachen, Germany, May 27-29, 2010

123

Editors Prof. Gondi Kondaiah Ananthasuresh Indian Institute of Science Bangalore 560 012 India [email protected]

Prof. Dr.-Ing. Burkhard Corves RWTH Aachen University 52056 Aachen Germany [email protected]

Prof. Victor Petuya University of the Basque Country 48013 Bilbao Spain [email protected]

ISSN 2211-0984 e-ISSN 2211-0992 ISBN 978-94-007-2720-5 e-ISBN 978-94-007-2721-2 DOI 10.1007/978-94-007-2721-2 Springer Dordrecht Heidelberg London New York Library of Congress Control Number: 2011940851 © Springer Science+Business Media B.V. 2012 No part of this work may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, microfilming, recording or otherwise, without written permission from the Publisher, with the exception of any material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)

Preface

The Workshop on Microactuators and Micromechanisms (MAMM 2010) is the first event of collaboration between the Technical Committee on Linkages and Mechanical Controls and the Technical Committee on Micromachines of the International Federation for the Promotion of Mechanism and Machine Science (IFToMM) that was held in 2010 at RWTH Aachen University, organized by the Department of Mechanism Theory and Dynamics of Machines. The scope of the workshop was to bring together scientists, industry experts and students. It was aimed at providing a special opportunity for exchange of knowhow and international collaboration in various disciplines related to microactuators and micromechanism technology. A follow-up workshop, MAMM 2012, will be held in January 2012 in Durgapur, India, to continue the successful interactions that were initiated in 2010. In addition to focusing on general topics of interest to microactuators and micromechanisms, MAMM 2012 will have a special session on microsurgery, possibly with a direct involvement of surgeons who will share their needs and research interests. The book is published in the Springer series “Machine and Mechanism Science” and contains peer-reviewed papers of the aforementioned workshop. The most recent research results in microactuators and micromechanism technology are presented in this book. The topics covered range from a piezoactuator-driven microrobot to an in-pipe micro mobile robot using peristaltic motion and from cellgrasping compliant mechanisms to a kinematics study of protein chains and the simulation of their motion. The editors like to express grateful thanks to IFToMM, the German National IFToMM Committee, the members of the MAMM 2010 International Scientific Committee for their support and cooperation: G. K. Ananthasuresh (Indian Institute of Science, Bangalore, India), Burkhard Corves (RWTH Aachen University, Germany), Amitabha Ghosh (Indian Institute of Technology, Kanpur, India), Antoni Gronowicz (Wroclaw University of Technology, Poland), Erwin-Christian Lovasz (University of Timisoara, Romania) Karl-Heinz Modler (Technical University Dresden, Germany), Victor Petuya (University of the Basque Country, Bilbao, Spain), Hidetsugu Terada (University of Yamanashi, Japan), Srikar Vengalattore (McGill University, Montreal, Canada),

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Preface

Yao Yan-An (Beijing Jiaotong University, P.R.China), Lena Zentner (Technical University Ilmenau, Germany). We thank the authors who have contributed excellent papers on various subjects covering a broad range of topics within the scope of the workshop. Also, we extend our thanks to the reviewers for the time and effort that they spent during the review process. Finally, our thanks are also with the personnel at Springer namely Nathalie Jacobs for their excellent and editorial support. Aachen, Summer 2011

Gondi Kondaiah Ananthasuresh Burkhard Corves Victor Petuya

Contents

Single Piezo Actuator Driven Micro Robot for 2-Dimensional Locomotion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . F. Becker, V. Minchenya, K. Zimmermann, and I. Zeidis Capsule Micromechanism Driven by Impulse . . . . . . . . . . . . . . . T. Ito, Y. Kito, S. Ishimori, A. Phunopas, and T. Hayashi

1 11

Development of In-Pipe Micro Mobile Robot Using Peristalsis Motion Driven by Hydraulic Pressure . . . . . . . . . . . . . . . . . . . Y. Nakazato, Y. Sonobe, and S. Toyama

23

Optimum Design of Mass Distribution of the Injection Molding Pantograph Mechanism with Constant Output Link Orientation . . . . M. Horie, Y. Hoshikawa, and D. Kamiya

31

Mathematical Synthesis of Compliant Mechanism as Cochlear Implant . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . L. Zentner

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Flexure Hinge-Based Parallel Manipulators Enabling High-Precision Micro Manipulations . . . . . . . . . . . . . . . . . . . . I. Ivanov and B. Corves

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Cell-Grasping Compliant Mechanisms with Real-Time Haptic Feedback . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Santosh D.B. Bhargav and Gondi Kondaiah Ananthasuresh

61

Fundamental Analysis of a Thin Film Type Conducting Polymer Actuator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . H. Terada and T. Yamagata

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Kinematics Study of Protein Chains and Protein Motion Simulation . . V. Petuya, M. Diez, M. Urizar, and A. Hernández

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Matrix Pad Transducer . . . . . . . . . . . . . . . . . . . . . . . . . . . L.M. Dehelean, N.M. Dehelean, and E.-Ch. Lovasz

101

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Contents

Ultrasonic Hot Embossing and Welding of Micro Structures . . . . . . K. Burlage, C. Gerhardy, and W.K. Schomburg

113

On Binary Topology Design of Electro-Thermally-Compliant MEMS . Pranay Sharma and Anupam Saxena

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Author Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Subject Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Contributors

Gondi Kondaiah Ananthasuresh Indian Institute of Science, Bengaluru, India, [email protected] F. Becker Department of Mechanical Engineering, Ilmenau University of Technology, Ilmenau, Germany, [email protected] Santosh D.B. Bhargav Indian Institute of Science, Bengaluru, India, [email protected] K. Burlage Konstruktion und Entwicklung von Mikrosystemen (KEmikro), RWTH Aachen University, Aachen, Germany, [email protected] B. Corves Department of Mechanism Theory and Dynamics of Machines (IGM), RWTH Aachen University, Aachen, Germany, [email protected] L.M. Dehelean Department of Mechatronics, “POLITEHNICA” University of Timisoara, Timisoara, Romania, [email protected] N.M. Dehelean Department of Mechatronics, “POLITEHNICA” University of Timisoara, Timisoara, Romania, [email protected] M. Diez Department of Mechanical Engineering, University of the Basque Country, Alameda de Urquijo s/n, 48013, Bilbao, Spain, [email protected] C. Gerhardy Konstruktion und Entwicklung von Mikrosystemen (KEmikro), RWTH Aachen University, Aachen, Germany, [email protected] T. Hayashi Ogasawara Precision Laboratory Ltd., Kanagawa, Japan, [email protected] A. Hernández Department of Mechanical Engineering, University of the Basque Country, Alameda de Urquijo s/n, 48013, Bilbao, Spain, [email protected] M. Horie Precision and Intelligence Laboratory, Tokyo Institute of Technology, Tokyo, Japan, [email protected]

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Contributors

Y. Hoshikawa Department of Mechano-Micro Engineering, Graduate school student, Tokyo Institute of Technology, Tokyo, Japan S. Ishimori Kyushu Institute of Technology, Faculty of Computer Science and Systems Engineering, Fukuoka, Japan, [email protected] T. Ito Faculty of Computer Science and Systems Engineering, Kyushu Institute of Technology, Kitakyushu, Japan, [email protected] I. Ivanov Department of Mechanism Theory and Dynamics of Machines (IGM), RWTH Aachen University, Aachen, Germany, [email protected] D. Kamiya Precision and Intelligence Laboratory, Tokyo Institute of Technology, Tokyo, Japan Y. Kito Kyushu Institute of Technology, Faculty of Computer Science and Systems Engineering, Fukuoka, Japan, [email protected] E.-Ch. Lovasz Department of Mechatronics, “POLITEHNICA” University of Timisoara, Timisoara, Romania, [email protected] V. Minchenya Department of Instrument-Making, Belarusian National Technical University, Minsk, Belarus, [email protected] Y. Nakazato Department of Innovative Systems Engineering, Nippon Institute of Technology, Saitama, Japan, [email protected] V. Petuya Department of Mechanical Engineering, University of the Basque Country, 48013, Bilbao, Spain, [email protected] A. Phunopas Kyushu Institute of Technology, Faculty of Computer Science and Systems Engineering, Fukuoka, Japan, [email protected] Anupam Saxena Indian Institute of Technology, Kanpur, UP 208016, India, [email protected] W.K. Schomburg Konstruktion und Entwicklung von Mikrosystemen (KEmikro), RWTH Aachen University, Aachen, Germany, [email protected] Pranay Sharma Indian Institute of Technology, Kanpur, UP 208016, India, [email protected] Y. Sonobe Department of Innovative Systems Engineering, Nippon Institute of Technology, Saitama, Japan, [email protected] H. Terada Graduate School of Medical and Engineering Science, University of Yamanashi, Yamanashi, Japan, [email protected] S. Toyama Institute of Symbiotic Science and Technology, Tokyo University of Agriculture and Technology, Tokyo, Japan, [email protected]

Contributors

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M. Urizar Department of Mechanical Engineering, University of the Basque Country, Alameda de Urquijo s/n, 48013, Bilbao, Spain, [email protected] T. Yamagata Graduate School of Medical and Engineering Science, University of Yamanashi, Yamanashi, Japan, [email protected] I. Zeidis Department of Mechanical Engineering, Ilmenau University of Technology, Ilmenau, Germany, [email protected] L. Zentner Technische Universität Ilmenau, Ilmenau, Germany, [email protected] K. Zimmermann Department of Mechanical Engineering, Ilmenau University of Technology, Ilmenau, Germany, [email protected]

Single Piezo Actuator Driven Micro Robot for 2-Dimensional Locomotion F. Becker, V. Minchenya, K. Zimmermann, and I. Zeidis

Abstract We analyse two micro robots for 2-dimensional locomotion on a flat surface. Forced bending vibrations of continua are used by both systems which are excited by piezoelectric bending actuators. These vibrations are transformed by non classical legs to complex trajectories at the contact points between robot and environment. The locomotion direction of the system can be controlled by the excitation frequencies of the actuation element. Models are developed and investigated to describe important motion effects of the robots. Furthermore some experimental results are presented. Keywords Micro robot · Piezoelectric actuator · Vibration of continua · Elastodynamic locomotion

1 Introduction Actual locomotion systems are dominated by rigid multibody systems with constant mass distribution. The modification of relative conditions is provided mostly by actuators in the joints. The authors are currently developing small micro robots for the movement in two dimensions on a flat ground based on vibration systems. The aim is to use forced vibration of continua, especially bending vibrations of beams and plates to realise locomotion. This motion principle, called elastodynamic locomotion, is especially useful for the creation of micro robots driven by piezoelectric actuators. These actuators are characterized by a high energy efficiency which converts more than 90% of the electrical energy into mechanical energy. Based on piezoelectric bending actuators several prototypes of micro robots were realised. Two of them are described in this article. Structural data are given in Table 1. A similar approach was followed by several persons for different environments. An inchworm locomotion device using a piezoelectric unimorph actuator F. Becker (B) Department of Mechanical Engineering, Ilmenau University of Technology, Ilmenau, Germany e-mail: [email protected]

G.K. Ananthasuresh et al. (eds.), Micromechanics and Microactuators, Mechanisms and Machine Science 2, DOI 10.1007/978-94-007-2721-2_1, C Springer Science+Business Media B.V. 2012

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F. Becker et al. Table 1 Structural data of the robots

Length x Width x Height Mass Max. velocity Actuator Excitation frequency

Beetle-Robot

Minch-Robot

(69 x 80 x 30) mm3 31,7 g 20 mm/s (on glass) circular piezo unimorph 12 - 70 kHz

(45 x 15 x 10) mm3 1,7 g 540 mm/s (on aluminium) rectangular piezo bimorph 1 - 45 kHz

for 1-dimensional motion on flat ground was presented by Lobontiu, Goldfarb and Garcia [5]. For the movement on the water surface Sitti and Song developed a water strider robot [7]. Other examples of biologically inspired robots using piezoelectric bending actuators and the described principle of motion are presented in [8] (flying robot), [4] (swimming robot) and [12] (robots with swarm application).

2 Theoretical Background In the context of this article locomotion is defined as “autonomous, internally driven change of location of human beings, animals or machines during which base of support and centre of mass of the body are displaced” [11]. Following this definition with [6] the later presented prototypes can be described as undulatory locomotion systems. A great number of locomotion systems are characterised by the overlay of “fast” actuation vibrations and a “slow” translocation. For the vector of general is the coordinates x this correlation is described in Fig. 1 and equation (1) where X “slow” component and ξ the “fast” component. ξ unlike X depends not only on t, but also on the “fast” time τ = ωt. ω is the frequency of the vibration. ξ is periodic with the period T = 2π/ω and it is supposed that the average value equals 0: 1 (t) + ξ (t, ωt) , with x (t) = X T

T

ξ (t, τ) dτ = 0.

(1)

0

For the creation of a directed locomotion an asymmetry in the system characteristic is required. The character of the system in the first half period of the vibration has to be another then in the second. The direction of the locomotion is characterised with an average value unequal 0. by X The maximum velocity of the system under consideration is observed near the resonance. In this case, the natural frequency ω0 of the elastic element, regarded as an elastic beam or thin plate, is close to the frequency ω of the exciting force: ω = ω0 + ε,

(2)

where ε is the off-resonance detuning with ε 1. When the excitation frequency passes through the resonance ( changes in sign) the motion of the micro robot

Single Piezo Actuator Driven Micro Robot for 2-Dimensional Locomotion

3

General coordinate x(t)

Fig. 1 Generation of locomotion

X ξ

Time t

changes in direction. This phenomenon was studied theoretically in [9] and [10] for a system that consists of two identical vibration-excited modules connected by a spring. The vibration exciters rotate with the same frequency in the same direction, but these rotations are shifted in phase relative to one another.

3 Minch-Robot 3.1 Design A piezoelectric bimorph is both the base body and the actuation element of MinchRobot (Fig. 2 and Table 1). The three contact points to the flat surface are realised by two legs and a tail. The legs are no classical legs in a biological context but bending transducers. The tail is a support.

Fig. 2 Minch-Robot [1]

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3.2 Principle of Motion and Control The use of forced beam vibrations is characteristic for the first prototype. The legs are excited by the transversal vibration of the piezo actuator. At their contact points to the surface transversal vibrations and longitudinal vibrations are performed. The overlay of the eigenmodes of different vibrations leads to the formation of complex trajectories at the end points of the legs. In connection to the geometry of the legs and the excitation frequency different forms can be provided. The trajectory depends on the relation between the amplitudes of the transversal and longitudinal vibrations. The relation can be controlled by the frequency of the actuator. This behaviour was confirmed by FEM simulations. For the control of the motion direction the asymmetry between the legs is used. It is the cause of a resonance shift between the legs, which leads to different amplitudes of the transversal vibrations. This relation is shown in Fig. 3.

3.3 Modelling and Simulation The locomotion of this prototype is dominated by two aspects: – asymmetric contact forces between the legs and the flat surface and – periodic deformation of the base body producing the actuation force. This phenomenon can be described by a mass point model (Fig. 4). It consists of the three mass points A, B and D which are connected by massless bars. Locomotion can be provided in the x-y-plane. The three points have continuously contact to the surface because of the gravitational force. Dynamics in the z-direction are not considered.

Fig. 3 Direction control of Minch-Robot [9]

Single Piezo Actuator Driven Micro Robot for 2-Dimensional Locomotion Fig. 4 Mass point model of the Minch-Robot

A(xA,yA)

5

Θ

D(xD,yD)

S(xS,yS)

y

B(xB,yB) x FRA NA

z 0

y

rS

FD

FRD

FRB

ND NB

x

With regard to the real motion behaviour periodic normal forces NA and NB are applied to the points A and B which lead in connection with the constant coeffi RB . In point RA and F cient of Coulomb dry friction μ to periodic friction forces F D are given. Applying RD and the periodic actuation force F D the friction force F the principles of linear momentum and angular momentum results in equations (3), (4) and (5), where J is the moment of inertia, mS the sum of the mass points and M1 , M2 and M3 are functions of geometric parameters and the linear and angular velocity. x˙ A x˙ B x˙ D mS x¨ S = − |FRA | − |FRB | − |FRD | + Fˆ D sin ωt cos ˙ ˙ ˙ rA rB rD

(3)

y˙ A y˙ B y˙ D mS y¨ S = − |FRA | − |FRB | − |FRD | + Fˆ D sin ωt cos ˙ ˙ ˙ rA rB rD

(4)

|F | ¨ = RA · M1 + J ˙ rA

|FRB | · M2 + ˙ rB

|FRD | · M3 ˙ rD

(5)

An example of the robot motion with a phase shift between the normal force functions of the points A and B is presented in Fig. 5. The movement of the centre of mass and the schematic robot are shown.

Fig. 5 Simulation of the mass point model for ϕ0 = 0◦ , ψ0 = 10◦ [1]

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3.4 Experiments The results of the experimental investigations agree with the simulations. In addition the influence of the surface material on the velocity of the micro robot is determined. These results are presented in [1] and [2] in detail.

4 Beetle-Robot 4.1 Design Beetle-Robot (Fig. 6 and Table 1) consists of the three components: information system, power supply (accumulator) and vibration system. The vibration system is formed by a circular piezoelectric unimorph actuator bonded on a triangular plate. At the corners of the plate three non classical legs are fixed. They serve as the contact points to the flat surface. The information system consists of a conductor plate with interfaces for programming, charging and telecommanding (infrared receiver). The framework is connected with three elastic elements to the vibration system.

4.2 Principle of Motion and Control Forced plate vibrations are used by the second prototype. The plate is excited by the bending vibrations of the actuator. According to the frequency different vibration forms are produced. At the contact points between robot and environment longitudinal and transversal vibrations are performed. The trajectory corresponds to the relation between the amplitudes of the vibrations. This is highly influenced by the unbalanced mass distribution of the carrying body. The motion direction can be controlled by the excitation frequency because of the resonance shift between the legs caused by the asymmetric system properties. Corresponding to the frequency the legs can be excited with different magnitudes.

1 Information system 2 Power supply 3 Vibration system

Fig. 6 Beetle-Robot

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Fig. 7 Overall strain of the FEM model of Beetle-Robot

Single Piezo Actuator Driven Micro Robot for 2-Dimensional Locomotion

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4.3 Modelling and Simulation A FEM model of the legs, the plate and the actuator was designed to formulate first assertions about the influence of the excitation frequency to the trajectories of the endpoints of the legs. The system is fixed at three points which correspond to the position of the connectors from the carrying body. A contact to the surface is not modelled. The actuator consists of a bending element. Complex trajectories at the endpoints of the legs are produced. The trajectories are influenced, on the one hand, by the design parameters like mass distribution, geometry and material properties and, on the other hand, by the control parameters like amplitude and frequency of the excitation. The overall strain of the system for a specific frequency over one period at four times is shown in Fig. 7. The undeformed state is shown by the light lines. It can be seen that the legs are excited by the plate vibration. The amplitudes of the legs are different. The period of the leg motion for the several coordinates is presented in Fig. 8. The difference in the amplitudes as well the phase shift between the leg vibrations can be seen. This behaviour is used to control the system motion.

4.4 Experiments The locomotion of the micro robot on different materials is investigated. The legs are activated by different frequencies. The vibration form of the legs and with it the

0.025 0.02

Leg I Leg II Leg III

Ampl., u x (o), uy (.), uz (x), [mm]

0.015 0.01 0.005 0 –0.005 –0.01 –0.015 –0.02 –0.025 n*T

Fig. 8 Trajectory of the legs

(n + 0.50)*T Normalized time t / T

(n + 1)*T

Single Piezo Actuator Driven Micro Robot for 2-Dimensional Locomotion

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Table 2 Locomotion of Beetle-Robot for different frequencies Frequency

Glass

Acrylic glass

Wood

Steel

30 kHz

45 kHz

53 kHz

60 kHz

locomotion of the robot also is influenced by the surface material. Some examples are given in Table 2. The start position of the schematic robot is presented solid. The dashed scheme shows the end position after some vibration periods. Furthermore the robot legs lose contact to the surface while the vibration. The locomotion is influenced by the resulting shock effects.

5 Conclusions and Outlook The above described two experimental micro robots Minch-Robot and Beetle-Robot can be classified as low cost systems. The author’s idea is to explore the mechanical properties of simple beams or plates, following the principle “intelligence in the mechanics” [3]. Knowing the resonance characteristics (eigenfrequencies and eigenforms) of vibrating continua, gaits for the locomotion of mobile robots on a rough surface are generated. Further investigations should be oriented to formulate the quantitative and qualitative relation between input parameters (frequency) and output parameters (trajectory of the legs). For this new models with lower grad of abstraction are needed. Further micro robots using the principle of undulatory locomotion are in the design process. New actuation concepts with regard to adaptive frequency control using intelligent piezoelectric actuators will be investigated. A special regard is set on swarm applications. Acknowledgments The work has been supported by the German Research Foundation (DFG) under grant Zi 540/11-1 as well as by the Free State of Thuringia via graduation scholarship.

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References 1. Abaza, K.: Ein Beitrag zur Anwendung der Theorie undulatorischer Lokomotion auf mobile Roboter. Dissertation at Ilmenau University of Technology, 2007. 2. Becker, F.: Modellbildung, Simulation und Entwurf schwingungsbasierter Lokomotionssysteme für 1D- und 2D-Bewegungen. Diploma thesis at Ilmenau University of Technology, 2009. 3. Blickhan, R.; Seyfarth, A.; Geyer, H.; Grimmer, S.; Wagner, H.; Günther, M.: Intelligence by Mechanics. In: Philosophical Transactions of the Royal Society 365 (2007), pp. 199-220 4. Kosé, G.; Shoham, M.; Zaaroor, M.: Propulsion Method for Swimming Microrobots. In: IEEE/ASME Transactions on Robotics 23 (2007) No. 1, pp. 137-150. 5. Lobontiu, N.; Goldfarb, M.; Garcia, E.: A Piezoelectric-driven Inchworm Locomotion Device. In: Mechanism and Machine Theory 36 (2001), pp. 425-443. 6. Murray, R. M.; Burdick, J.; Lewis, A. D.; Ostrowski, J.: The Mechanics of Undulatory Locomotion: The Mixed Kinematic and Dynamic Case. In: IEEE International Conference on Robotics and Automation 2 (1995), pp. 1945-1951. 7. Song, S. Y.; Sitti, M.: Surface-Tension-Driven Biologically Inspired Water Strider Robot: Theory and Experiments. In: IEEE/ASME Transactions on Robotics 23 (2007), No. 3, pp. 578-589. 8. Wood, R. J.: The First Tabkeoff of a Biologically Inspired At-Scale Robotic Insect. In: IEEE/ASME Transactions on Robotics 24 (2008), No. 2, pp. 341-347. 9. Zimmermann, K.; Zeidis, I.; Behn, C.: Mechanics of Terrestrial Locomotion. Berlin. Springer, 2009. 10. Zimmermann, K.; Zeidis, I.; Bolotnik, N.; Pivovarov, M.: Dynamics of a Two-module Vibration-driven System Moving Along a Rough Horizontal Plane. In: Multibody System Dynamics 22 (2009), No. 2, pp. 199-219. 11. IFToMM Dictionaries online. Available at: http://130.15.85.212/terminology/ TerminologyWeb/1031_2057/frames.html (2009-12-08). 12. http://www.ipr.ira.uka.de/i-swarm/MainPage/Robots/R_1.htm, (2009-10-12).

Capsule Micromechanism Driven by Impulse T. Ito, Y. Kito, S. Ishimori, A. Phunopas, and T. Hayashi

Abstract We have developed a traveling small capsule, which has a smooth outer surface and is driven by inertia force and friction force. Measuring only 7 mm in diameter and 12 mm in length, it is sufficiently small to be placed in the human gullet or intestines. The capsule contains a small magnet and a coil, and an electric pulse drives the magnet to move the capsule. To investigate the feasibility of our traveling capsule, we did the theoretical analysis and the computer simulation using a simple model. We performed an experimental investigation on making our capsule travel on a plastic plate. We also showed that it can travel on the surface of a pig’s intestine. Our capsule may be useful for medical treatments such as inspection, drug delivery and operation. Keywords Capsule · Micromechanism · Magnetic force · Friction force

1 Introduction Seventy percent of the human body is composed of soft tubes with diameter ranging from μm order to cm order. Therefore, capsules which can travel inside these tubes are useful for medical treatments such as inspection, drug delivery and operation. Various kinds of machines for this purpose have been proposed [1] but most of them had hands in order to crawl in tubes [2-6]. However, the outer surface of the machine should not have any projections so as not to injure the surrounding site. Machines that have a smooth outer surface and crawl have been developed. Among them, some utilized a fluid actuator to move [7], [8], but it was more than 30 mm long and needed a high-power fluid pump. To avoid using legs or hands to crawl, eel-like mechanisms were theoretically analyzed [9], [10], and inchworm-type robots were developed [11], but they had relatively complicated mechanisms and it was difficult to make them as small as medicine tablets. This paper describes a traveling small T. Ito (B) Faculty of Computer Science and Systems Engineering, Kyushu Institute of Technology, Kitakyushu, Japan e-mail: [email protected]

G.K. Ananthasuresh et al. (eds.), Micromechanics and Microactuators, Mechanisms and Machine Science 2, DOI 10.1007/978-94-007-2721-2_2, C Springer Science+Business Media B.V. 2012

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capsule, which has a smooth surface and is driven by inertia force and friction force. Measuring only 7 mm in diameter and 12 mm in length, our capsule is sufficiently small to be placed in the human gullet or intestines.

2 Theoretical Analysis 2.1 Structure of the Traveling Capsule The outside appearance of the capsule is shown in Fig. 1. Our capsule travels by a to-and-fro motion of an inner mass. The capsule consists of the body (M) with coil and of the moving mass (m) as shown in Fig. 2 and Fig. 3. The coil is made of φ 0.05 [mm] copper by 200 turns. The moving mass is permanent magnet of NdFe-B and it is driven by the magnetic force fm by giving step shaped current to the coil. The physical model of the capsule is shown in Fig. 3. The movement of mass m is restricted between two stoppers A and B. The resistance force fr acts against the movement of the body M from the base. For making the subject simple, we neglected friction force between m and M, which is relatively very small and not play major role in the propulsion of the capsule. To conduct the theoretical analysis, the motion of the capsule should be better to be divided into following four steps. [Step 1] As shown in Fig. 4(i), M and m pull each other by magnetic force fm . The mass m that starts from stopper A is accelerated by the magnetic force fm and

Fig. 1 Photograph of a traveling capsule

Body Coil

Permanent magnet

Fig. 2 Main parts of the capsule

Capsule Micromechanism Driven by Impulse

13 l = 12 mm

Fig. 3 Schematic illustration of the capsule (cross section)

Coil

a = 3.2 mm

d = 7 mm

Permanent magnet B

A

m

M

Fig. 4 Traveling mechanism of the capsule

a x

B

u

A

fm

(i)

m M

x0

u0

fr

B

v0

A m

(ii)

xT x1 B

A (iii)

m M

fr also the body M is accelerated by the force (fm - fr ) until m collides with M at stopper B. Defining that M moves by distance x0 to right side and m u0 to left side in time t0 by that motion, we will be able to determine these values. [Step 2] As shown in Fig. 4(ii), assuming that after collision, M and m moves together with initial velocity v0 and decelerated by friction force fr and lastly they will stop. Defining that M and m move by x1 to the left within time t1 by that motion as shown in Fig. 4(iii), we will be able to determine these values. [Step 3] Just similarly as [Step 1], giving magnetic force –fm ’ by adding (-) step shape current to the coil, M and m push each other. The mass m that starts from stopper B is accelerated by magnetic force fm ’ and also the body M is accelerated by the force (fm ’-fr ) until m collides with M at stopper A. Defining that M moves by distance x0 ’ to left within time t0 ’ in that motion, we will be able to determine these values.

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[Step 4] Just similarly as [Step 2], M and m moves together with initial velocity v0 ’ and decelerated by friction force fr and after that stop. Defining that M and m moves by x1 ’ to the right within t1 ’ in that motion, we will be able to determine these values. In the result, defining that the body M moves xT to the left within time tT , they will be expressed by equations (1) and (2) as follows, xT = (x1 − x0 ) − x1 − x0

(1)

tT = t0 + t1 + t0 + t1

(2)

We should design to make the larger value of xT and the smaller value of tT .

2.2 Equations of Capsule Motion We can obtain equations of motion in each step as the followings. [Step 1] We define that x and u are displacements of M and m respectively, and that a is total gap between moving mass and stoppers. For M and m, equations of motion are expressed as follows. M · x¨ + fr = fm

(3)

m · u¨ = fm

(4)

Actually, magnetic force fm varies depending on the displacement x, u but to make the subject simple, we set fm to be constant for approximation. From above equations (3) and (4), the velocities x˙ , u˙ and the displacements x, u become as follows, x˙ =

fm − fr · t, M

x=

fm − fr t2 · M 2

(5)

fm · t, m

u=

fm t 2 · m 2

(6)

u˙ =

As the collision occurs when x + u = a, the time t0 and the displacement x0 at that moment become as follows, 1 2aM (7) t0 = √ Kt Kt = fr (n + 1) f − 1 x0 =

f −1 a. (n + 1) f − 1

There, the mass ratio “n” and force ratio “f” are defined as follows,

(8)

Capsule Micromechanism Driven by Impulse

n=

M m

15

and

f =

fm . fr

(9)

[Step 2] Assuming that the collision is inelastic, that is, the coefficient of restitution e = 0, the initial velocity v0 of the body (combined mass M+m) is expressed as follows, 2afr m · u˙ − M · x˙ n ν0 = = . (10) √ M+m M + 1) + 1) f − 1 (n (n t=t0 So the equation of the motion about the combined mass becomes as follows, (M + m) x¨ + fr = 0,

(˙x)t=0 = ν0 .

(11)

Solving above equation, x˙ = ν0 −

fr · t, M+m

x = ν0 t −

fr t2 · M+m 2

(12)

As the combined mass moves until x˙ = 0, the time t1 and displacement x1 at this moment are expressed as follows, 2aM 1 t1 = √ (13) fr (n + 1) f − 1 x1 =

n a (n + 1) {(n + 1) f − 1}

(14)

[Step 3] Similar equations as used in [Step 1] can be used. However, the direction of motion x become opposite and the value of driving force fm ’ must be different from fm . So the values of t0 ’ and x0 ’ are obtained as follows. t0

1

=

(n + 1) f − 1 x0 = −

2aM fr

f − 1 a (n + 1) f − 1

(15)

(16)

[Step 4] Similar equations as used in [Step 2] can be used changing the direction of x and changing fm to fm ’ the values of t1 ’ and x1 ’ are obtained as follows. 1 2aM (17) t1 =

fr (n + 1) f − 1 x1 =

n a (n + 1) {(n + 1) f − 1}

The motions obtained from these equations are summarized in Fig. 5.

(18)

a

x0’

m

M+m

M

x1

x0

M

xT

x

Fig. 5 Summary of the result of analyzed motion

x1’

T. Ito et al. displacement

16

t time

a

M+m

m t0

t0’

t1

t1’

tT

2.3 Investigation on the Theoretical Analysis Important results on the above theoretical analysis are as the followings. (1) About the travelling, stroke xT is expressed by following equations. x = x f → f

(19)

(2n + 1) − (n + 1) f (n + 1) {(n + 1) f − 1}

(20)

t = t f → f

(21)

2 Ct = √ (n + 1) f − 1

(22)

xT = x − x , x = Cx · a ,

Cx =

(2) About the period tT for a stroke, tT = t + t , t = Ct · Kt ,

(3) About the traveling speed, it should be most important feature for designing the travelling capsule. From above analysis, it is clear that one stroke motion of inner mass m dominates the total speed. To see the tendency of force-speed relation, one stroke motion is considered first as follows. The equations on travelling speed S are expressed as follows, S=

x = CS · KS t

Cx (2n + 1) − (n + 1) f CS = , √ = Ct 2 (n + 1) (n + 1) f − 1

(23) KS =

a · fr 2M

(24)

The outline of the effect of n and f to the coefficient of travelling speed Cs is shown in Fig. 6. In the figure, force ratio f (= fm /fr ) should be greater than 1, because friction force between the capsule and the base cannot be greater than magnetic

Capsule Micromechanism Driven by Impulse 0.4 coef. of travering speed Cs (S = Cs*Ks)

Fig. 6 Speed-force characteristics (calculation)

17 n = 0.5 n=1 n=2 n=3 n=4 n=5

0.2 0 −0.2 −0.4 −0.6 −0.8

1

2

3

4

5

6

force ratio f ( = fm/fr)

force fm while the capsule is moving. From the figure, it is expressed that we can choose the parameters as follows to design high speed capsule. (a) Mass ratio n should be small. (b) Force ratio f should be large.

3 Experiments and Results 3.1 Traveling Tests We made a traveling capsule as shown in Fig. 1 and 3. The capsule was put on the flat plastic plate and the step shaped current was given to the coil. The capsule traveled just as we predicted by theoretical analysis. The travelling speed measured in the experiment is shown in Fig. 7. As the voltage at the coil increased, which means the magnetic force also increased, the direction of travel changed and the speed characteristics were similar to the calculated result as shown in Fig. 6 above. We tested making our capsule travel on the surface of a pig’s intestine (Fig. 8). Although the speed of the capsule decreased to about half of that on the plastic plate, the capsule could also travel on the pig’s intestine.

traveling speed [mm/s]

15

Fig. 7 Speed characteristics measured in the experiments

10 5 0 −5 −10

1

2

3 4 voltage [V]

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Fig. 8 Capsule traveling on the surface of a pig’s intestine

3.2 Friction Force Measurement To utilize the results of theoretical analysis, and to improve the capsule traveling capability, it is necessary to measure parameters of the actual capsule by experiments. First, we measured friction force fr between the capsule and a plate. For the plate material, plastic, rubber, and phantom which is a plastic material and has similar elasticity characteristics to living body, were chosen. The measurement setup is shown in Fig. 9 and the results are shown in Table 1.

3.3 Magnetic Force Measurement Also, magnetic force fm was measured to fix the parameter. The measurement setup is shown in Fig. 10 and the result is shown in Fig. 11. As shown in Fig. 11, within 4 mm displacement, the magnetic force increases depending on the displacement of the permanent magnet. Therefore, impact force at stopper A in Fig. 3 is bigger than the one at stopper B. This asymmetric structure causes the capsule to travel in one direction.

Capsule Sample fr

Fig. 9 Friction force fr measurement setup

fr

Digital force gauge

Capsule Micromechanism Driven by Impulse

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Table 1 Summary of friction force measurement Capsule

Aluminum

Sample

Rubber plate

Phantom

Sample condition

Dry

Dry

Wet

Dry

Friction force fr [N] (Average of 10 measured values) Standard deviation

0.020

0.015

0.018

0.005

0.0034

0.0021

0.0016

0.0004

Fig. 10 Magnetic force fm measurement setup

Plastic plate

Digital force gauge fm Displacement

magnetic force fm [N]

Coil

0.10 0.09 0.08 0.07 0.06 0.05 0.04 0.03 0.02 0.01 0

Permanent magnet

V = 3.5[V] V = 3.0[V] V = 2.5[V] V = 2.0[V] V = 1.5[V]

0

1

2 3 4 displacement [mm]

5

6

Fig. 11 Displacement–force characteristics

4 Computer Simulation For the theoretical analysis in chapter 2, we set magnetic force fm to be constant for approximation. But the experimental result in Fig. 11 above shows that fm is not constant and is in function of distance. We considered that the dependence of force on distance is expressed by setting fm and fm ’ to different values. The force fm of the going inner mass is set to be greater than the force fm ’ of the returning inner mass. The collision between inner mass “m” and shell “M” at the stopper at both ends of the capsule is the major source of propulsion. The force when inner mass “m” is just before collision at the stopper is more effective than when the inner mass is leaving the stopper.

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This approximation works well: the calculation and experimental results coincide well as shown between Fig. 6 and Fig. 7. Therefore, in the theoretical analysis, we set the force fm and fm’ to be constant to simplify the calculation. To improve the capsule propulsion by conducting a precise simulation and calculating the motion with force varying as a function of distance, a computer simulation with numerical integration is necessary. Since the actual values of the parameters of our capsule were obtained as mentioned above, we conducted computer simulation of capsule motion, using these parameters and magnetic force in function of distance. The computer simulation was conducted using Runge-Kutta method. Using these parameters, time – displacement relation graph was obtained as shown in Fig. 12 and was compared with the result of theoretical analysis mentioned in chapter 2. In the figure, the result of theoretical analysis in chapter 2 is shown as graph (A) and the result of computer simulation (numerical analysis) is shown as graph (B). The characteristics of motion shown in the graph are similar

(A)Theoretical analysis

(B)Numerical analysis

Travel distance [mm]

0.4 0.3 0.2 0.1 0 −0.1 −0.2 −0.3

0

0.005

Fig. 12 Results of computer simulation

Fig. 13 Computer graphics animation (solid model)

0.01 0.015 Time [s]

0.02

0.025

Capsule Micromechanism Driven by Impulse

21

but the total displacements after 4 steps of motion differ. This result shows that we can obtain precise estimation of capsule motion by numerical computer simulation. To show the result of our computer simulation graphically, we made computer graphics animation. The animation data is generated by the computer simulation numerical analysis mentioned above. One of the results is shown in Fig. 13. The graphical user interface is also made for the computer graphics animation display tool.

5 Arranging Signal for Speedup To make the capsule travel faster, we examined the theoretical analysis. We gave the capsule a standard rectangular input signal as shown in Fig. 14 (i). The capsule proceeded with to-and-fro vibration. Although the capsule moves forward, its backward motion is inefficient. Therefore, the capsule can proceed efficiently, if a greater input is given in the forward motion of the moving mass and a smaller input is given in the backward motion of the moving mass. The input signal shown in Fig. 14 (ii) was given to the capsule coil and the speed increased. The speed of the capsule with the proposed waveform (14 mm/s) was about twice as fast as that with the conventional waveform (6 mm/s).

6 Small Circuit for Traveling Capsule To make the capsule wireless, the capsule should be driven by small batteries inside the capsule. We made the small electronic circuit that is made of chip ICs driven by batteries in the capsule. This circuit can drive the to-and-fro motion of the magnet inside the capsule by DC power with just one set of electromagnetic coil.

(i)

(ii)

Fig. 14 Improvement of input voltage wave form: (i) conventional; (ii) proposed

voltage [V]

voltage [V]

2.5 0 −2.5 2.5 0 −1.5 0.05[s]

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7 Conclusion Although the capsule does not have wheels nor legs, it can travel utilizing its inertia force and friction force. We conducted theoretical analysis for the capsule and showed how the capsule mechanism worked. To increase capsule speed, new input waveform was proposed and tested to prove that the new waveform can make the capsule speed about twice as fast as conventional one. Our capsule is supposed to be useful for medical treatment as inspection, drug delivery or operation. Acknowledgments This research was supported by Grant-in-Aid for Scientific Research from Japan Society for the Promotion of Science (#20560244).

References 1. Taylor, R. H., A Perspective on Medical Robotics, Proceedings of The IEEE, Vol. 94, No. 9, pp. 1652-1664, 2006. 2. Masuda N., Hayashi T., and Cai Y. Developments of Guidance Machine for Colonoscope, Int. Journal of JSPE, Vol.28, No.1, 1994. 3. Oura, M. and Hayashi T., Traveling machine with six legs for inside of tube, Proc of JSPE 1997 Spring Conference, 1997. 4. Nakazato, Y., Ishii, T., Sato, H., and Ariga, Y., Development of In-pipe Mobile Robot Driven by Hydraulic Pressure, Proc of The 3rd . IFToMM Int. Micrimechanism Symposium, pp. 13-16, 2001. 5. Takahashi, K.e, Japan Patent #H05-212093, 1992. 6. Adachi, H., Japan Patent #H06-154191, 1992. 7. Yoshida, K., Park, Jung-Ho, Shimizu, T., and Yokota, S., A Micropump-Mounted In-Pipe Mobile Micromachine Using Homogeneous Electro-Rheological Fluid, Proc of The 3rd . IFToMM Int. Micrimechanism Symposium, pp. 2-7, 2001. 8. Yokota, S., Functional Fluids from Point of View of Actuators, Journal of the Robotic Society of Japan, Vol. 24, No. 4, pp.25-31, 2006. 9. Boyer,F., Porez, M., and Khalil, W., Macro-Continuous Computed Torque Algorithm for a Three-Dimensional Eel-Like Robot, IEEE Transactions on Robotics, Vol. 22, No. 4, pp. 763-775, 2006. 10. Wakimoto, S., Suzumori, K., and Kanda, T., A Bio-mimetic Amphibious Soft Cord Robot, Transactions of The Japan Society of Mechanical Engineers, Series C, Vol. 72, No. 714, pp. 471-477, 2006. 11. Hirano, S., Luo, Zhi-Wei, and Kato, A., Development of An Inchworm-type Searching Robot, Journal of the Robotic Society of Japan, Vol. 24, No. 7, pp. 838-844, 2006.

Development of In-Pipe Micro Mobile Robot Using Peristalsis Motion Driven by Hydraulic Pressure Y. Nakazato, Y. Sonobe, and S. Toyama

Abstract In this paper, we developed an in-pipe mobile robot which operates in the blood vessels. For this purpose, the diameter of the robot was designed to be equivalent to or smaller than that of blood vessels, assuming the use of the robot in the human aorta. Thus, the diameter of the robot was designed to be less than 2-3 mm. Furthermore, we adopted a mechanism that operates normally even when machining accuracy is not good. Taking into account the scale effect, a design was considered in which the robot is operated in an environment where the effects of friction and surface tension are large and the effects of gravity and inertia are small. As a result, we did not select a mechanism that moves with the use of wheels, but instead adopted a mechanism that utilizes peristalsis to move the robot. In addition, due to the possibility of leakage of electric current, we did not use an actuator operating on an external power supply but one which is operated by hydraulic pressure. With these conditions, we fabricated an in-pipe mobile robot, and the operational characteristics of the robot were studied. Keywords In-pipe robot · Scale effect · Peristalsis motion · Hydraulic pressure · Blood vessel

1 Introduction We developed an in-pipe mobile robot which operates in the blood vessels. For this purpose, the diameter of the robot was designed to be equivalent to or smaller than that of blood vessels, assuming the use of the robot in the human aorta. Thus, the diameter of the robot was designed to be less than 2-3 mm. Furthermore, we adopted a mechanism that operates normally even when machining accuracy is not good. Taking into account the scale effect, a design was considered in which the robot is operated in an environment where the effects of friction and surface tension are large and the effects of gravity and inertia are small. As a result, we did not select a mechanism that moves with the use of wheels, but instead adopted a mechanism that utilizes peristalsis to move the robot. In addition, due to the possibility of leakage of Y. Nakazato (B) Department of Innovative Systems Engineering, Nippon Institute of Technology, Saitama, Japan e-mail: [email protected] G.K. Ananthasuresh et al. (eds.), Micromechanics and Microactuators, Mechanisms and Machine Science 2, DOI 10.1007/978-94-007-2721-2_3, C Springer Science+Business Media B.V. 2012

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electric current, we did not use an actuator operating on an external power supply but one which is operated by hydraulic pressure. In this study, we propose a mobile device, a mobile microrobot, that has a pistonlike hydraulic pressure generator at its end and achieves peristaltic motion by changing its body length and width by injecting and ejecting a driving fluid into and from the driving section of the device.

2 Travelling Mechanism and Actuator Suitable for Operation in the Blood Vessel In designing an in-pipe mobile robot, the travelling mechanism and an actuator suitable for operation in blood vessels were developed. In selecting the travelling mechanism, crawlers and wheels were not considered. Wheels are not suitable for driving the robot in blood vessels whose internal structures are complicated. For example, when wheels are used, it is difficult for the robot to climb over a bump with a height greater than the radius of the wheels [1-3]. The travelling mechanism using a crawler, which is considered to be suitable for traversing rough surfaces, may cause some damage on the internal walls of the blood vessels. Furthermore, both mechanisms require highly accurate manufacturing processes for fabrication of wheels and shaft holes, thus high precision processing is required, and this is an obstacle for miniaturization of the robot. On the basis of the above considerations, we studied the travelling mechanism of nematodes and earthworms, which use peristalsis to move their bodies. Now, we consider the scale effect. In general, when the diameter of a machine decreases to 2-3 mm, the effects of inertia and gravity decrease and the effects of friction and surface tension increase. In particular, in water whose viscosity is higher than that of air, these phenomena are apparent. When we study the traveling mechanism of microorganisms in water, we find that they use flagella or generate peristaltic motion. For this study, we noted that many organisms of this size, i.e., nematodes, use peristalsis, in which the driving mechanism shrinks and stretches the body in the direction of movement, and we attempted the fabrication of a similar system to mechanically drive the robot. In selecting an actuator, considering the use of the robot in the human body, we selected a driving mechanism that does not require heat or electricity, as even a very weak voltage may have a significant effect on the body. Considering various factors, we selected a hydraulic pressure driving mechanism that makes use of an isotonic sodium chloride solution.

3 Mechanisms of Prototype Devices 3.1 Principle of Motion In this study, we propose a mobile device, a mobile microrobot, that has a pistonlike hydraulic pressure generator at its end and achieves peristaltic motion by changing

Development of In-Pipe Micro Mobile Robot Using Peristalsis Motion Driven. . .

25

its body length and width by injecting and ejecting a driving fluid into and from the driving section of the device. We develop an in-pipe mobile device with peristaltic motion, which comprises two segments that are arranged in series in the direction of motion. Each segment is made of crude rubber or silicon, which are highly compatible with living bodies; therefore only physiological saline solution, as the driving fluid, and the crude rubber or silicon are inserted into living bodies. The details of the peristaltic motion are as follows. First, the driving fluid is injected into the rear segment to allow it to expand in both forward and circumferential directions; thus, the rear segment becomes thick and long. Next, the driving fluid is also injected into the front segment, causing it also to become thick and long. At this time, the thickened rear segment is in contact with the inner wall of a pipe and remains stationary because of friction, causing the front segment to be pushed forward. Subsequently, the driving fluid is evacuated from the rear segment to cause it to contract; thus, the rear segment becomes thin and short. At this time, the thickened front segment comes into contact with the inner wall of the pipe and is thus stationary because of friction; therefore, the contracted rear segment is detached from the inner wall and drawn forward owing to the decreased friction. Extensional waves propagate from the front to the rear segments during the repetition of these motions, causing the two-segment device to move by peristaltic motion. Figure 1 shows a schematic of the principle of the two-segment mobile device.

Fig. 1 Schematic illustration of principle of motion

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Fig. 2 Mobile device driven by two-tube pumping

(a) Schematic illustration

(b) Photograph of mobile device

3.2 Experimentally Fabricated Robot Figures 2(a) and (b) show the in-pipe mobile robot fabricated with the assumption that it moves in pipes of 7 mm inner diameter. In order to enable the operation of the robot in pipes of various diameters, the diameter of the robot was set at 8 mm and was designed to pass through a pipe with a minimum 4 mm diameter. The total length of the robot was 18 mm when shrunk. The weight of the robot was 3.4 g without fluid in the body of the robot. By altering the length of the stretchable section, the total length of the robot can be reduced or increased. Acrylic material was used for the nodes of the robot, and silicone rubber (0.2 mm thick) was used for the external wall. A saline solution was introduced through a vinyl pipe via a 1.5-mm-diamater hole located at the back of the robot. The robot was stretched and shrunk by the pressure applied to the saline solution.

4 Driving Experiment 4.1 Outline of System We designed the robot with the aim of operating it in blood vessels, however, for the following reasons we did not carry out the operation in actual blood vessels.

Development of In-Pipe Micro Mobile Robot Using Peristalsis Motion Driven. . .

27

(i) Quantitative observation was difficult due to variability of data caused by the difference in the freshness of blood vessels. (ii) Since blood vessels are opaque, we were unable to observe the operation of the robot. (iii) Acquisition of blood vessels was difficult In the experiment, we used a clean silicon rubber tubes (inner diameter, 6 mm; outer diameter, 8 mm). A robot was placed inside the acrylic pipe, and the operation was studied. The acrylic pipe was arranged both horizontally and vertically with respect to the ground. The travelling speed and the amount of strokes for one reciprocated movement of the syringe piston were measured. The crude rubber coating the bodies expands and contracts when the driving fluid that fills the syringes is pumped and evacuated. Electric actuators that move straight back and forth are connected to the piston sections of the syringes, thus establishing a system that can control the position and velocity of the piston motion. Figures 3 and 4 show the straight reciprocation actuators attached to the syringes and the outline of the system used in our experiments, respectively. Physiological saline solution was used as a driving fluid considering the minimization of the damage that may be caused by the leakage of the driving fluid inside blood vessels when our devices are used in practice. Moreover, silicon rubber tubes and a 5-mPas-viscosity mixture of glycerin and pure water were used in place of blood vessels and blood, respectively. Table 1 summarizes the mechanical characteristics of human blood vessels and blood and those of the silicon rubber tubes and the mixture used in this experiment.

4.2 Experimental Methods Silicon rubber tubes are placed almost horizontally in the mixture, as explained in section 4.1, at room temperature. The amounts of saline pumped into the syringes were 0.30. This value, with which the maximum level of expansion is ensured

Balloon

Bulkhead Pipe line

Piston

Cylinder

Saline

Fig. 3 Straight reciprocation systems attached to syringes

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Y. Nakazato et al.

Fig. 4 Outline of experimental system

Table 1 Characteristics of blood and blood vessels, and mechanical properties of the materials used in this experiment

Artery: Outer diameter Artery: Inner diameter Young’s modulus of blood vessel Viscosity coefficient of blood

Human

Experimental materials

8[mm] 6[mm] 1[MPa] 4.7[mPas]

8[mm] 6[mm] 2[MPa] 5[mPas]

without breakage of the device, are obtained in the preliminary experiment. The measurement was carried out in nine steps by changing the evacuation rate by 0.09 ml/s from 0.90 ml/s. The time required for the mechanism to move 30 mm in a pipe was measured using the front end of the device as the measurement point. The behavior is photographed using a video camera, and each measurement was carried out by analyzing the obtained images.

5 Experimental Results Figure 5 shows the experimental results for the peristaltic mobile devices driven by the two pumping methods. The robot can move at a speed of 0.38 mm/s in silicon rubber tubes 6 mm inner diameter. The highest speed was obtained at the evacuation rate of 0.90 ml/s.

6 Discussion and Conclusions We proposed a microscopic mobile device that can move inside 2-3-mm-diameter blood vessels by peristaltic motion achieved by repeated expansion and contraction using hydraulic pressure, in particular, using a physiological saline solution as the

Development of In-Pipe Micro Mobile Robot Using Peristalsis Motion Driven. . .

29

Fig. 5 Experimental results for mobile devices driven by two- and one-tube pumping methods

driving fluid. Therefore, the diameter of the robot was designed to be either equal to or smaller than that of the human aorta. Assuming the use of the robot in the aorta, the diameter of the robot was set at 2-3 mm or smaller. Accordingly, the use of wheels to move the robot was avoided, and instead we adopted a mechanism which uses peristaltic movements. Also, considering the possibility of leakage of electric current, we did not use an actuator which requires an external power supply, and selected an actuator which can be operated by hydraulic pressure. We then fabricated a robot which satisfies the above conditions, and experimentally studied the operation of the robot. Although we were unable to perform driving experiments in actual human blood vessels, we confirmed that the robot can move at a speed of 0.38 mm/s in silicon rubber tube of 6 mm inner diameter. Acknowledgments A Part of this study was supported by Grant-in-Aid for Scientific Research C(20500397).

References 1. S. Kato and T. Noguchi.: Fabrication of An IN-Pipe Mobile Micromachine Driven by a GusLiquid Phase-change Actuator. In: Proceedings of Tenth World Congress on The Theory of Machine and Mechanisms, Tokyo, 1999, pp. 862 – 867. 2. Y. Hasegawa K. Ito, H. Izawa and T. Ito : Development of Micro Mobile Machine with Wheels. In: Proceedings of 6th. International Symposium on Micro Machine and Humane Science, 1995, pp. 219 – 224. 3. T. Miyagawa, Koichi Suzumori, Masanobu Kimura, and Y. Hasegawa : Development of MicroInspection Robot for Small Piping. In: Proc. of Tenth World Congress on The Theory of Machine and Mechanisms, Tokyo, 1999, pp. 856 – 861.

Optimum Design of Mass Distribution of the Injection Molding Pantograph Mechanism with Constant Output Link Orientation M. Horie, Y. Hoshikawa, and D. Kamiya

Abstract In this paper, an optimum design of an injection molding pantograph mechanism is discussed. This mechanism will be used to the miniature surface mount system in one room factory. First, a reduction of force acting at hinge caused by the movement of the mechanism is discussed. And the injection molding pantograph mechanism is synthesized based on the result of a numeric calculation of the algorithm. Moreover, the force acting at hinge of this mechanism is analyzed, and the algorithm that reduces force acting at hinge by changing the shape and dimension of links considering the influence of the movement of the mechanism is proposed. In addition, the shape and dimension of links to which force acting at hinge of this mechanism is reduced from the result of a numeric calculation of this algorithm is designed. Keywords Kinematics · Optimum design · Injection molding pantograph mechanism · Reduction of joint forces · Changing the shape and dimension of the links

1 Introduction Electronic devices have been getting smaller and smaller with one-millimeter or a few-millimeters squared micro-parts being attached to the electronic circuit cards. Consequently, a small surface mounting system with an injection molded pantograph mechanism was proposed [1]. In the pantograph mechanism, the hinges are used instead of bearings. The hinge is clarified by the bending fatigue test repeating that the repetition bend of one million times can be endured in experiments by Horie [1]. The pantograph mechanism is made by integral molding with polypropylene. It consists of large-deflective hinges (JX1 , J12 , J14 , J23 , J27 , J28 , JY3 , JY4 , JY5 , J56 , J57 , and J68 ), placed in contraposition to each other, and links (L1 , L2 , L3 , L4 , L5 , L6 , L7 , and L8 ) as shown in Fig. 1. The output displacement in the x direction is increased four times the input displacement, while the output displacement in the y direction M. Horie (B) Precision and Intelligence Laboratory, Tokyo Institute of Technology, Tokyo, Japan e-mail: [email protected]

G.K. Ananthasuresh et al. (eds.), Micromechanics and Microactuators, Mechanisms and Machine Science 2, DOI 10.1007/978-94-007-2721-2_4, C Springer Science+Business Media B.V. 2012

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M. Horie et al. J11(F11) J14(F14) J23(F23) J27(F27)

JX1(FX1)

J57(F57) J56(F56) J28(F28) JY3(FY3) J68(F68) JY4(FY4)

JY5(FY5)

Fig. 1 A pantograph mechanism, its hinge parts view and forces

is increased five times the input displacement in the mechanism. The hinges are constantly under various combinations of load, such as tension, compression, shear, and bending. It has been found that such loads cause hinge fracture, eventually resulting in the pantograph breaking down. It has also been found that the lifespan of the hinges increases when the force acting on the hinges is reduced to about one third by Horie [2]. Therefore, this study will theoretically calculate the force acting on the hinges and figure out the dimensions of the links using a computational algorithm so that the force on the hinges will be reduced.

2 Theoretical Analysis of Force Acting on the Hinges A pantograph model, consisting of rigid body links and revolute-pair hinges, is shown in Fig. 2. In this study, output points of the pantograph mechanism were assumed to show parabolic motion with 10 Hz of repetition frequency. In this case, the input motion Sx and Sy were given as sinusoidal waves for the time. The force acting on each link in the mechanism was defined as in Fig. 1, and motion equations were solved to obtain the force acting on the hinges. The calculation was based on the assumption that the hinges are revolute pairs, which have no mass or volume, and the force acting on the hinges and the force acting on both the hinges and links comply with the action reaction law. It was found that the maximum amount of force acted on hinge JY4 , with a value of 1.46N.

3 The Algorithm for the Link Shape and Dimensions 3.1 Definition of the Link Shape and Dimensions The algorithm for the link shape and dimensions aims to calculate both the link shape and dimensions which will enable the force acting on the hinges to be reduced.

Optimum Design of Mass Distribution of the Injection Molding Pantograph. . .

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Fig. 2 Schematic diagram of pantograph mechanism Fig. 3 Shape and dimension of each cross section (win and hin are shown in Fig. 6)

When link shape and dimension are changed, the mass, center of gravity, and inertia moment around the center of gravity of each link change, and the force acting on the hinges will consequently be reduced. Links of initial shape and dimensions were divided into cross sections, and the height and width of each cross section were given for calculation. The changed links were defined as having a square pipe shape with the height and width shown in Fig. 3. Taking a straight line, which connects center points of the hinges on both ends of a link, as x direction, the links were divided vertically to the x direction. L1 and L2 were divided into one hundred, while L3 , L5 , and L6 were divided into eighty. L4 , L7 , and L8 were divided into twenty.

3.2 Constraints by the Interference and Strength of Links The algorithm for the link shape and dimensions has a constraint so that interference of each link does not occur. When the stress by inertia force of a link on each cross section was calculated, the maximum normal stress was 1.58 MPa, and the maximum shearing stress was 0.27MPa. The rupture stress of polypropylene used in the mechanism is 28 MPa, which means the links have sufficient strength. As a former study in [2] by Horie confirmed the part of a link about 1mm from the hinge on the link fractured when the hinge fractured. Shape and dimensions of the parts of a link 3mm from the ends were not changed in this study.

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3.3 Constraints by the Rigidity at Output Points Links undergo elastic deformation, and a displacement error occurs at the output points due to inertia force affecting each link in the pantograph mechanism. In the links of initial shape and dimensions, the force acting on each cross section, and output displacement error due to elastic deformation caused by the force, were calculated while the mechanism is being operated. The output displacement error due was 15.4 μm. Therefore, this study made it a constraint that output displacement error due to elastic deformation of links after the shape and dimensions were changed, be smaller than or equal to 15μm.

3.4 Shrinkage of the Link Cross Section Area and Parameters of the Algorithm Shape and dimensions of the links were changed to decrease the cross sectional area of each link by applying shrinkage repeatedly. Shrinkage A is applied by the following Equation (1), using parameters, W1 , W2 , and W3 . ΔA = W1 (W2 α - W3 β)

(1)

The evaluated value was the maximum force acting on hinges. Using the Polytope Method which is one of the optimization method, the parameters were varied in finding link shape and dimensions when the force acting on the hinges became smaller. α is the force generated by the inertia of each part of the pantograph mechanism. As the value increases, the mass of the part should become smaller. β is the amount of output displacement error due to elastic deformation of each part of the pantograph mechanism. As the value increases, the mass of the part should not become smaller. The values of α and β of each cross section in the pantograph mechanism are shown in Fig. 4. Represented is the proportion of each value to the maximum value, assuming the maximum value is 1, that is, whether how many times the value α max (or β max ) the value α (or β) are understood.

Fig. 4 Values of α and β of each cross section

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4 Changes in the Link Shape and Dimensions 4.1 Changes in the Shape and Dimensions of the Link Cross Section Six methods (Type 1∼Type 6 shown in Fig. 5) to change the shape and dimensions of the cross section were applied to the computational algorithm for link shape and dimensions to obtain six different links. Table 1 shows the maximum force acting on the hinges, the position on which the force acts, displacement error of the output point, and the mass of the pantograph mechanism when the mechanism with links of obtained shape and dimension is operated. This is done so that the output point moves, drawing a parabolic trajectory with 10Hz of repetitive frequency. From the results, the force acting on hinges was the smallest in Type 1, and the value was 0.59N (40.4%). Also, the shape of Type1, Type 4, Type 5, and Type 6 is that of a square pipe shape while that of Type 2

Fig. 5 Method of change of cross section (Type 1∼Type 6) Table 1 Maximum force acting at hinge, mass of pantograph mechanism, and error of position (Type 1 ∼ Type 6)

Rate of maximum force acting at hinge % Mass of pantograph mechanism % Position error of output point % Hinge of maximum force acting

Original

Type 1

Type 2

Type 3

Type 4

Type 5

Type 6

100.0

40.4

58.1

56.4

41.1

43.8

44.4

100.0

40.7

62.1

60.9

50.6

51.7

51.9

100.0

53.2

97.8

61.1

50.6

51.7

51.9

JY4

JY4

JY4

J14

JY4

JY4

JY4

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and Type 3 is not pipe shaped. When the two groups are compared to each other, the maximum values of the force acting on the hinges in addition to the output displacement error of the square-pipe-shape types were smaller. From these results, it is considered that the square pipe type link is useful in reducing the force acting on the hinges if the output displacement error is not large. Of course, the square pipe type can change to I-type when both side parts of the square pipe gathers to center of the square section. This is because the bending stiffness of both type is same and the mechanism with I-type is made by an injection molding machine.

4.2 Changes in the Shape and Dimensions of Initial Links Though the maximum force acting on the hinges was able to be reduced by changing the shape and dimensions of each link, the value was not reduced to the desired onethird. That does not meet the purpose of this study. Therefore, initial link shape and dimensions were changed and applied to the computation algorithm for link shape and dimensions. The methods of change were six (Type 7∼Type 12). Link 1, and Link 4 were changed to the solid-core shape because, as illustrated in Fig. 5, they were considered to be a part of the pantograph mechanism in which the mass should not be made small. There were four methods of change in shape and dimensions of the cross section of each link: a method to change the shape to hollow, a method to change the shape to a solid-core, a method to reduce the width, and a method to reduce the height, which are shown in Fig. 6. Table 2 shows the maximum value of the force acting on the hinges, the place on the hinges on which the force acts, displacement error of the output points, and the mass of the pantograph mechanism when the mechanism with links of obtained shape and dimensions is being operated. This is done so that the output point moves

Fig. 6 Method of change of cross section (Type 7∼Type 12)

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Table 2 Maximum force acting at hinge, mass of pantograph mechanism, and error of position (Type 7∼Type 12)

Rate of maximum force acting at hinge % Mass of pantograph mechanism % Position error of output point % Hinge of maximum force acting

Original

Type 7

Type 8

Type 9

Type 10

Type 11

Type 12

100.0

32.8

31.6

31.9

30.0

30.6

30.6

100.0

34.6

33.7

35.9

32.1

35.2

34.4

100.0

51.2

45.4

39.2

44.4

51.0

49.2

JY4

J14

J14

J14

J14

JY4

JY4

showing parabolic trajectory with 10 Hz of repetitive frequency. The force, acting on the hinges in the pantograph mechanism with links of obtained shape and dimensions, was reduced to about 30%. From the results, it was possible to reduce the force further by imposing the condition on the algorithm that the shape of the initial link is a pipe 0.5mm thick. Figure 7(a) and (b) show the design result obtained by theoretically and experimentally, respectively, where the mechanism’s link section is I-Type. Figure 8 shows five output link position Pi (i=1-5) on output locus. Table 3 shows statically the orientation of five points on the output locus. The orientation is measured by laser sensors. The mechanism has two liner actuators inputs, however, when the orientation are measured, the actuators are not used. In the results, it was confirmed that the output link L8 has a 90 deg. orientation angle. About the dynamic positional accuracy and repeatability of the injection molding pantograph mechanism with three parallelogram, we have not investigated yet. However, the maximum errors of output displacements of the injection molding pantograph with one parallelogram was 340 μm, while the maximum hysteresis errors were 130 μm. Moreover, the accuracy ratios of positioning repeatability at ending points P1 (pick) and P5 (place) were measured after having the locus of the supposed

Output link

Inputs

100 mm

(a) Theory

(b) Experiment (Polypropylene)

Fig. 7 A molded pantograph mechanism with constant orientation of the output link

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Fig. 8 Five output link position on output locus

P3

P2

P4

P1

P5 Pic

Table 3 rad.)

Place

Orientation of five points on the output locus (UNIT: degree or π/180 ∗ bellow values P1

P2

P3

P4

P5

Experimental result

90.58 90.56 90.58 90.96 90.95

90.38 90.15 90.39 90.58 90.48

90.58 90.68 90.70 90.72 90.8

90.71 90.58 90.24 90.14 90.23

90.61 90.68 90.75 90.30 90.52

Average

90.73

90.40

90.70

90.38

90.57

surface mounting job moved back and forth between P1 and P5 . Measuring the accuracy 15 times showed that the accuracy of positioning repeatability at P1 was ±9μm, while that of P5 was ±11μm, in [1].

5 Conclusion (1) This study analyzed the force acting on the hinges in pantograph mechanism by modelling the mechanism, which consists of rigid body links and point contact pairs. It showed that the maximum force acted on hinge JY4 , with the value being 1.46 N while the mechanism is being operated. This was done so that the output point moves drawing a parabolic trajectory with 10 Hz of repetitive frequency. (2) Links in the pantograph mechanism in this study were divided into cross sections to calculate tensile strength, compression, shear, and bending moment, which are generated from inertia force acting on each cross section when the mechanism is being operated. This causes elastic deformation of each part of the links, leading to output displacement error in the mechanism. This study calculated the output displacement error and showed that the maximum value was 15.4μm. (3) This study confirmed that the maximum force due to the inertia force of each part of the pantograph mechanism, acted on hinge JY4 , and calculated the value as well as the output displacement error due to the elastic deformation of each part of

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the mechanism. Additionally, it showed that the mass of the mechanism should be reduced for L2 , and L6 , while the mass should not be reduced for L1 , L3 , and L4 . (4) This study proposed an algorithm for link shape and dimensions with constraints imposed regarding link interference and displacement error at output points. Using the algorithm and methods of change, link shape and dimensions were obtained, with which the force acting on the hinges was reported as 0.64N (43.8%), and the maximum output displacement error was 7.1μm (46.1%). In the methods of change, the shape of the link was changed to a square pipe shape and the height of the cross section was decreased. Also, the second moment of inertia concerning the z-axis of each cross section was reduced to about 60%. (5) Initial link shape and dimensions were changed and applied to the algorithm for link shape and dimensions. The shape and dimensions of a pantograph mechanism with a link 0.5mm thick in the center part were changed, and link shape and dimensions were obtained, enabling the maximum force acting on the hinges to become 0.49N (32.8%) and the maximum displacement error at the output point to become 7.9μm (51.2%). Dimensions which will enable the force acting on the hinges to be reduced are proposed. And L4 of the solid-core and other links with pipe-shaped center part 5mm thick, were changed. Consequently, link shape and dimensions were obtained which enabled the maximum force acting on the hinges to be 0.48N (31.6%). (6) It was confirmed that the output link L8 has an orientation angle near 90 degrees which was theoretically expected.

References 1. Horie M., Uchida T., and Kamiya D.: A Pantograph Mechanism with Large-deflective Hinges for Miniature Surface Mount Systems, ROMANSY 13-THEORY AND PRACTICE OF ROBOTS AND MANIPULATORS, pp. 93-102, 2002 2. Horie M, Okabe Y., Yamamoto M., and Kamiya D.: Study on Long Life Large-Deflective Hinges in Molded Pantograph Mechanisms based on Cyclic Load-Bending Fatigue Test, Proc. of 2005 International Symposium on Electronics Materials and Packaging (EMAP2005), pp. 137-142, 2005 3. Horie, M., Ishii, Y., and Kamiya, D., A Dynamic Analysis of Molding Pantograph Mechanism with Large-Deflective Hinges and Links, Proceeding of 3rd IFToMM International Micromechanism Symposium, pp. 30-33, 2001.

Mathematical Synthesis of Compliant Mechanism as Cochlear Implant L. Zentner

Abstract Cochlear implants can be successfully used to reduce the inner ear profound deafness. The implant is inserted into the inner ear by the surgeon’s hand. Because the cochlea has a spiral-like structure (cochlear duct), the insertion of the implant is often difficult, furthermore the basilar membrane could be easily damaged. One of the aims of our investigation is to develop a mathematical model based on the synthesis method for implants with hydraulic actuation. This hydraulic actuation, which is integrated into the implant, facilitates the insertion of the implant structure to the shape of cochlear duct. Thus, the implant can follow the spiral-shaped cochlear duct without damaging the sensitive tissue of the basilar membrane. Some examples for hydraulic actuated cochlear implants based on compliant mechanisms technology are presented in this paper. Keywords Compliant mechanism · Cochlea implant · Hydraulic device · Mathematical modelling

1 Introduction Cochlear-implants are implanted for patients with profound deafness. The people, who have implantation directly after hearing loss, are still able to communicate. Early treated children develop their language proficiency and speaking reproduction in such a way that a great number of them are able to go to normal schools. Since the first implantation 45 years ago, cochlear-implants are being developed more and more intensively. All the implants applied nowadays, which are implanted into the scala tympani (Fig. 1), consist of an electrode array, a receiver and a stimulator unit for signal, an electrical transmission and a receiving antenna. In the Fig. 3a there is a schematic representation of an implant from MED-EL (MED-EL, Innsbruck, Austria). 12 platinum electrode pairs are embedded in one soft silicone-carrier. The cochlear hair cells and auditory nerve fibres are located on the inner side of scala L. Zentner (B) Technische Universität Ilmenau, Ilmenau, Germany e-mail: [email protected]

G.K. Ananthasuresh et al. (eds.), Micromechanics and Microactuators, Mechanisms and Machine Science 2, DOI 10.1007/978-94-007-2721-2_5, C Springer Science+Business Media B.V. 2012

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Fig. 1 a – Cochlear duct; b – Cochlea

a

Basilar membrane Scala tympani

b

tympani, from above the scala tympani is terminated with a thin sensitive basilar membrane of the remaining part of cochlear duct (Fig. 1). By insertion of the implant into the cochlea the tissue may be damaged, which may cause the destruction of reminder hearing. The preformed implants can also cause undesirable injuries [1]. An implant, which can deform itself during the operation and suit bit by bit to the shape of the cochlear duct, can simplify the insertion procedure and can prevent the insertion trauma of cochlea in this way. This deformation can be achieved via a design modification of a compliant mechanism [4], [5]. There are two ways of realizing the required deformation: 1. concentrical hollow in the silicone carrier with the geometric asymmetry. The geometric asymmetry can be realized by embedding the materials with different mechanical properties in the silicone carrier or with the help of a special arrangement of the electrode wires in the silicone carrier 2. non-concentrical placement of the hollow in the silicone carrier [6]. After that the form of the implant with an embedded fibre, which corresponds to the form of the cochlea under pressure in the hollow, is searched.

Mathematical Synthesis of Compliant Mechanism as Cochlear Implant

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2 Representation of the Cochlea Centre Line as a Space Curve The form of the centre line of the cochlea duct is shown in the Fig. 2 in the cylindrical coordinate system with coordinates r and z, which are functions of the angle ϕ [2]: r=

k1 (k2 + π ) , (2k2 + π ) (k2 + ϕ)

(1)

z = k3 ek4 ϕ − 1 .

(2)

The constants in these equations are: k1 = 10, k2 = 1, k3 = 0.8, k4 = 0.1.

(3)

The length of the curve element of the cochlea centre line is ds =

dr2 + dz2 .

(4)

Division by dϕ yields ds = dϕ

dr dϕ

2 +

dz dϕ

2 .

(5)

The associated boundary condition is s(0) = 0. This is a non-linear equation in terms of s(ϕ). It can be solved only numerically. For further calculations ϕ(s) is also necessary. Now the curvature κ3 and the torsion κ1 of the cochlea centre line can be expressed by derivatives of Cartesian coordinates with respect to ϕ:

z [mm] 2 2 2 4 6

Fig. 2 Form of the centre line of the cochlear duct

8 x [mm]

ϕ r

y [mm]

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L. Zentner

2 x 2 + y 2 + z 2 x 2 + y 2 + z 2 x x + y y + z z 2 κ3 (ϕ) = − 3 3 , x 2 + y 2 + z 2 x 2 + y 2 + z 2 x y z x y z x y z κ1 (ϕ) = 3 . κ32 x 2 + y 2 + z 2

(6)

(7)

Using the numerically calculated term ϕ(s), the curvature and torsion of the centre line can be expressed depending on s. The parameters κ1 (s) and κ3 (s) are well suitable to describe the form of the cochlea duct.

3 Modelling the Implant An insertion implant from MED EL Innsbruck is shown in Fig. 3a. In Fig. 3b-c the structure is shown, which is modelled. The radius of the implant changes from ra = 0.65 mm to re = 0.25 mm. The function r(s) can be expressed by second-order polynomial: r (s) =

ra − re (s − l)2 + re . l2

(8)

a ra = 1.3 mm

ri = 0.2 mm

re = 0.5 mm

A

B

A

B

b A-A hollow c

B-B

fibre

Fig. 3 a – Schematic representation of an implant from MED EL Innsbruck; b – Geometric parameters of the implant model; c – Cross-section views of the implant model

Mathematical Synthesis of Compliant Mechanism as Cochlear Implant

45

Geometrical moments of inertia are expressed by equations (9). π I1 = 2I2 = 2I3 = 2

ra − re (s − l)2 + re l2

4 − ri4

.

(9)

The matrix A with E and G as Young’s modulus and shear modulus is expressed as follows: ⎛ ⎞ GI1 0 0 A = ⎝ 0 EI2 0 ⎠ . (10) 0 0 EI3 In the implant model, there is a hollow with the constant radius ri . In order to achieve the bending of the implant, an unstretchable thin fibre of length l is embedded in the wall with h distance from the symmetry axes of the implant (Fig. 4). With inner pressure of fluid p in the hollow, the implant structure will bend towards the embedded fibre. The following model is set up, in order to find the form of the fibre for nondeformed shape of implant. The form of cochlea duct should be reproduced by the implant, which is under pressure. The model is based on the theory of curved beams with hollows [3]. The linear material law is supposed for this limited deformation but some large displacements are possible. The fibre corresponds to the neutral fibre of the implant. We introduce two orthogonal coordinate systems: fixed a Cartesian coordinate system xj and a moving one with unit vectors ej (Fig. 4), attached to the neutral line. The distance between the neutral line (embedded material) and the centre of mass

x2 x1 x3

e1 Center of Mass e2

e3 Fig. 4 Beam with embedded material and with round cross section

e2

e3

h e1

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L. Zentner

is h, which is small in comparison to the length and the radius of curvature of the implant. Therefore the parameter s in equation (4) corresponds approximately to the length of an arch of the neutral line. It is measured from the fixed end to the free end. = Q1 e1 + Q2 e2 + Q3 e3 as the vector of internal The following notations are used: Q = M1 e1 +M2 e2 +M3 e3 , forces, with axial force Q1 and transverse forces Q2 , Q3 ; M i.e. vector of internal moments, where M1 is torsion moment, M2 , M3 are bending moments; P0 = pπ ri2 is force on the inner cross-section of the beam (implant). The parameter κ is determined by the following relation: dei = κ × ei . ds

(11)

The initial form of the neutral fibre is given by κ10 , κ20 and κ30 . The form of the beam under pressure is described by following vector-equations: d P0 e1 dQ − = 0, ds ds

dM = 0, + e1 × Q ds

= A ( M κ − κ 0 ) .

(12)

The force equilibrium conditions for the cochlea implant have the following form: dQ1 + Q3 κ2 − Q2 κ3 = 0, ds dQ2 + (Q1 − P0 ) κ3 − Q3 κ1 = 0, ds dQ3 + Q2 κ1 − (Q1 − P0 ) κ2 = 0. ds

(13)

The corresponding boundary conditions are: Q1 (l) = P0 ,

Q2 (l) = 0,

Q3 (l) = 0.

(14)

The moments can be expressed by κ1 , κ2 and κ3 : EI3 EI2

dκ3 dκ30 − ds ds dκ20 dκ2 − ds ds

GI1

dκ20 + EI2 κ2 − κ1 − GI1 (κ1 − κ10 ) κ2 + Q2 = 0, ds

dκ10 + GI1 κ1 − κ3 − EI3 (κ3 − κ30 ) κ1 + Q3 = 0, ds

dκ1 dκ10 − ds ds

dκ30 + EI3 κ3 − κ2 − EI2 (κ2 − κ20 ) κ3 = 0. ds

(15)

Mathematical Synthesis of Compliant Mechanism as Cochlear Implant

47

x2 [mm]

Fig. 5 Form of fibre in the Cartesian coordinate system 5 x3 [mm] 2 0

10 x1 [mm]

The corresponding boundary conditions have the form: κ30 (l) = κ3 (l) −

P0 h , EI3 (l)

κ20 (l) = κ2 (l) ,

κ10 (l) = κ1 (l) .

(16)

The solution of these equations of a static problem is the unload shape of the implant for cochlea implant κ10 (s), κ20 (s) and κ30 (s). This shape of the implant is deformed under definite pressure to the end-form corresponding with the form of cochlea duct. The Fig. 5 shows the form of fibre in the Cartesian coordinate system. The transformation formulas for κ10 (s), κ20 (s) and κ30 (s) into Cartesian coordinates are not presented here because of the complexity of the expressions. The calculations of the deformation of a three-dimensional structure were carried out with the parameters l = 31.5 mm, h = 0.25 mm, E = 12.6 kN/m2 and the inner pressure 3 kN/m2 .

4 Summary In this paper it is shown that it is possible to realize an active bending of an implant. The theory of curved beams allows the description of deformation of the implant. It was shown that the form of the implant, which corresponds to the cochlea duct under a defined pressure can be found. As an alternative possibility, thermo-gels are examined. During the insertion of the implant into the cochlear duct, the temperature of the gel increases to the value of the body temperature. Thereby the gel volume enlarges. The inner pressure in the hollow of the implant increases. As a result, the implant is deformed and facilitates the surgery in this way.

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References 1. Marangos, N, Laszig, R.: Cochlear Implants, HNO, Springer-Verlag, Physics and Mystery (1998) 46: pp. 12-26 2. Rau, T.; Eilers, H,; Leinung, M.; Hussong, A.; Lenarz, T.; Majdani, O.: Geometriemodellierung des Innenohres für die Cochlea Implantation – anatomische Variabilität und patientenspezifische Insertionsplanung ; 79. Jahresversammlung der Deutschen Gesellschaft für Hals-NasenOhren-Heilkunde, Kopf- und Hals-Chirurgie. Bonn, 30.04.-04.05.2008 Düsseldorf: German Medical Science GMS Publishing House; (2008) 3. Zentner, L.: Untersuchung und Entwicklung nachgiebiger Strukturen, Ilmenau ISLE Verlag, ISBN 3-932633-77-6, (2003) 4. Zentner, L.; Böhm, V.: On the Classification of Compliant Mechanisms. - In: Proceedings of the EUCOMES 08 / European Conference on Mechanism Science ; 2 (Cassino, Italy) : 2008.09.1720. - Berlin : Springer (2009), pp. 431-438 5. Zentner, L.; Böhm, V.; Minchenya, V.: On the new reversal effect in monolithic compliant bending mechanisms with fluid driven actuators. - In: Mechanism and machine theory. - Amsterdam [u.a.]: Elsevier Science, Bd. 44 (2009), 5, pp. 1009-1018 6. Zentner, L.; Keskeny. J.; Westhofen, M.; Huba, A.: Hydraulic actuation for the navigation of a cochlear implant. - In: Actuator 2006 / International Conference on New Actuators; 10 (Bremen): 2006.06.14-16. - Bremen: HVG Hanseatische Veranst.-GmbH, Div. Messe Bremen (2006), pp. 980-984

Flexure Hinge-Based Parallel Manipulators Enabling High-Precision Micro Manipulations I. Ivanov and B. Corves

Abstract Parallel manipulators are very suitable for the realization of planar and spatial high-precision micro manipulations, especially with flexure hinges bringing many advantages. The goal is to investigate the possibility of flexure hinges being implemented into parallel manipulators. The characteristics of typical flexure hinges are compared at first. Orthogonal parallel manipulators with a regular spatial translation of the moving platform are assessed afterwards. For a dimensioned flexure hinge and a selected parallel manipulator, a flexure hinge-based parallel manipulator is monolithically designed and analysed. Keywords Flexure hinges · Parallel manipulators · Flexure hinge-based parallel manipulators

1 Introduction A serial manipulator has one kinematic chain with a fixed base and a moving platform at the ends. Between them, links are serially connected by actuated joints and therefore heavily loaded. For this reason, a low positioning accuracy and a poor load capacity are available. A significant stiffness enhancement without strengthening individual links can be attained by using parallel kinematic structures. In a parallel manipulator, a moving platform is coupled with a fixed base by several separate kinematic chains, so-called limbs. Because of load distribution on the limbs, a good load capacity and a high positioning accuracy are achieved. The dynamic behaviour is also improved [1]. Parallel manipulators are very suitable for the realization of planar and spatial high-precision micro manipulations. High-precision requirements are met best with parallel kinematic structures, whose limited working spaces are not drawbacks for micro manipulations. A micro manipulation typically covers a working space up to millimetre range and a positioning accuracy up to nanometre range. Such a small working space and such a high positioning I. Ivanov (B) Department of Mechanism Theory and Dynamics of Machines (IGM), RWTH Aachen University, Aachen, Germany e-mail: [email protected]

G.K. Ananthasuresh et al. (eds.), Micromechanics and Microactuators, Mechanisms and Machine Science 2, DOI 10.1007/978-94-007-2721-2_6, C Springer Science+Business Media B.V. 2012

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accuracy do not demand an extreme miniaturization, so that a micro manipulator is distinguished from a micro machine [2]. However, the micro manipulator can be implemented hardly with conventional joints, but successfully with flexure hinges. They make a monolithic design possible, which is characterized primarily by a radical reduction of backlash and friction [3]. Some applications of flexure hinge-based parallel manipulators should be mentioned: sample positioning in microscopy, wafer lithography, manufacture and assembly in precision engineering and micro system technology, etc.

2 Requirements The selection of degrees of freedom of the moving platform depends on the function of a micro manipulator. All six degrees of freedom ensure a full mobility, but that entails high costs and a complex control. Three or four degrees of freedom are usually sufficient for a micro manipulation, namely three translations, if necessary enhanced with one rotation. The remaining degrees of freedom have to be kinematically constrained. In precision engineering, the working space of the moving platform is normally a couple of cubic millimetres large. Since the installation space for a micro manipulator is often quite restricted, a relatively wide motion range of the flexure hinges is necessary. The motion accuracy of the flexure hinges has to be as high as possible at the same time. Because of a monolithic design (practically no backlash in flexure hinges), environmental disturbances mainly affect the repeatability of the moving platform. Therefore, the mechanical stability (a high stiffness) and the thermal stability (a low thermal expansion) of a micro manipulator are of vital importance. Concerning calibration costs, the positioning accuracy of the moving platform should also not be neglected. The performance test of flexure hinges or an entire micro manipulator in scanning electron microscopy is possible if applied materials are non-magnetic. For example, only austenite in case of steel, whose strength limits (yield strength and endurance strength) are rather low, is acceptable. A high ratio between the strength limits and the modulus of elasticity is preferable. However, using thermoplastics is not reasonable, because of a low modulus of elasticity. These conditions can be fulfilled with some light metal alloys (Table 1). Table 1 Physical properties of Ti-6Al-4 V used in further research Physical property

Symbol

Value

Mass density Modulus of elasticity Shear modulus Yield strength Endurance strength

ρ E G σ0,2 σD

4430 kg/m3 114 GPa 44 GPa 885 MPa 515 MPa

Flexure Hinge-Based Parallel Manipulators Enabling High-Precision Micro. . .

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In this paper, the characteristics (motion range and accuracy, stiffness) of typical (corner filleted notch and right circular notch) flexure hinges are compared at first. A few orthogonal parallel manipulators (3 PRRRR, 3 PRRR and 3 R R) with a regular spatial translation of the moving platform are assessed afterwards. For a dimensioned (right circular notch) flexure hinge and a selected parallel manipulator (3 R R), a flexure hinge-based parallel manipulator is monolithically designed by means of pseudo-rigid-body modelling and analysed by means of finite-element method. Accordingly, the parasitic rotations of the moving platform, the maximum stress in the flexure hinges and the stiffness of the micro manipulator are determined.

3 Flexure Hinges Design – If possible, revolute joints are usually combined into a universal or spherical joint for the purpose of shortening kinematic chains in case of spatial motions. A universal or spherical compliant joint (Fig. 1a-b) can be monolithically designed, but it possesses a low stiffness in all directions. A prismatic compliant joint (Fig. 1c) can be monolithically designed only as the combination of revolute compliant joints [4]. Therefore, the implementation of revolute compliant joints into parallel manipulators may be an optimal solution. Among a large number of designs, a corner filleted notch flexure hinge (Fig. 2a) and a right circular notch flexure hinge (Fig. 2b) are considered before the other ones. The characteristics of an elliptical notch flexure hinge (Fig. 2c) and similar designs stand between those of the corner filleted notch flexure hinge and the right circular notch flexure hinge [5].

Fig. 1 Examples of universal (a), spherical (b) and prismatic (c) compliant joint

Fig. 2 Corner filleted notch (a), right circular notch (b) and elliptical notch (c) flexure hinge

a)

b)

a)

c)

b)

c)

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Motion range and accuracy – In order to maximize the efficiency with regard to the motion range, a flexure hinge can be dimensioned for the maximum rotation angle (δmax ) corresponding to the maximum stress (σmax ) near to the strength limit (σ0,2 or σD ) [6] σmax =

6 · K · δmax ≤ σD b · t2

(1)

where K is the stiffness of the flexure hinge around the rotation axis, namely KCF = KRC =

E · t3 · b 12 · l

for corner filleted notch

2 · E · t2.5 · b 9 · π · R0.5

(2)

for right circular notch

(3)

flexure hinges according to [7]. The design parameters of corner filleted notch and right circular notch flexure hinges are shown in Fig. 3. The design parameter b is the width of flexure hinges. If the working space of the moving platform of 4 x 4 x 4 mm3 , which approximately needs the maximum rotation angle of the flexure hinges of ± 0.02 rad with the length of the links of 100 mm, is intended, the following design parameters can be obtained using equations (1)-(3) (Table 2): Generally, for similar lengths, a corner filleted notch flexure hinge shows a slight stress concentration and a big rotation axis drift, while a right circular notch flexure hinge has a stabile rotation axis and an intensive stress concentration (Fig. 4) (Table 3). Stiffness - In contrast to a conventional joint, theoretically with no stiffness in moving directions and an infinitely high stiffness in constrained directions, a flexure hinge possesses a finite stiffness in all directions. Accordingly, it is necessary to achieve adequate stiffness ratios between moving and constrained directions by the design of flexure hinges.

Fig. 3 Design parameters of corner filleted notch (a) and right circular notch (b) flexure hinges

a)

b)

Table 2 Design parameters of flexure hinges used in further research (see Fig. 3) Corner filleted notch (r = 0.2 mm)

l = 2 mm

t = 0.4 mm

b = 20 mm

Right circular notch

R = 2 mm

t = 0.4 mm

b = 20 mm

Flexure Hinge-Based Parallel Manipulators Enabling High-Precision Micro. . . Fig. 4 Stress distribution in corner filleted notch (a) and right circular notch (b) flexure hinge (FEM)

53

a)

b)

Table 3 Maximum stress and rotation axis drift of flexure hinges for rotation angle of ±0.02 rad (FEM) Flexure hinge

Max. stress

Axis drift

Corner filleted notch Right circular notch

263.1 MPa 419.2 MPa

5.067 μm 3.699 μm

Table 4 Stiffness values of flexure hinges Load type

Corner filleted notch

Right circular notch

Bending around rotation axis Bending around constrained axis

6.08 Nm/rad 15.20 kNm/rad

11.54 Nm/rad 17.06 kNm/rad

Using the stiffness matrix according to [7], it can be calculated that the right circular notch flexure hinge is bending stiffer around the rotation axis than the corner filleted notch flexure hinge (Table 4). That as well as a higher torsion stiffness are proven by means of finite-element method (FEM) (Table 5). Because of more suitable characteristics (motion accuracy, torsion stiffness), the right circular flexure hinge is implemented into a selected parallel manipulator here.

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I. Ivanov and B. Corves Table 5 Eigenfrequencies of flexure hinges (FEM)

Eigenmodes

Corner filleted notch

Right circular notch

Bending around rotation axis Bending around constrained axis Torsion around constrained axis

10.27 Hz 372.5 Hz 367.1 Hz

13.93 Hz 381.8 Hz 538.8 Hz

4 Parallel Manipulators In order to compensate the effects of thermal expansion, a micro manipulator should have a symmetric fully parallel kinematic structure. Accordingly, all the limbs possess identical kinematic chains standing in a uniform circular arrangement and orientation. Moreover, an orthogonal arrangement and orientation of the limbs (Fig. 5) is preferable in case of a regular spatial translation of the moving platform [6]. Besides, all the limbs are driven in the same way. Among existing drive concepts, one with all the actuators on the fixed base shows optimal characteristics [8]. Various approaches have been used for the structure synthesis of parallel manipulators with fewer than six degrees of freedom. They have usually been based either on the group theory [9] or on the screw theory [10]. A combined approach including the group theory and the screw theory with the specifics of micro manipulation is applied here. The results are also compared with those of other approaches [11]. Three limb structures being able to build orthogonal parallel manipulators with a regular spatial translation of the moving platform are preselected and briefly assessed below. PUU or PRRRR limb (Fig. 6) has five degrees of freedom and comprises two parallel universal joints (U) or two pairs of parallel revolute joints (R) as well as one

Fig. 5 Orthogonal arrangement and orientation of limbs in parallel manipulator

Flexure Hinge-Based Parallel Manipulators Enabling High-Precision Micro. . .

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Fig. 6 Px Rz Ry Ry Rz limb

Fig. 7 Pz Rz Rz Rz limb

linear actuator (P). An orthogonal parallel manipulator with three PUU or PRRRR limbs shows the following characteristics: + The maximum rotation angles of all the joints are similar. − The installation size is large because of an in-line arrangement of the links and the linear actuator. PRRR limb (Fig. 7) has four degrees of freedom and comprises three parallel revolute joints (R) as well as one linear actuator (P). An orthogonal parallel manipulator with three PRRR limbs shows the following characteristics: − The maximum rotation angle of the intermediate revolute joint is approximately two times larger than those of the peripheral revolute joints in case of the same link lengths in the limb. + Because of an angular arrangement of the links and the linear actuator, the installation size is small. ΠRΠR limb (Fig. 8) has four degrees of freedom and comprises two parallel revolute joints (R) and two perpendicular parallelograms with four parallel revolute

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Fig. 8 x Rz z Rz limb

joints ( ). The parallelogram connected with the fixed base is driven ( ). An orthogonal parallel manipulator with three R R limbs shows the following characteristics: + The maximum rotation angles of all the joints are similar. + Because of an angular arrangement of the links, the installation size is small.

5 Monolithic Design A micro manipulator to be monolithically designed is based on the implementation of the dimensioned right circular notch flexure hinge into the selected orthogonal parallel manipulator with three R R limbs. A pseudo-rigid-body model (PRBM) [12] of the micro manipulator being composed of rigid links and conventional revolute joints instead of the flexure hinges is made. Using inverse kinematic calculation, the link lengths are so optimized that the maximum rotation angles of all the revolute joints are similar and not larger than ± 0.02 rad for the working space of the moving platform of 4 x 4 x 4 mm3 . The distances between the parallel revolute joints of 100 mm and 120 mm are assumed (Table 6). A flexure hinge-based R R limb is monolithically designed (Fig. 9). The limbs are firmly connected with a cubic moving platform (20 x 20 x 20 mm3 ) in an orthogonal arrangement and orientation. The computer-aided design model of the micro manipulator is further analysed by means of finite-element method (FEM).

6 Results The computer-aided design model is analysed with respect to the parasitic rotations of the moving platform (Table 7), the maximum stress in the flexure hinges (Table 8) and the stiffness of the micro manipulator (Table 9). Displacing the moving platform to the border of the cubic working space (4 x 4 x 4 mm3 ), parasitic rotations up to 0.4 mrad are obtained. A maximum stress

0 0 2

-0.0000 -0.0002 -0.0186

-0.0184 -0.0184 -0.0186

0.0000 -0.0000 0.0202

-0.0002 -0.0186 -0.0186

0 2 2

2 2 2

0.0202 0.0202 0.0202

Limb Y

Limb X

Limb Z

Limb X

Limb Y

Joints 2, 3, 4, 5

Joint 1

Displacements of moving platform [mm]

Rotation angles of joints [rad]

0.0000 0.0202 0.0202

Limb Z 0.0002 0.0186 0.0186

Limb X

Joint 6

0.0000 0.0002 0.0186

Limb Y

0.0184 0.0184 0.0186

Limb Z

0.0168 0.0202 0.0202

Limb X

0.0002 0.0170 0.0202

Limb Y

Joints 7, 8, 9, 10

0.0032 0.0034 0.0202

Limb Z

Table 6 Rotation angles of conventional revolute joints for given displacements of moving platform and optimized rigid link lengths in case of orthogonal parallel manipulator with R R limbs (PRBM)

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Fig. 9 Monolithic design of flexure hinge-based R R limb (without drive unit)

34

4 13

5

2

6 2 3

7 8 167

1

9 10

Table 7 Displacements and corresponding parasitic rotations of moving platform (FEM)

x [mm] y [mm] z [mm] θx [μrad] θy [μrad] θz [μrad]

Case 1

Case 2

Case 3

2.0 0.0 0.0 1.4 129.3 -343.0

2.0 2.0 0.0 -341.7 130.7 -213.8

2.0 2.0 2.0 -212.4 -212.4 -212.4

Table 8 Maximum stress in flexure hinges (FEM)

Critical hinges σmax [MPa]

Case 1

Case 2

Case 3

2,3,4,5 413.6

2,3,4,5 418.8

2,3,4,5 426.9

Table 9 Eigenmodes and eigenfrequencies of micro manipulator (FEM)

Non active drives Active drives

Translation

Rotation

≥ 19.7 Hz -

≥ 496.9 Hz ≥ 553.9 Hz

Flexure Hinge-Based Parallel Manipulators Enabling High-Precision Micro. . .

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Fig. 10 First eigenmode when non active drives (19.7 Hz) (FEM)

in the flexure hinges up to 430 MPa is detected then. This stress value is in accordance with the calculation using equations (1)-(3) (σmax = 432.8 MPa). As expected, the micro manipulator with non active drives (three translational degrees of freedom of the moving platform) possesses a low translation stiffness (20 Hz) (Fig. 10), but a high rotation stiffness (500 Hz). When the drives are active (no degrees of freedom of the moving platform), the rotation stiffness is even higher (550 Hz) (Fig. 11), while the translation stiffness is extremely high.

Fig. 11 First eigenmode when active drives (553.9 Hz) (FEM)

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7 Summary Two typical (corner filleted notch and right circular notch) flexure hinges are dimensioned according to the motion range and compared at first. The right circular notch flexure hinge shows more suitable characteristics (motion accuracy, torsion stiffness) for the implementation into a parallel manipulator. Using a systematic approach, three limb structures (PRRRR, PRRR and R R) being able to build orthogonal parallel manipulators with a regular spatial translation of the moving platform are preselected and briefly assessed. Favourable characteristics of the

R R limb are highlighted. For the dimensioned right circular notch flexure hinge and the selected orthogonal parallel manipulator with three R R limbs, a micro manipulator is monolithically designed and analysed. Thereby, small parasitic rotations of the moving platform and a high stiffness of the micro manipulators are achieved. Therefore, a further research through the realization and the test of an experimental model is intended.

References 1. Merlet, J.-P., Parallel robots, Springer, 2006. 2. Pernette, E., Henein, S., Magnani, I., Clavel, R., Design of parallel robots in microrobotics, Robotica, Vol. 15, 1997, 417-420. 3. Smith, S., T., Flexures, Elements of elastic mechanisms, Gordon and Breach, 2000. 4. Trease, B., P., Moon, Y.-M., Kota, S., Design of large-displacement compliant joints, Journal of mechanical design, Vol. 127, 2005, 788-798. 5. Lobontiu, N., Compliant mechanisms, Design of flexure hinges, CRC Press, 2003. 6. Xu, Q., Li, Y., Mechanical design of compliant parallel micromanipulators for nano scale manipulation, International conference on nano/micro engineered and molecular systems, 2006, 653-657. 7. Koseki, Y., Tanikawa, T., Koyachi, N., Arai, T., Kinematic analysis of translational 3-DoF micro parallel mechanism using matrix method, International conference on intelligent robots and systems, 2000, 786-792. 8. Koseki, Y., Arai, T., Sugimoto, K., Takatuji, T., Goto, M., Design and accuracy evaluation of high-speed and high precision parallel mechanism, International conference on robotics and automation, 1998, 1340-1345. 9. Herve, J., M., The Lie group of rigid body displacements, a fundamental tool for mechanism design, Mechanism and machine theory, Vol. 34, 1999, 719-730. 10. Kong, X., Gosselin, C., M., Type synthesis of 3-DoF translational parallel manipulators based on screw theory, Journal of mechanical design, Vol. 126, 2004, 83-92. 11. Carricato, M., Parenti-Castelli, V., A family of 3-DoF translational parallel manipulators, Journal of mechanical design, Vol. 125, 2003, 302-307. 12. Howell, L., L., Compliant mechanisms, Wiley, 2001

Cell-Grasping Compliant Mechanisms with Real-Time Haptic Feedback Santosh D.B. Bhargav and Gondi Kondaiah Ananthasuresh

Abstract We present a technique that enables both grasping and injecting a biological cell with real-time haptic force feedback by using miniature compliant mechanisms. The compliant mechanisms serve the dual purpose of grasping and force-sensing. The setup developed comprises an inverted microscope, two XYZ stages for micro-positioning, two usage-specific polydimethylsiloxane (PDMS) tools, a haptic robot, and a camera for image capture. Soft PDMS grippers help in holding the cells gently without excessive force because their stiffness can be matched with that of the cells. The setup allows the transfer of user-induced motion from the stylus of the haptic device (master) to the miniature grasper/injector (slave) and, in reverse, the force senses at the grasper is returned to the user with suitable deamplification and amplification, respectively. It is demonstrated that a single haptic device can be used to grasp and inject by switching between two modes by toggling a button on the stylus of the device. The haptic cell-manipulation system was tested by grasping and injecting a zebrafish egg cell. Keywords Compliant mechanisms · Cell-manipulation · Remote-haptics · Miniature gripper · Intracytoplasmic injection

1 Introduction In this paper, we report an update on our on-going work on bio-micromanipulation setup that includes a haptic interface. In our earlier work [1], we demonstrated haptic feedback for either grasping the cells or injecting them because we use only one haptic device. In this paper, we describe how we overcome that limitation even with a single haptic device. Some additional features and new experimental results are also described here.

S.D.B. Bhargav (B) Indian Institute of Science, Bengaluru, India e-mail: [email protected]

G.K. Ananthasuresh et al. (eds.), Micromechanics and Microactuators, Mechanisms and Machine Science 2, DOI 10.1007/978-94-007-2721-2_7, C Springer Science+Business Media B.V. 2012

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1.1 Background Holding and manipulating single or isolated biological cells is becoming increasingly important in biological studies. There are many techniques for biomicromanipulation: aspiration using pipettes, laser traps and tweezers, custommade fluidic traps, magnetic traps, and mechanical grippers. Each has its own advantages and disadvantages [2, 3]. Our focus is on gripper-based techniques because they are minimally-intrusive, inexpensive, automatable, and parallelizable. Additionally, compliant mechanism-based miniature grippers allow in-built force-sensing, haptic interface, and operation without extensive training and skill. Compliant mechanisms transmit and transform motion/force using elastic deformation rather than with joints. Because of the joint-less, one-piece compliant design, a grasping tool can also be turned into a force sensor and thus eliminating the need for a separate sensor which is not easily miniaturizable and bio-compatible. We use the concept of vision-based force-sensing [4,5] wherein the deformation of a compliant gripper is used to estimate the force through computation. In simple cases, the force is computed based on pre-computed force vs. displacement characteristic [1] or, in general situations, it is computed by solving an inverse problem in elasticity known as the Cauchy’s problem [6]. In the former case, it is possible to meet the update rate of the haptic device, i.e., 1000 Hz. It can be seen at Fig. 1 that the whole process of cell-grasping and injection is done in a sequential manner almost eliminating the question of damaging the cell because of the visual and haptic feedback [7].

Fig. 1 Conceptual diagram of the technique of cell-grasping and injection with a haptic interface

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2 Methodology and the Setup The in-house developed bio-micromanipulation system consists of two 3-degree-of-freedom (dof) XYZ micro-positioners (also called a micromanipulator, MP-285, Sutter Inc.), an inverted microscope with 2-dof motorized positioning stage (IX71, Olympus Inc.), a charge-coupled device (CCD) camera (SSCDC54AP, Sony Inc.), and a complementary metal oxide semiconductor (CMOS) camera (SC-08, Smart Infocomm Pvt. Ltd.) for vision based force-sensing and injector-cum-force sensor polydimethylsiloxane (PDMS) compliant mechanism. The setup is shown in Fig. 2 with details shown in the close-up views. Of the two XYZ stages, one is used for actuating the gripper and the other for injecting. The miniature compliant gripper’s motion is controlled by the user through a haptic device (PHANTOM Premium 1.5/6DOF HF, SensAble Technologies Inc.) and a PC controller. The actuating force (measured using the position of the actuator) and the cell grasping/injection force (measured using the vision-aided force-sensing) are magnified and are transmitted to the user through the haptic device. Grasping and injection are done using a single haptic device alternately at the discretion of the user. This paradigm helps us in holding a biological cell as gently as possible. As shown in Fig. 3, the block diagram for the cell-grasping and injection system consists of four types of loops: the haptic loop, the micro-robot loop, the video loop, and the computation loop. The haptic loop helps fetch the position of the haptic device to the personal computer (PC) and sending the calculated force to the user in real-time. The micro-robot loop sends the current position (in real time) from the PC either to the XYZ stage that actuates the injection system or to the XYZ stage actuating the gripper. This is done with the help of the button present in the stylus of the haptic device. The video loop manages to get the video data from the cameras to the PC and then to the display system in real-time. The computation loop performs the image processing to calculate the reaction forces in real-time in the case of cell injection and uses the actuator’s position for getting the actuating force in the case of the gripper.

2.1 Calibration of the Gripper The gripper used in our work is a compliant mechanism that works with a singlepoint actuation. The gripper adopted in our work was originally designed by Sahu [8] using topology optimization. Certain dimensions of the Gripper were modified to suit our requirements and is fabricated in-house by vacuum-casting PDMS in a mould made using wire-cut electro discharge machining (EDM) of aluminum mould. The geometric model of the gripper is shown in Fig. 4a and the fabricated gripper in Fig. 4b. The gripper fits within a foot-print of 12 mm × 12 mm area and has anchors that extend beyond this. These anchors (the large squares seen at the bottom of Fig. 4a) are attached rigidly to the arms that are in turn attached to a fixed stand so that the gripper’s jaws are positioned at the center of the field of view of the microscope.

64 Fig. 2 Bio-micromanipulation setup

S.D.B. Bhargav and G.K. Ananthasuresh

Cell-Grasping Compliant Mechanisms with Real-Time Haptic Feedback

Fig. 3 Block diagram of the system

Fig. 4a Geometric model of the gripper (All dimensions are in mm)

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Fig. 4b Fabricated PDMS gripper of 12 mm × 12 mm size

In order to get the force vs. displacement characteristic of the gripper, nonlinear finite element analysis (FEA) was done using ABAQUS [9] finite element software. Here, the actuation force depends on the stiffness of the object held by the gripper. Since the object grasped in our experimentation (the zebrafish egg) has varying stiffness at different stages of its development and after the egg is released outside, the eggs are injected as soon as they are taken out of the belly of zebrafish to reduce the inconsistency. The large-displacement finite element analysis is conducted a priori by giving different actuation forces starting with 54 μN and with an increment of 54 μN in each trial. Fig. 5 shows the force of actuation vs. displacement of the actuation point of the gripper. This is used as a calibration curve to estimate the force based on the displacement of the gripper. Thus, the displacement of the actuation point of the gripper is necessary to compute the force of actuation. This displacement originates at the haptic device’s stylus and is tracked by the haptic device. It is then de-amplified to transfer to the XYZ stage that actuates the gripper. In order to keep things simple, the XYZ stage is positioned such that it touches the gripper’s actuation point at the beginning of the experiment. Therefore, any relative increment in the position of the actuator is nothing but the displacement of the actuation point, Thus, the force can be updated in real time. In order to ease the grasping of egg cells, an arrangement is made to move the petridish containing egg cells using the motorized stage of the microscope that is independent to the compliant gripper.

Cell-Grasping Compliant Mechanisms with Real-Time Haptic Feedback

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Fig. 5 Actuation force vs. displacement of the miniature gripper

2.2 Design and Fabrication of the Housing Housing is designed to hold the glass slide on which the gripper is fixed. Using an exterior support, the entire housing is made to float over the petridish that contains the eggs to help one to independently move the petridish (with help of positioning stage) to locate an egg and place it between the jaws of the gripper. We used a slide of dimension 75 mm long, 25 mm wide, and 1.35 mm thickness and the housing is designed to suit these dimensions. Fig. 6a shows the geometric model of the housing and Fig. 6b, the fabricated aluminium piece made in-house using wire-cut EDM.

Fig. 6a Geometric model of the housing

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Fig. 6b The fabricated housing along with the slide containing the gripper (The gripper is seen at the top-right corner of this picture)

3 Testing and Results Experiments were done with our set-up on zebrafish egg cells as shown in Figures 7a-d. The process of injection and its corresponding force feedback worked smoothly with the aid of haptic and visual feedback. Egg cells could be moved with ease because of which grasping them became very easy. We were able to hold the egg cells with a gentle force which was just sufficient for cell’s injection. Then, we were able to move them out of the jaw region once they were released by the gripper. This feature enabled us to sequentially inject quite a number of egg cells. After several experiments, we could gauge the amount of force that is to be applied at the actuation point of the gripper. It was found to be about 7.5 mN. It should be noted that the grasping force will be much less than this. Time history of the amplified actuation force felt by the user is shown in Fig. 8. The two humps seen in the Figure indicate that the user, after the initial effort, the user is able to inject by adjusting the position of the egg cell and increasing the grasping force, and this makes the user a part of the overall feedback loop.

4 Closure In this work easy cell-grasping and injection with real time haptic feedback is demonstrated. A paradigm of cell-grasping and injection using haptics has been established. This set up helps in manipulation of the cell and hence cell injection

Cell-Grasping Compliant Mechanisms with Real-Time Haptic Feedback Fig. 7 Grasping and injecting a zebrafish egg cell. (a) the cell is held in the gripper and the pipette is moved to inject, (b) the cell is injected after bringing the jaws closer, (c) the cell is released from the gripper; a small spurt is seen and this is because of not providing a compensating pressure while injecting, and (d) the cell is moved out of the jaw region by moving the Petridish

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Fig. 8 Amplified injecting force felt by the user at the haptic device during cell-injection

can be done effectively even by unskilled users. Ongoing computational work aims towards estimating the force without pre-calibrated curves for arbitrary manipulative forces on the compliant grippers. Acknowledgments The authors would like to thank V. Mallikarjuna Rao for the initial set up, G. Ramu, B. M. Vinod Kumar and A. Ravi Kumar for their help in fabrication, Sajeesh and Suma for their help in procuring the egg cells. This work is supported in part by the Swarnajayanthi fellowship of the Department of Science and Technology (DST), Government of India, to the second author as well as the Math Biology grant from DST (No. SR/S4/MS: 419/07).

References 1. V. Mallikarjuna Rao and G.K. Ananthasuresh, “Haptic Feedback for Injecting Biological Cells using Miniature Compliant Mechanisms”, 14th National Conference on Machines and Mechanisms (NaCoMM-09), December 17-18, 2009 2. Robert M. Hochmuth, “Micropipette aspiration of living cells”, Journal of Biomechanics, Vol. 33, 2000, pp. 15-22. 3. Wang, W., Liu, X., Gelinas, D., Ciruna, B., and Sun, Yu, “A Fully Automated Robotic System for Microinjection of Zebrafish Embryos,” PLoS ONE, www.plosone.org, Sep. 2007, Issue 9, e862. 4. Yu, S. and Nelson, B.L., “Autonomous Injection of Biological Cells using Visual Servoing,” in Experimental Robotics VIII, LNCIS 271, D. T. Rus and S. Singh (eds.), 2001, pp. 169 178. 5. Wang, X., Ananthasuresh, G.K., and Ostrowski, J., “Vision-based Sensing of Forces in Elastic Objects,” Sensors and Actuators, A Physical, 94(3), 2001, pp. 142-156. 6. Reddy, A.N. and Ananthasuresh, G.K., “A Method for Computing the Forces from the Noisy Displacement Data of an Elastic Body,” International Journal of Numerical Methods in Engineering, 76 (2008), pp. 1645-1677.

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7. Bhargav, D. B. S., Rao, V. Mallikarjuna, and Ananthasuresh, G. K., “Haptic Feedback for Grasping and Injecting Biological Cells using Miniature Compliant Mechanisms,” in review for IEEE Transactions on Robotics, April, 2011. 8. Sahu, D.K., “Topology Optimization and Prototyping of Miniature Compliant Grippers for Micromanipulation”, Master of Engineering Project Report, Department of Mechanical Engineering, Indian Institute of Science, 2008. 9. ABAQUS finite element analysis software, www.simulia.com.

Fundamental Analysis of a Thin Film Type Conducting Polymer Actuator H. Terada and T. Yamagata

Abstract For the micro machine under the atmosphere, a new actuator by conducting polymer is developed. The polypyrrole is one of the conducting polymers. Especially, in cases in which this polymer is used, it is easy to make very thin and arbitrary shape sheets. So, this actuator has a bimorph structure which consists of polypyrrole and acetate thin films. In general, the conducting polymers expand and shrink with doping and dedoping, respectively, driven electro-chemically, in the electrolyte. However, this actuator deforms with shrinkage. This motion is based on a discharge of a water molecule by the Joule heating. In this paper, to realize a positioning control, the fundamental characteristics of this actuator are analyzed experimentally. It has been confirmed that the prototype actuator can be moved correctly under humidity 55–73%. Keywords Conducting polymer · Polypyrrole · Bimorph actuator · PWM control · Positioning

1 Introduction In general, a slanted-fiber sheet and the vibration motor with a large inertia are used for the actuator of micro moving robots [1-2]. Figure 1 shows the example of a slanted-fiber sheet type robot made by Sato [3]. And this type robot is driven by a vibration of inertia and the difference of the contact friction between the forward direction and the reverse direction. So, the motion principle has been analyzed using the mathematical model as shown in Fig. 2 [4]. In cases in which that micro moving robot is miniaturized more, the inertia size becomes smaller. Also, this miniaturization causes that a vibration power is reduced and a mobility of that actuator drops abruptly [5]. Therefore, it is necessary that the slanted-fiber sheet can flex or extend itself without inertia vibration, just like an insect leg. The shape memory alloy (SMA) is popular to use for micro machine H. Terada (B) Graduate School of Medical and Engineering Science, University of Yamanashi, Yamanashi, Japan e-mail: [email protected]

G.K. Ananthasuresh et al. (eds.), Micromechanics and Microactuators, Mechanisms and Machine Science 2, DOI 10.1007/978-94-007-2721-2_8, C Springer Science+Business Media B.V. 2012

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Fig. 1 Slanted-fiber sheet type micro moving robot

Vibration

Gravity center Vibration of body part

Mass 1

Slanted fiber sheet Reverse Friction

Mass 2

Spring Gravity center of leg part

Friction

Forward Friction

Fig. 2 Motion principle of a conventional slanted – fiber sheet type micro moving robot

actuator. However, the SMA has low deformation which is less than 5% [6]. And a long SMA is needed to generate the large deformation [7]. It is not suitable to the slanted fiber for micro moving robot. So, we develop the new bimorph actuator using a polypyrrole which is one of the conducting polymers. This actuator deforms with shrinkage. This motion is based on a discharge of a water molecule by the Joule heating. Also, in cases in which this actuator is used, it is easy to make very thin and arbitrary shape sheets. It is suitable for the micro machine actuators. In this report, the fundamental characteristics of polypyrrole film are analyzed experimentally. Also a positioning control method is proposed. And a prototype is tested to investigate usefulness.

2 Motion Principle of a Bimorph Actuator In general, the conducting polymers expand and shrink with the doping and the de-doping, respectively, driven the electro-chemically, in the electrolyte [8-9]. This phenomenon is caused by a volume change based on a change of water content in a polypyrrole. However, an expansion or shrinkage ratio of a polypyrrole is less than 0.9%, which ratio is that expansion length per the initial length. And when the slanted-fiber sheet type micro machine moves under the atmosphere, it is difficult to dope and de-dope electro-chemically.

Fundamental Analysis of a Thin Film Type Conducting Polymer Actuator Electrode Electrode Polypyrrole film +VCC

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Water molecules

Discharge GND

Acetate film Voltage impression Flexion Shrinkage

Shrinkage

Fig. 3 Motion principle of a laminated polypyrrole and the acetate films

We paid attention to the discharge phenomenon of water molecules inside this polypyrrole film. In other words, we should investigate a discharge of these molecules that is performed forcibly. Therefore, we suggest one of the solutions; the Joule heat occurs in a polypyrrole film by the DC voltage impression. And water molecules, which are in this film, vaporize by this heat. Based on this phenomenon, we have newly developed the bimorph structure, as shown in Fig. 3. A polypyrrole film and an acetate film are laminated for this structure. Especially, an acetate film does not discharge water molecules by the Joule heat. And the shrinkage of that film does not almost occur. Therefore, this film bends to a polypyrrole side. This flexion path length is longer than the simple shrinkage length of a polypyrrole film itself.

3 Structure of a Bimorph Actuator Based on this motion principle, we have developed a thin film actuator which consists from a cantilever structure as shown in Fig. 4. Especially, this structure considers the assignment of electrodes. And, these electrodes serve as the fixed section. Also, the specifications of this prototype are shown as Table 1.

4 Fundamental Characteristics of a Bimorph Actuator Using the developed actuator, we analyze the characteristics experimentally. At first, a relation between an actuating time and a generated pull-off force is measured, using an electric chemical balance (HL-200, A&D Co. Ltd.), as shown in Fig. 5. That pull-off force calculates from a reduction of the initial weight value. So, this prototype actuator has a non-linear characteristic, and it is clear that generating pull-off force becomes constant 43 seconds later, as shown in Fig. 6.

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Fig. 4 Prototype of a bimorph actuator

Electrode section

30 mm

7 mm

7 mm 1 mm

Table 1 Specifications of a bimorph actuator

Items

Values

Material of a deformation film Length Width Thickness

Polypyrrole 30mmx2+1 mm 7mm 30μm

Material of a base film

Acetate 30mm 15mm 0.11mm

Length width Thickness Total weight

0.1gf

Electrode (+VCC) Electrode (GND) Test actuator

Fig. 5 Pull-off force test of the prototype actuator at the flexion direction

Electronic chemical balance with weight

Fundamental Analysis of a Thin Film Type Conducting Polymer Actuator 25

Generated pull-off force mN

Fig. 6 Relation between an actuating time and a generated pull-off force for the prototype actuator

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This relation between an actuating time t and a generated pull-off force F, can approximate to equation (1). F = −0.0068t2 + 0.7804t

(1)

It is because that discharge of water molecules by the Joule heat matches with absorption from the atmosphere. And when a DC voltage is kept more than 43 seconds, it is assumed that an actuator is damaged by the heat seriously. Also, the ratio of the pull-off force per actuator weight itself is 21.5. Also, we have to consider the temperature and humidity around that actuator. So, another polypyrrole film is needed to compensate for them. In cases in which the compensation film is 50 mm length and 10 mm width, a relation between humidity and an electric resistance of that film is shown as in Fig. 7.

Electric resistance Ω

400

Fig. 7 Relation between humidity and an electric resistance of a Polypyrrore film type compensation sensor

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This electric resistance r can approximate as the equation (2), using humidity h. r = −0.0038h3 + 0.6338h2 − 29.453h + 618.03

(2)

5 Fundamental Characteristics of a Positioning with a PWM Control Method Considering the fundamental characteristics, we have developed the positioning control system. And we propose the control method in which the system uses a pulse width modulation (PWM) method, which consists of a one-chip CPU, a MOS-FET transistor driver and the humidity compensation system, as shown in Fig. 8. And for the evaluation method of a positioning, a CCD camera and a visual capture system are used. Also, a motion path of a cantilever tip is evaluated. At the constant PWM duty, relations between an actuating time and a motion path length for flexion motion are evaluated. At the starting part, these motions are similar, as shown in Fig. 9. However, after 8 seconds, these behaviours are different. So, a motion speed of this cantilever tip is calculated from a visual capture data, as shown in Fig. 10; it is clear that a motion speed is not constant, and changes complicatedly. Especially, the motion speed increases until 2 seconds. And the speed fluctuation does not depend on the humidity. On the other hand, after 2 seconds, the fluctuation of each speed depends on the humidity. Because it is difficult to discharge a water molecule under

PWM pulse

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Micro CPU board

PWM current

GND

+9VDC Current changes

MOS-FET Driver

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Bimorph actuator Flexion: Voltage impression

Polypyrrole humidity sensor

Extension: Without voltage impression

Fig. 8 Positioning system using a PWM control method with humidity compensation system

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the higher humidity circumstance, a shrinkage motion is reduced. At each humidity condition, the flexion motion speeds v52 , v62 , v72 can approximate to the equations (3)-(5), using an actuating time t. Humidity 52%: v52 = −2.0 × 10−6 t6 + 0.0002t5 − 0.0060t4 +0.0922t3 − 0.7523t2 + 2.9328t

(3)

v62 = −1.0 × 10−6 t6 + 0.0001t5 − 0.0037t4 +0.0662t3 − 0.6202t2 + 2.689t

(4)

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Humidity 72%: v72 = −2.0 × 10−6 t6 + 0.0001t5 − 0.0043t4 +0.0716t3 − 0.6281t2 + 2.6266t

(5)

Then, at the constant PWM duty 80%, the relations between an actuating time and a velocity for extension motions are evaluated, too. These extension motions depend on humidity larger than a flexion motion, as shown in Fig. 11. Especially, a polypyrrole film absorbs the water molecules from the atmospheres, so the extension speed is lower than the flexion speed. And, to clarify the influences of PWM duty, relations between an actuating time and a motion path velocity are evaluated, as shown in Fig. 12. It is clear that the

Absolute velocity mm/sec.

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Fig. 11 Relations between an actuating time and a velocity for extension motion (PWM duty80%)

Humidity 55% 1.5

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Fig. 12 Relations between an actuating time and a velocity for flexion motion at the constant humidity (Humidity 58%)

Motion path velocity mm/sec.

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Fundamental Analysis of a Thin Film Type Conducting Polymer Actuator 20 PWM duty for position holding %

Fig. 13 Relations between humidity and a PWM duty for position holding

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motion speed is not in proportion to the PWM duty. Especially, in cases in which that duty is over 80%, a motion speed is saturated. Therefore, this duty should be used less than or equal to 80%. In general, for a positioning control, an actuator should drive to the required positions. It needs to keep the same position, too. Considering this point, relations between humidity and a PWM duty for holding position, are evaluated, as shown in Fig. 13. A PWM duty to keep this position increases linearly until humidity 78%. So, the holding duty pwh can approximate to the equations (6) using humidity h. pwh = 0.1885h − 0.4426

(6)

6 Positioning Control Test Considering the fundamental characteristics of a bimorph actuator, a positioning control method is evaluated. Especially, for holding position, it has been clear that has a large influence of humidity from the fundamental analysis. So, to realize the flexion motion smoothly, we have planned the PWM duty patterns as shown in Fig. 14. To keep the required position, these PWM patterns have different duties at the holding motion. Also, to investigate the usefulness of this method, we made a slanted cantilever model in place of the slanted fiber, using the prototype actuator. Figure 15 shows the evaluation results of a positioning for flexion motion with a variable PWM duty and humidity compensation. At each condition of humidity, the

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Fig. 14 Input PWM duties for flexion motion with the humidity compensation

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Fig. 15 Positioning for flexion motion with a variable PWM duty and humidity compensation

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absolute positioning errors are less than 1.5 mm, as 45.4 mm to 46.5 mm. Also, these speeds are shown in Fig. 16. The velocities are compensated at a position holding motion. And these velocities have few fluctuations. So, it is clear that proposed PWM duty pattern is useful to control for holding an arbitrary position. Figure 17 shows the flexion motion of the slanted cantilever model using the proposed control method. At the start time, this model is slanted as 30degrees. And 20 seconds later, this is slanted to 100degrees, and after that keeps the pose.

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Fig. 16 Positioning velocities for flexion motion with a variable PWM duty and humidity compensation

Humidity 55%

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a) Start time

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d) After 17.0 sec.

e) After 20.0 sec.

f) After 22.0 sec

Fig. 17 Positioning test at the slanted cantilever model using the prototype actuator

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7 Conclusions To realize a micro moving robot under the atmosphere, a polypyrrole film actuator is developed. The fundamental characteristics of that actuator are analyzed. Also, a positioning control method is shown. And to investigate the usefulness, the prototype actuator is tested. So it is clear that the polypyrrole actuator has a power with a large flexion. It is very useful for micro machines. And this actuator can move to the arbitrary position with a PWM control method. In future work, to realize slanted-fiber sheet type micro moving robot which is a sub-millimeter size, this bimorph actuator will be improved to smaller shape. Acknowledgments The author is grateful to Prof. Okuzaki for cooperating to make the polypyrrole film.

References 1. T. Shin-ei, K. Yuyama, M. Ujihara, K. Mabuchi: Reduction of Insertion Force of Medical Devices into Biological tissues by Vibration. In: Japanese journal of medical electronics and biological Engineering 39(2001) No.4, p. 292 -296. 2. K. Isaki, A. Niitsuma, M. Konyo, F. Takemura, S. Tadokoro: Development of an Active Flexible Cable by Ciliary Vibration Drive for Scope Camera. In: Proceedings of the 2006 IEEE/RSJ International Conference on Intelligent Robots and Systems, (2006), p. 3946-3951. 3. http://www.micro.mse.kyutech.ac.jp/MM/new/index.html 4. T. Fukuda, N. Mitsumoto, F. Arai, H. Matsuura: A Study on Micro Mobile Robot: 1st Report, Design, Experiment and Mathematical Model of Micro Mobile Robot. In: Trans. of the Japan Society of Mechanical Engineers. Series C, 59(1993) No.562, p. 1787-1794. 5. T. Hayashi: From the Contest of Mountain Climbing Micro-mechanisms. In: Journal of the Japan Society of Precision Engineering, 56(1990) No.12, p. 2189-2192. 6. http://www2.toki.co.jp/biometal/products/WhtsBM.php 7. A. Miyazaki, A. Minemura, K. Yuasa, Y. Nakazato: Development of Micro-SMA Actuator for Small Medical Rehabilitation Equipment. In: Preprints of the JSME Symposium on Welfare Engineering 2006, (2006), p. 218-219. 8. T. Okamoto, K. Tada, M. Onoda: Examination of the Motion Property and Bending Mechanism of Polypyrrole Fiber Actuator. In: The Transactions of the Institute of Electrical Engineers of Japan. Series A, 120(2000) No.8, p. 829-834. 9. H. Okuzaki, N. Shirai: Contractile Behavior of Polypyrrole Films under AC Voltages. In: Synthetic Metals, 153(2005) No.1-3, p. 109-112.

Kinematics Study of Protein Chains and Protein Motion Simulation V. Petuya, M. Diez, M. Urizar, and A. Hernández

Abstract Proteins play an essential role in biochemical processes. Few years ago, a new viewpoint arose within protein researches, based on the parallelisms between proteins and mechanisms. In this paper the authors present an approach to obtain protein motion paths based on computational kinematic considerations. A potential energy field formula for potential energy checks is presented. Additionally, a normalization algorithm with the purpose of reducing the errors in experimental data and obtaining more stable structures is introduced. Finally, the simulation process for a specific protein is presented. Keywords Micromechanisms · Proteins · Kinematics

1 Introduction The discovery of the human genome was a milestone in the study of genetics, especially in the area of proteins. The human genome yields unique working tool, providing the opportunity of coming across new proteins and therefore obtaining information about the biological processes that take place within each cell. Proteins are one of the most important chemical compounds of living beings because they participate in most of the functions necessary for life. Their roles comprise tissue formation, defense against external agents, catalysis of chemical reactions and transport of other chemicals. Nowadays, numerous researches have focused on proteins, ranging from their formation to their diverse functions and synthesis. For example, the protein folding aims to get the tertiary structure of proteins, also called native structure, coming from their amino acid sequence or primary structure. The protein docking studies protein-protein and protein-ligand iteration. Molecular dynamics studies the movement of proteins by analyzing the interatomic forces acting on them. Finally, loop closure problem investigates how to fill the gaps in the structures of proteins. These investigations show the extensive field of study offered by proteins. V. Petuya (B) Department of Mechanical Engineering, University of the Basque Country, 48013, Bilbao, Spain e-mail: [email protected]

G.K. Ananthasuresh et al. (eds.), Micromechanics and Microactuators, Mechanisms and Machine Science 2, DOI 10.1007/978-94-007-2721-2_9, C Springer Science+Business Media B.V. 2012

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One of the most important topics within the proteins’ research is the study and collection of protein structures. To define the function of a protein is necessary to know its tertiary structure, which can be obtained either by experimental methods or analytical methods. The experimental methods, such as Nuclear Magnetic Resonance (NMR) and the X-Ray Crystallography, get photographs of proteins. These methods provide an accuracy between 1−4Å and are currently the reference methods for obtaining protein structures. Their main disadvantage is the great postprocessing they need to get the final structure, usually requiring an iterative process of refining. On the other hand, analytical methods focus on different approaches. There are two main families of methods. The first one focuses on the evaluation of a potential function searching for its minima, which corresponds to the tertiary structure. The remaining methods rely on the comparison between proteins’ primary structure so as to obtain the tertiary structure. New approaches try to combine these methods in order to achieve computationally low cost methods capable of solving any protein. Currently 96% of the structures stored in the Protein Data Bank [1] are experimentally obtained, so analytical methods still have a long way to go. Few years ago, a new approach made its way in the proteins field. This new approach, which could be designated as Biokinematics, tries to apply techniques and concepts of robotics and kinematics to the study of proteins. In this sense, Probabilistic Roadmap Mapping has been applied to simulate the folding of proteins and certain protein-ligand interactions [2]. In these methods simplified versions of potential energy functions are used, usually considering only the Van der Waals interactions in a simplified manner so as to save computational cost. In [3] modal analysis methods are used to obtain information regarding the possible movements of proteins around a given position. These tests are conducted on models of proteins, in which all interatomic bonds are replaced by springs. After the analysis, those eigenvectors with zero eigenvalues define the possible movements of the protein for that particular position. In [4] the authors use the potential energy function so as to obtain the efforts in the protein. Then, through these efforts, the equivalent torques in the degrees of freedom of the protein are calculated. Later, by minimizing these values the tertiary structure of the protein can be obtained. In [5] stiffness tests are performed in the chain of the protein to detect mobile and rigid zones.

2 Protein Structure Basically, a protein is a sequence of amino acids, which are joined together forming a chain. There exists 22 different amino acids and their combination, in order and number, is what creates the different types of proteins. All amino acids share a main chain consisting of a nitrogen atom, two carbon atoms and one oxygen atom linked by a double bond to the last carbon atom (see Fig. 1). From the central carbon atom, also called Cα, comes a group of atoms called secondary chain (as shown in Fig. 1). The secondary chain is different in each amino acid providing unique chemical properties.

Kinematics Study of Protein Chains and Protein Motion Simulation

Fig. 1 Biochemical model

Atoms inside prefered zones: 92% Atoms in allowed zones: 7% Outsider atoms: 1%

Fig. 2 Ramachandran plot of 1K20 protein (obtained with WinCoot)

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Proteins are formed by joining amino acids by a bond between the last carbon (C) and the nitrogen (N) of the next amino acid. This bond is called peptide bond, and its chemical characteristics force the relative angle between the front and back bonds in the chain of the protein, named ω, to be 0◦ or 180◦ . These angles impose the main chain atoms of the protein to be placed on planes, called peptide planes, composed of atoms Cαi − Ci − Oi − Ni+1 − Cαi+1 . The bonds between atoms N − Cα and Cα − C possess certain rotation motion. The relative angles in these aforementioned links are called dihedral angles, being φ and ψ respectively. When a protein folds, because of potential clashes between the secondary chains, these degrees of freedom (dof) do not have total freedom of rotation. Ramachandran et al. [6] showed how, if the values of dihedral angles are represented in a φ − ψ chart, all the proteins tend to have their angular values in certain areas (see Fig. 2). This graphical representation of the dihedral angles of a protein is called Ramachandran plot. The importance of this chart resides in that only the values of φ, ψ inside the preferred areas have a biological sense.

3 Protein Kinematic Modelization Taking into account proteins chemical characteristics and considering as constant the bond angles values, there can be found some parallelisms between proteins and kinematic chains. Assuming this hypothesis, and knowing that the chemical characteristics of the peptide bond rotation has its value restricted 0◦ or 180◦ , peptide planes may be treated as rigid structures inside the protein chain. As discussed previously, N − Cα and Cα − C bonds have certain ability to rotate, so they can be considered as rotation dof. This way the movement of proteins is defined by the rotation of peptide planes due to the variation of dihedral angles. This movement shares similar characteristics to that of serial manipulators although the number of dof is significantly higher, i.e. it exceeds 3000 dof. To comprehend how proteins work is essential to understand the nature of the movements that occur in the protein chain when it performs its function. The experimental methods cannot obtain the trajectories of the movements of a protein, because although obtaining the initial and final position can be relatively simple, obtaining the intermediate positions is almost impossible. There exists other programs that simulate the movement of proteins. In [7], [8], interpolation functions are used to obtain intermediate positions between two positions of the same protein. In [8], the process consists in superposing the two positions, and then applying the interpolation function to the cartesian coordinates of atoms. After each interpolation, an energy minimization function is applied to the protein so as to regain its biochemical characteristics. In [7], the authors do not carry out a minimization process since the distortions caused by small movements can be neglected and in large movements these distorsions can be avoided by adding intermediate steps to the simulation. Simulations obtained by these methods are only estimations of the real movements of the protein, since in practice there is no real variation of the dof of the protein.

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Our approach is focused on the simulation of the motion of a protein between two known positions by varying its dof, Δψ and Δφ. Starting positions are obtained experimentally. Data can be extracted from the PDB, the global database of proteins’ structures and sequences. To calculate the values of dihedral angles in the initial and final structures a reference plane has been chosen, called principal plane. The dihedral angles’ values are the angles between the principal plane and the previous and next peptide planes, as shown in Fig. 3, representing only three of the five atoms that make up each plane. Therefore, the modeling of the protein will be performed as a set of planes linked together by revolute joints. To perform our simulations, we have chosen the inorganic Pyrophosphatasa protein (corresponding to the entry in the PDB 1K20). The protein under study is an enzyme that takes part in the process of hydrolysis of pyrophosphate. The initial and final positions of the protein can be observed in the Fig. 4. This protein consists of 304 amino acids with a total of 4732 atoms. Overall there exist 302 possible rotations in each of the angles φ, ψ and ω. So as to compare the error, intermediate positions of the protein motion have been obtained from the morphviewer kinematics server [9]. This server simulates the movement of proteins through interpolation algorithms and energy minimization.

Fig. 3 Peptide and principal planes

Fig. 4 Initial (a) and final (b) positions of 1K20 protein (courtesy of Accelrys DS visualizer)

(a)

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4 Protein Potential Energy Calculus Regarding proteins’ kinematics, in order to obtain their motion, considering the evolution of the potential energy function is essential. This function provides information about the interactions between different atoms of the protein. There exist different methods across proteins research. Monte Carlo methods, molecular dynamics or molecular mechanics, implement different ways of evaluating the potential energy of proteins. There are several potential fields to evaluate the energy of proteins. CHARM, OPLs, AMBER etc. [10] are some examples of potential fields currently used for the study of proteins. All potential fields are governed by a similar formula but differ in the experimental coefficients. These coefficients are obtained from both experimental results and quantum mechanical simulations of simple compounds in different solvents [11]. The differences in the coefficients trigger different reactions in molecular dynamics simulations, encouraging or restricting some reactions to others. However, overall all potential fields behave similarly, increasing the energy when two atoms approach or when a bond tends to break. For the simulations we have used the AMBER potential field with the parameters proposed by Cornell et al. [11]. This potential field is governed by the formula presented in (1).

E= dihedrals

Vn 2

Kθ (θ − θo )2 + Aij Bij qi qj 1 + cos (nϕ − γ ) + 12 − 6 + ε Rij

bonds

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angles

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Rij

where Kr , kθ and Vn are constants that depend on the experimental bond tested, n is a multiplying factor function of the torsion bond which is being evaluated. The parameters r0 , θ 0 and γ are respectively the standard bond distances, angles and torsions of the protein structure obtained experimentally, and r, θ and ϕ are the present values. Rij is the distance between two atoms, qi,j are the partial charges calculated experimentally between two atoms, ε is the dielectric constant and Aij and Bij are: Aij = εij R∗12 ij

(2)

Bij = εij R∗6 ij

(3)

√ where R∗ij is the sum of the Van der Waals radii of i, j atoms and εij = εi εj , εi,j being the Van der Waals parameter for i, j atoms. The expression in Eq. (1) can be separated into two distinct parts, one corresponding to the bonded energies (the first three terms) and the remaining one corresponding to the non-bonded ones. The bonded energies measure the energy due to the bond created between atoms. The first term of the expression in Eq. (1) evaluates the energy by the increment or decrement of the distance of the bond. The second term corresponds to the energy due to the approximation of two links of a single atom, and the third term determines the energy generated by the rotation

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around certain bonds. The last term of the expression in Eq. (1) is the one corresponding to the non-bonded energies. This term evaluates the Van der Waals and electrostatic energies. The Van der Waals energy is very sensitive to the distance between non-bonded atoms. The electrostatic energy, on the other side, is dependent on the electric charge of atoms. The modeling presented in section 3 allows simplification of the formula. Since the distances and bond angles are considered as constant, the first three terms do not vary in value throughout the simulations, only the last term being the one that provides useful information concerning the increment or decrement in protein energy. As can be observed in Eq. (1) the last term is highly dependent on the interatomic distance. It has been evaluated that for interatomic distances greater than 9Å energy can be neglected.

5 Protein Structure Normalization Algorithm As mentioned in section 1, 96% of the available protein structures in the PDB have been obtained experimentally. When performing the simulations, it is important to know the quality of the data and the possible errors that experimental methods introduce during the process of obtaining proteins’ structures. The vibrational nature of the atoms introduces errors that alter the internal shape of the structures by changing the interatomic lengths and angles. These inaccuracies cause the principal planes used to calculate the dihedral angles not to be equal in the initial and final structure, resulting in some erroneous values. Although this may seem a minor problem because they do not imply mayor changes in atoms’ coordinates due to the large number of dof and the accumulation of errors, the simulations can be affected. Another consequence of this phenomenon is the disappearance of peptide planes and, hence changes in peptide angle ω between the initial and final position. In order to reduce these internal errors and obtain more stable structures, a normalization algorithm is being developed. This algorithm corrects the internal errors regarding peptide planes and the interatomic bond lengths. The algorithm consists of two stages. First, Ci , Oi and Ni+1 corresponding to i and i+1 amino acids are projected onto the middle plane formed by Cαi , Ci , Ni+1 and Cαi+1 (see Fig. 5). The middle plane calculus is made using a least squares fit method, Eqs. (4) and (5). S=

(xi − f (zi , yi ))2

(4)

i=1..m

f (yi , zi ) = b · yi + c · zi + d

(5)

where S is the function to minimize, xi , yi , zi are the coordinates of the atoms in the peptide plane, b, c, d are constants of the plane to get and m is the number of atoms in peptide plane. The process prevents the Cα atoms from moving, which act as pivots between peptide levels and the change in their position could disrupt a plane already normalized.

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Fig. 5 Projection onto the middle plane π

In a second stage, the algorithm applies distance constraints [12] to all bonds of the protein chain in order to ensure that the distances between two atoms ni , nj in the initial and final structures are identical to those proposed by Pauling in [13]. The restriction is defined by the following system of equations: → p p nj ni = d ji → p p−1

nj ni p−1

→ p p

× nj ni = 0

(6) (7)

where ni is the position of ni atom before applying the distance restriction and p p ni is the new obtained position, nj is the position of nj atom during application of the restriction and dji is the normalized distance of the link. Equation (6) defines a sphere in space, so to univocally define the distance constraint two more equations are needed. These equations are obtained by adding new conditions resulted from forcing the restriction to be applied onto the line formed by the two atoms (Eq. (7)). In Fig. 6, the graphic representation of the distance constraint in space is depicted. Due to high deviation in the peptide bond angle ω of the available experimental data, the normalization of the peptide planes in this protein results on a destabilized protein structure. Because of this reason, only bond length normalization is going to be applied to the current protein structure. The energy of the protein under study before bond length normalization process was 67.095K cal/mol and after applying the normalization algorithm decreases to 57.458K cal/mol. That is, after normalization algorithm the energy has been reduced by 15%. This means that the normalization process places the protein into a more stable situation. To validate the algorithm, is necessary to determine whether the protein has been disrupted. Thus, apart from the energy evaluation, it must be ensured that the proteins’ dihedral angles remain in the preferred regions of the Ramachandran plot. In Fig. 7, the

Kinematics Study of Protein Chains and Protein Motion Simulation

Fig. 6 Distance constraint in the space

Atoms inside preferred zones: 88% Atoms in allowed zones: 9% Outsider atoms: 3%

Fig. 7 Ramachandran plot after the normalization algorithm (obtained with WinCoot)

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Ramachandran plot of the protein after performing the normalization algorithm is depicted. We observe that the protein remains in the preferred regions of the chart, only 3% of the atoms being outside those regions. Thus preserving the biological sense of it. However, despite the implementation of the algorithm and the improvement obtained in both the protein structure and energy, internal differences still exist. The angles between the links of a single atom do not remain the same in the initial and final structure. This fact still produces errors in the measurement of dihedral angles. A new algorithm that includes the normalization of the angles between bonds as well as a more precise normalization of the peptide planes is currently being developed.

6 Protein Motion Paths Simulation To carry out the simulations a software called GIMPRO is being developed (see Fig. 8). This software is capable of displaying a protein reading standard ∗ .pdb format. Current efforts are focused on implementing simulation algorithms in this software and simulating the movement of proteins. Since all protein dof are of angular type, all calculations imply working only with angular parameters, using the Cartesian coordinates of atoms for the representation of the protein and the calculus of the potential energy. As mentioned previously the initial and final positions will be used as data for simulation process

Fig. 8 GIMPRO software main view

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and intermediate positions, obtained by morphviewer server, will be used only for the evaluation of the error along the movement. In the analysis, the values of dihedral angles φ, ψ and peptide bond ω angle for each amino acid will be computed, at both initial (0) and final (f) experimental positions. Then the simulation will be carried out rotating gradually each dof, according to Eq. (8), until the final configuration is reached, obtaining throughout the process the protein motion paths. The rotations in each dof are given by: f

φi =

φi − φi0 ; p

ψi =

ψi − ψi0 ; p

f

(8)

f

ωin =

ωi − ωi0 p

where p represents the number of steps or intermediate positions in the simulation. Increasing the number of steps implies improving the simulation but also enlarging the computational cost. The process progresses from the first dof to the last one. ei axes are unit vectors whose directions are defined by the bonds Ni − Cαi for the case ψ i , Cαi − Ci for φ i and Ci − Ni+1 for ωi . The vectors to be rotated, defined as rkj , are defined from the atom origin of ei to the atom to be rotated. In Fig. 9 the representation of these vectors for the case of the N − Cα is shown (only carbon atoms rotation vectors are represented). The rotations in each dof are made by the vector form of the Rodrigues rotation formula, used in analysis and simulation of mechanisms and adopted nowadays in VRML (Virtual Reality Markup Language): rjk+1 = u + v · cosφi + d · sin φi

Fig. 9 rkj vector representation in a protein chain section

(9)

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where k is the actual position. Rotated vector rjk+1 is obtained by the sum of three vectors: v is the component in the plane defined by rkj and ei , d is the normal component of this plane and u is the projection of rkj on ei : v = rkj − ei · rkj · ei ; d = ei × rkj ;

(10)

u = ei · rkj · ei v and d vectors are multiplied by cosφi and sinφi respectively, so rjk+1 vector obtained in equation (9) is decomposed as shown in Fig. 10.

Fig. 10 Graphic representation of rkj vector rotation

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It is necessary to mention that Eq (9) presents no singularity in any position including 0◦ and 180◦ . The relative error between experimental and simulated structures (including intermediate positions) is obtained by calculating the mean square error (rmsdl ) of the two superimposed structures: N 1 di2 rmsdl = N

(11)

i=1

where di represents the distance between ni atoms of both superimposed structures and N is the number of atoms of the protein. First results show an acceptable evolution of the root mean square error, maintaining at any time the dihedral angles within the preferred areas of the Ramachandran plot. On the other hand, in certain intermediate positions, potential energy presents high peaks. This is due to the excessive approximation or even collisions between atoms, thus obtained motion paths present errors in localized zones of the proteins. It can be noticed that the RMSD measures the error of the protein overall while the energy gives information about relative locations between specific atoms. For this reason, we are working in two algorithms that introduce the energy in the process of calculation. In this approach, we include the evaluation of the potential energy of the protein throughout the simulation but avoiding the potential energy or other function minimization that usually falls in local minima. The energy function is used as data for checking the validity of one position and proceeds to its change if necessary. The proposed algorithm checks whether the increment in energy is higher than a value ε% defined by the user, and then acts accordingly. Two strategies are being developed. The first algorithm, described in Algorithm 1, consists in blocking the dof when detecting an energetic peak. The algorithm begins by rotating the current dof. Then it assesses all the potential energy and store protein energy increment generated by the action of this dof in an array for later use. When all dof have been rotated, potential energy is evaluated. If it has increased in more than ε%, that position is considered incorrect. As energy increment caused by every dof has been stored, it is possible to undo only those dof that produce the highest increments. This process is repeated until the energy decreases to an acceptable value. Then the algorithm restarts to find the next position. The algorithm is repeated until the required p positions by the user are obtained or until the protein reaches an energy barrier. The other approach modifies the application ratio of each dof by adjusting calculated increment values. When all dof have been rotated, the energy evaluation is carried out. As in the previous algorithm, if the energy exceeds ε% value, the dof with the highest energy increment is selected. The increment value of this dof is divided by an amount defined by the user and the rotation is applied again. If the new potential energy exceeds ε% value, the dof rotation is undone and the algorithm proceeds with the next dof. The process is repeated until the energy decreases to an

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Algorithm 1 Energetic algorithm 1 for a single step of the procedure 1: 2: 3: 4: 5: 6: 7: 8: 9: 10: 11: 12:

E0 ← Evaluate protein potential energy foreach Dof j in the protein do Rotate the jth dof (ψj ||φj ) Ej ← Evaluate Potential Energy Ej ← Ej − Ej−1 end foreach g if j=0 Ej /E0 ≥ ε then g while j=0 Ej /E0 ≥ ε do Unrotate dof j related to the highest Ej Ej = 0 end while end if

acceptable value. If the energy has decreased to an acceptable level, the position is considered correct and the algorithm restarts to find the next position. First results show an acceptable progress both in the global error and energy evolution of the protein motion. However, the motion itself seems quite artificial. It seems that blocking the dofs in an iteration produces some kind of vibration in the protein motion. The second approach is aimed to solve this problems as it does not block the rotation of the dofs but reduce its value.

7 Conclusions In this paper a methodology for obtaining protein motions paths is presented. This methodology uses proteins’ real dof for the calculus of successive positions of their movements. A normalization procedure has been described, which minimizes the errors in the protein structure and brings the protein to a more stable position without losing its biological sense. A potential field has been presented for the proteins’ potential energy calculus. Finally, two algorithms has been summarized for the inclusion of the potential energy into the simulation process. Acknowledgments The authors wish to acknowledge the financial support received from the Spanish Government through the Ministerio de Educaciy´ Ciencia (Project DPI2008-00159), the FEDER funds of the European Union and the Basque Regional Government (Project GIC07/78).

References 1. Helen Berman, Kim Henrick, Haruki Nakamura, and John L. Markley. The worldwide protein data bank (wwpdb): ensuring a single, uniform archive of pdb data. Nucl. Acids Res., 35(suppl1):D301–303, 2007. 2. Shawna Thomas, Xinyu Tang, Lydia Tapia, and Nancy M. Amato. Simulating protein motions with rigidity analysis.

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3. Gregory S. Chirikjian. A methodology for determining mechanical properties of macromolecules from ensemble motion data. Trends in Analytical Chemistry, 22:549–553, 2003. 4. Kazem Kazerounian, Khalid Laif, and Carlos Alvarado. Protofold: A succesive kinetostatic compliance method for protein conformation prediction. Journal of Mechanism Design, 127:712–717, 2005. 5. Donal J. Jacobs, AJ. Rader, Leslie A. Kuhn, and Mf Thorpe. Protein flexibility prediction using graph theory. Protein: Structure, Function and Genetics, 44:150–165, 2001. 6. G. N. Ramachandran, C. Ramakrishnan, and V. Sasisekharan. Stereochemistry of polypeptide chain configurations. Journal of Molecular Biology, 7:95–99, 1963. 7. Rajarshi Maiti, Gary H. Van Domselaar, and David S. Wishart. MovieMaker: A web server for rapid rendering of protein motions and interactions. Nucl. Acids Res., 33(suppl2):W358–362, 2005. 8. Werner G. and Mark Gerstein. The morph server: Af standarized system for analyszing and visualizing macromolecular motions in database framework. Nucl. Acids Res., 28:1665–1675, 2000. 9. S Flores, N Echols, D Milburn, B Hespenheide, K Keating, J Lu, S Wells, EZ Yu, M Thorpe, and M Gerstein. The database of macromolecular motions: new features added at the decade mark. Nucleic Acids Res, 34:D296–301, 2006. 10. Tamar Schlick. Molecular Modeling and Simulation. Springer, 2006. 11. Wendy D. Cornell, Piotr Cieplak, Christopher I. Byly, Ian R. Gould, Jr Kenneth M. Merz, David M. Ferguson, David C. Spellmeyer, Thomas Fox, James W. Caldwell, and Peter A. Kollman. A second generation force field for the simulations of proteins nucleic acids and organic molecules. Journal of American Chemical Society, 117:5179–5197, 1995. 12. V. Petuya, A. Alonso, Ch. Pinto, O. Altuzarra, and A. Hernandez. A new general purpose method to solve the forward kinematic problem in parallel manipulators. Advanced Robotics, 2008. 13. Linus Pauling and Robert B. Corey. Atomic coordinates and structure factors for two helical configurations of polypeptide chains. Proceedings of the National Academi of Sciences, 37, 1951.

Matrix Pad Transducer L.M. Dehelean, N.M. Dehelean, and E.-Ch. Lovasz

Abstract Human trait detection could be a useful job for an automat system. Animal abilities of space detection are strictly oriented to help them to survive. Dog use, first, the smell receptivity, but snake uses the infrared sensors. The matrix pressure sensor for human gait detection needs such a structure in order to be able to acquire a set of data to describe the human footprint as a spatial-temporal function p(x,y,t). Any element of the transducer takes a position that is defined by the matrix coordinate. All the elements are pressure sensors. A difficulty of this transducer design is the achievement of the signal. A simple grid connection is not adequate to obtain p(x,y,t) versus s(t) signal. The analogical signal has to be converted to digital one. Finally the matrix must be analyzed with an image strategy: segmentation, ROI establishing, Fast Fourier Analyze etc. Keywords Matrix · Transducer · Pressure sensor · Pad · Recognition

1 Introduction Matrix pad transducer is an important component of an automatic system that could be able to recognise a human typology. Considering the observation, that human proceed to recognise a person by gait specific signature, it proposes a new (technique) procedure [5] to do a similar activity by an automatic system. Human uses, in recognition endeavour, a complex mental activity that proceeds to evaluate the sound of the walking person in order to do the recognition of a specific person. Automatic system could use the same data sampling. But sound is drastic affect by the noise produced in the public halls. To avoid this deficiency it observes that only the interaction between foot and floor is the issue of the walking sound. Supposing there is a similarity between the pressure distribution of the foot step on ground and the sound that is emitted by the walking stroke, it becomes necessary to replace the sound of walking signal with a pressure signal to reach the target declared below. L.M. Dehelean (B) Department of Mechatronics, “POLITEHNICA” University of Timisoara, Timisoara, Romania e-mail: [email protected]

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In order to acquire a pressure complex signal p(x, y, t) it is necessary a special (dedicate) step pressure sensor. It can easily observe a similarity between p(x, y, t) signal and B(x, y, t) specific in the field of moving image signal (TV). The special sensor could be a matrix pressure sensor (MPS) able to provide an image signal of pressure walking trail. This image signal should be primary data source for a set of integral transform procedures, even Fourier transform procedure. A fast Fourier transform could provide a useful signature to operate with data base. This one will be process to build up a stochastic hierarchy. The discrimination of the main task into subtasks guides the research to a sound method of people recognition. This method is based on following principles: A. Every human comes in contact with his environment and generates a specific trail; B. The basic human trail is, most probably, alters by the person psychical state of the moment; C. Each trail can be parameterised; D. A large set of trails should improve the trust degree of the analyse; E. The certain person perception is impossible, as consequence, it is unnecessary to develop an exhaustive person search system.

2 The Person Detect System Starting with an overlook on the well-known models that were yet published in the field of person detection it is possible to propose a new detection system structure of human recognition. In [13] there is presented a method of monitoring people behaviours in large and complex environments using multiple cameras. Many authors approach to the problem in two steps. A process of low-level visual data from the cameras; that produces a stream of events which are interpreted by a recognition module to produce high-level description of the people activities in the environment and finally a process of classification in a Layered Hidden Markov Model “LHMM”. The high-level behaviour recognition module needs to be based on a framework that facilitates the modelling of and reasoning with uncertainly. In [13] is proposed an Abstract Hidden Markov Memory “AHMEM” in order to organise the people behaviour into a stochastic hierarchy. Each of behaviour can be refined into sequence of more simple behaviours at lower levels. The system structure consists of two modules: the low-level tracking module and the high-level behaviour recognition module. The low-level module is based c movement model on a compressed movement model A that replaces the complete A = Pr s |s, π . For level behaviour π in a region R Pr s |s, π represents the probability for all states s in R and for all neighbouring states s of s.

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Pnorhtwest Pnorth Pnortheast Pcenter Peast Ac = Pwest Psouthwest Psouth Psoutheast

(1)

Pnorthwest represents the probability that a person moves to northwest; Pnorth represents the probability that a person moves to north and so on. The system has to learn different movement behaviour. It has a low performance according with our day expectation, but it needs to keep the essence of method, as an auxiliary device. Much more elaborate methods are oriented to interpreted human motion. In this area it finds: – – – –

Movement trajectory recognition; Face and gesture recognition; Eye movements; Language and speech recognition.

Some other procedures like fingerprint, iris and retinal patent can generate specific signature to identify person to a high level of certitude, but all of them imply the cooperation of people. Gait perceives is better then procedures as mentioned above. It makes data acquisition non-invasive, convenient and easy to hide from the crowd watching (surveillance). This procedure offers the possibility to decrease the number of the cameras placed in a public hall. Gait data acquisition has to be done in such a manner that does not attract human attention. It is well known that humans have a natural ability to recognise friends by their walk. Psychological studies confirmed that it can be discriminate the gender of a walker by its dynamics. The walking styles of children and adults have been categorised via computer vision technique. In [2] the gait signature of a particular subject consists of the phase and the magnitude components of the Fourier description of the thigh and lower leg rotation measured from a gait cycle. Here, the significant features of periodic motion are captured. Statistic analysis is necessary to establish the basis of determining which feature to use in creating a useful gait signature for discrimination purpose. The recognition rata of running is encouraging since running has more variability across the population compared with walking. This affirmation is consistent with biomechanical analysis, because running involves increasing muscle activities and force; and there exist different manners in which the foot contacts the ground [16]. The features appear to have an individual mapping between the feature space of walking and running an individual class basis. This may suggest that a mapping might exist that could make the signatures invariant. In the field of walking research two new models have used: the bilateral symmetric and the analytical model of a forced coupled oscillator [2].

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Fig. 1 Ground reaction

Fig. 2 Velocity diagram

Another way to person recognition is the gait style research. In Fig. 1 it is show a ground reaction force diagram (black for right step and pink for the left one) and a velocity one is show in Fig. 2. (black for pressure and brown for velocity). Therefore in gait analysis it is necessary to normalise data of the gait cycle, which means it needs to know when initial-contact (IC) and toe-off (TO) occur. In the case of low-pass filter using, the diagram of velocity from Fig. 2 becomes a diagram like Fig. 3. The anterior-posterior kinematics is show in Fig. 4. Considering A, B, C, D and E principles the paper adds a new recognise automatic system with the structure schema that is shown in Fig. 5. The system works like Local Area Network LAN and command the automat barriers, doors lock, security alarm and so on.

Fig. 3 Filtered velocity

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Fig. 4 Gait kinematics

All the sub-systems (ESAS), (ISS), (GMDS) and (SMDS) (Fig. 5) work synchronous using a time signal generated by the Global Signature Generator in order to obtain a set of signatures that represent rigorously the same person. The global signature must be recorded in a data base as a knowledge element in a knowledge structure.

3 Overview on Pressure Detectors In [12] it is shown a general kinestatics model of a multi-fingered robot hand manipulating an object. Using this model, which takes into account the motion of the contact points on the fingers due to the relative sliding and/or rolling between the object and the fingers, two problems are discussed: 1) a general kinematics velocity control method; 2) shape reconstruction of unknown objects during manipulation. In [9] two techniques for slip detection with a rubber-based tactile matrix sensor are presented. The described results have been obtained within a common research activity between the Robotics and Automation Laboratory of the University of Bologna and the Control Laboratory of the Delft University of Technology. The first technique is based on a frequency analysis of the position of the centre of force distribution. The main idea is that before a slip situation really occurs, it is possible to detect a micro movement of the object due to the elasticity of the rubber. By implementing a Fast Fourier Transform of the centre of distribution and by testing the frequency components the slip is identified before it practically occurs. The second approach is based on the principle that the normal forces measured by the tactile sensor fluctuate with a certain frequency during slip because of the rubber elasticity. This fluctuation is due to a “catch and snap back” effect, which is present when an object is slipping over the sensor’s surface. By testing the frequency domain of the normal force a slip condition can be detected an even predicted. A

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L.M. Dehelean et al. Image Surveillance System (ISS) Face shape, body shape, gesture shape, strange move detection, speed detection, trajectory

Hidden set of cameras Airport Gates

Hidden set of microphones

Matrix Pressure Sensor

Floor Heavy Sensor Standing Manner Detection System (SMDS)

Gait Manner Detection System (GMDS)

Global Signature Generator The stream of gait manner signatures Some relevant methods of the human gait signature: 1. Eigenvectors method-Human walking images were projected The stream of sound signatures in the eigen-space in order to obtain eigenvectors [14]; 2. Canonical Analysis combined with eigen-space transformation; 3. The potential ofimage-selfsimilarity method [1]; Data Base 4. Aria-based metrics [7]; Stochastic 5. Static body parameters [11]; Hierarchy 6. Velocity moment and symmetry [15]; 7. Velocity Hough Transform (VHT) and simple pendulum model; 8. VHT with Fourier transforms.

The stream of standing signatures The streamof shape signatures Physical Diagnose Expert System

Fig. 5 The structure schema of the automatic person recognise system

Fuzzy Decision Maker

Operative Commander

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comparison between the two approaches is presented and discussed on the basis of experimental results obtained in both laboratories. In [10], some new uses of a rubber-based tactile matrix sensor to perform shape and grasp force adaptation in robotic manipulation are presented. The sensor consists in a 16x16 matrix and a rubber whose resistance changes with the applied force. It is shown how this sensor, besides the usual information such as shape recognition, contact point position, pressure measurement and so on, can be profitably used for shape adaptation and grasp force adaptation. In this way, the sensor can replace more sophisticated and complex sensory devices needed for advanced manipulation tasks. In particular a heuristic algorithm able to achieve a maximum local contact area between a manipulated object and a robotic finger as well as a new approach to detect the relative slip is presented. In [8] it is shown a multi-sensory parallel jaw gripper system for complex object manipulation purposes of an autonomous robot disassembly system. The jaws of the gripper integrate different types of sensors. First an optical array of pulsed IR-diodes enables detection of object presence between the gripper jaws. Furthermore, a tactile matrix sensor is integrated, measuring contact force distribution over its surface using conductive rubber. It provides the system with information about the quality of an established grasp, the resulting normal grasp force, and it can be used for slip detection of the object, which is the most important use of tactile sensors during object manipulation. Therefore, a respective fast and simple method is presented with experimental results proving its reliability. An interesting structure [4] of the matrix pressure sensor is shown in Fig. 6. The structure of this new matrix transducer is complex enough in order to acquire a complex set of data required by the system. It will be used to describe the footprint as a spatial-temporal function p(x, y, t). Any element of the transducer takes a position that is defined by the matrix coordinate. The elements are pressure sensors. Each of

• conical piece • piezoelectric transducer • electric contact • steel plate • soft rubber • hard rubber coat • virtual foot print

Fig. 6 Matrix piezoelectric pressure sensor

• gait sensor pad

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them consist of a conical piece attach to a piezoelectric sensor. The rubber coat has a special shape to create a minimal influence between the neighbour elements. The main difficulty of this transducer design is the achievement of the signal. A grid connection is not adequate to obtain p(x, y, t) versus s(t). There are necessary m(n+1) connections for a matrix of m rows and n columns. Thus, it is necessary to implement a segmentation strategy such as the strategy used to the digital TV image sampling. The analogical signal has to be converted to a digital one by a sampling and coding process. Finally the matrix must be analyzing with an image strategy: segmentation, ROI establishing, Fast Fourier Analyze etc. In [6] it is describe an original and ingenious pressure transducer shown in Fig. 7. The hydro cell from Paromed (Gmbh, Germany) consists of an inbuilt Wheatstone bridge, inserted in a capsule filled with incompressible fluid, which results in a pressure from the different components of the ground reaction force. The cell is sensitive to total mechanical stress which has three components: pressure acting normally (z) on the surface and antero-posterior (y) and medio-lateral (x) shear stress acting tangential to the surface. The cell revealed realistic measures of pressure acting under the foot because it is sensitive to normal and shear stress. The Hydrocell is calibrated by the manufacturer and a calibration file is provided for each sensor. Join the technical solution from matrix pad in Fig. 6, with the idea of Hydrocell in Fig. 7 it comes out a new pad matrix solution Fig. 8. The first advantage of this new pad is his low thickness comparing with the solution in Fig. 6. The matrix pad hydro-transducer, like any other matrix pad, needs an electronic schema to explore the signal that is provided by each cell of the matrix. The schema should have two multiplexers that work synchronous to swap the 0x and 0y directions. The exploration and the sampling strategies are the same as the strategies that are used in the TV images techniques. It is established an analogy between B(x, y, t) from image process and p(x, y, t). Fy

Fx

Fz p

Cell body

Fig. 7 Hydrocell from Paromed

Incompressible fluid Pressure transducer

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Fig. 8 Matrix pad hydro-transducer

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4 Conclusions A reliable classification of selected gait recognition algorithms is presented in [3]. All the existing person recognition systems use simple signature. None of them try to reach this purpose by complex signature that embedded a large set of person behaviour characteristics [3]. The difficult task of person recognition could be reached by a complex intelligent system. The hardware complexity includes a large number of sensors. Some sensors are very singular and out of the ordinary typology. The main constrain of the system requires that its presence has to be discrete and the tested person does not observe the sensors and the cameras. The system has to work in real time and simultaneous with a large number of people – in a very noise conditions. Therefore it comes to be necessary a new competent matrix transducer.

References 1. Abdelkader, C. B., Cutler, R., Nanda, H., Davis, L.: Eigen-Gait: Motion-Based Recognition Using Image Self-Similarity. In: Third Proceedings of the Audio- and Video-Based Biometric Person Authentication, Halmstaadt, Sweden, 2001. 2. Chew Yean Yam, Nixon, M. S., Carter, J. D.: Automated Person Recognition by Walking and Running Via Model-Based Approaches. In: The Journal of the Pattern Recognition Society, 2003. 3. Daehee, K., Seungwon, L., Jooki, P.: Active Shape Model-Based Gait Recognition Using Infrared Images. In: International Journal of Signal Processing, Image Processing and Pattern Recognition, Vol.2, No.4, 2009. 4. Dehelean, L. M., Dehelean, N. M.: On Matrix Sensor Category Dedicated to a Gait Detection System. In: Scientific Journal of Polytechnic Institute from Ia¸si, Vol. LII(LVI), Issue 7A, 2006, p. 101-106. 5. Dehelean, L. M., Dehelean, N. M., St˘anescu, D.: A Minimal System Structure for Human TraitDetection, In: Proceedings of the 7th Conference on Technical Informatics CONTI’2006, Timi¸soara, 2006, p. 189-194. 6. Descatoire, A., Thevenont, A., Moretto, A.: Baropodometric Information Return Device for Foot Unloading. In: Medical Engineering and Physics 31(2009), p. 607-613, www.elsevier. com/locate/medengphy. 7. Foster, J., Nixon, M., Prugel-Bennett, A.: New Area Based Matrices for Automatic Gait Recognition. In: Proceedings of the British Machine Vision Conference, Manchester, UK, 2001. 8. Hohm, K., Weigl, A., Krüger B., Schwartz, M., Tolle, H.: Using a Multisensory Gripper System for Robot Assisted Disassembly of Electronic Devices. Darmstadt University of Technology, Control System Theory and Robotics Dept, Darmstadt, Germany. 9. Holweg, E. G. M., Hoeve, H., Jongkind, W., Marconi, L., Melchiorri, C., Bonivento, C.: Slip Detection by Tactile Sensors: Algorithms and Experimental Results. In: ICRA’96, IEEE International Conference on Robotics and Automation, Minneapolis, MN, 1996. 10. Holweg, E. G. M., Eusebi, A., Marconi, L.: Reflex Control by a Rubber-Based Tactile Sensor. In: “Advances in Robotics. The ERNET Perspective”, Proceedings of the Research Workshop of ERNET, C. Bonivento, C. Melchiorri and H. Tolle Eds., p.117-126, 1996.

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11. Johnson, A. Y., Bobick, A. F.: A Multi-View Method for Gait Recognition Using Static Body Parameters. In: Third Proceedings of the Audio- and Video-Based Biometric Person Authentication, Halmstaadt, Sweden, 2001. 12. Marconi, L.: Tactile Sensor Data Elaboration for Object Recognition and Interpretation. In: Second TELEMAN Students Congress, Leeuwenhorst Congress Centrum, Noordwijkerhout, the Netherland, 1995. 13. Nguyen, N. T., Venkatesh, S., West, G., Bui, H.: Learning People Movement from Multiple Cameras for Behaviour Recognition. BMVC99, 1999. 14. Niyogi, S. A., Adelson, E. A.: Analyzing and Recognizing Walking Figures in XYT. In: Proceedings of the Conference of Computer Vision and Pattern Recognition, Seattle, WA, 1994. 15. Shutler, J. D., Nixon, M. S., Harris, C. J.: Statistical Gait Recognition via Temporal Moments. In: Fourth IEEE Southwest Symposium on Image Analysis and Interpretation, Austin, Texas, 2000. 16. Thordarson, D. B.: Running Biomechanics. Clin. Sports Med. 16(2), 1997.

Ultrasonic Hot Embossing and Welding of Micro Structures K. Burlage, C. Gerhardy, and W.K. Schomburg

Abstract Ultrasonic hot embossing allows the fabrication of micro structures from polymer films by moulding from a master tool. The fabrication process is completed within seconds and the investment costs are low. With micro patterned tools, structured surfaces can be created on one or both sides of polymer films. For micro whistles and micro fluidic devices such as micro mixers or flow sensors, sealed structures are created by welding a cover film on embossed structures. Furthermore, moulded interconnection devices can be fabricated by welding polymer coated metal films onto polymers. Keywords Ultrasonic microstructures

welding

·

Ultrasonic

hot

embossing

·

Polymer

1 Introduction Ultrasonic welding has been used for welding thermoplastic materials for decades. Frictional heat caused by ultrasonic vibration locally melts a thermoplastic material where compressive force is applied through protruding structures on a tool or on the material itself. Ultrasonic welding and ultrasonic hot embossing are applicable for a wide range of polymer micro structures and micro systems and exceptionally suitable for the production of prototypes. Contrary to injection moulding and hot embossing, the investment costs for ultrasonic welding machines are low and manipulation and retooling are comparatively easy. While injection moulding and hot embossing require complete melting of the polymer, the directed energy input and locally restricted melting achieved by ultrasonic welding lead to reduced shrinkage and heat distortion, which facilitates tool design. At KEmikro, several different products have been manufactured by ultrasonic welding and hot embossing. Different one-sided and double-sided micro structures were embossed into various materials, sealed micro channels, micro fluidic devices and micro whistles were K. Burlage (B) Konstruktion und Entwicklung von Mikrosystemen (KEmikro), RWTH Aachen University, Aachen, Germany e-mail: [email protected]

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produced and moulded interconnect devices manufactured. Each of these products requires specific tools and process parameters which were developed and successfully implemented. All products which are shown in this paper were manufactured with the Dynamic 745, a 35 kHz ultrasonic welding machine produced by Rinco Ultrasonics AG, Switzerland.

2 Ultrasonic Hot Embossing of Micro Structures in Polymer Films 2.1 One-Sided Ultrasonic Hot Embossing The ultrasonic embossing process (Fig. 1) starts with placing two polymer films between the ultrasonic horn and the metal tool. The ultrasonic horn is then driven downwards and presses the polymer films onto the tool. The pressure is increased until a preset value is reached at which point the ultrasonic vibration is started. The ultrasonic vibration is converted into heat energy where protruding micro structures on the tool are in contact with the polymer. The temperature in these areas increases above glass transition temperature and the melting polymer adapts to the metal tool. After reaching the required moulding depth, which typically takes about 0.1 to 1 s, the ultrasonic vibration is switched off while the horn continues to apply pressure to the polymer during the subsequent cooling and solidification phase. This normally takes 2-3 times longer than the ultrasonic time to ensure sufficient filling of the mould. Afterwards the embossed structures can easily be de-moulded by hand. The production of grooves and channels (Fig. 2), but also of protruding micro structures on the surface of polymer films (Fig. 3) is possible. It has proved to be advantageous to employ two polymer films instead of a single layer. Less energy is needed to achieve the same embossing depth as the heat is generated at the contact surface between the polymer layers which are molten

Fig. 1 Ultrasonic hot embossing: (a) positioning of polymer films on the tool, (b) embossing by compressive force and ultrasonic vibration, (c) de-moulding [1]

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Fig. 2 Section through a rectangular channel embossed into 2 layers of 250 μm thick polyvinyl chloride films

Fig. 3 Protruding micro structures formed with a LIGA mould by ultrasonic hot embossing [2]

and welded into a single embossed workpiece. Experiments showed that embossing force and ultrasonic time can be reduced by up to a third when two layers are used instead of one. In some cases, reaching the desired embossing depth with one layer was impossible, since burning of the polymer occurred before the depth could be reached. Using two layers also leads to better moulding results and smooth surfaces around the embossed areas, whereas embossing into a single layer leads to the formation of a knoll around the embossed structure. The respective results of embossing ito a single layer and two layers of polypropylene are shown in Figs. 4 and 5.

2.2 Double-Sided Ultrasonic Hot Embossing The process of double-sided ultrasonic hot embossing is the same as for one-sided embossing, but in addition to the structure on the metal tool, the ultrasonic horn is

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Fig. 4 Section through a chamfered channel embossed into a single layer of 250 μm thick polypropylene [1]

Fig. 5 Section through a chamfered channel embossed into two layers of 150 μm thick polypropylene [1]

Fig. 6 Section through a corrugated polypropylene membrane manufactured by double-sided ultrasonic hot embossing [1]

also structured. The two opposite structures have to be precisely aligned to achieve the desired result. An example of double-sided ultrasonic hot embossing is the fabrication of corrugated membranes which are realized by a design of protruding concentric circles on the metal tool and the ultrasonic horn (Fig. 6).

3 Ultrasonic Hot Embossing and Welding of Sealed Structures Channels or grooves produced by ultrasonic hot embossing can subsequently be sealed by ultrasonic welding a lid on top of the embossed structures. Sealed channels are necessary for a number of applications. Among other products, micro T-mixers and ultrasonic whistles were manufactured at KEmikro. Sealing a structure can be achieved by using a welding tool which encloses the structure or by creating energy directors i.e. protruding structures around the grooves or channels during the embossing process. The first method was used for the production of micro T-mixers

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Fig. 7 Polypropylene micro T-mixer and schematic representation of the configuration for welding the lid [2]

(Fig. 7). After the mixing channel is embossed into two layers of polypropylene, a third layer is welded on top of the channel by using an enclosing tool which fits around the outer rim of the channel. Ultrasonic welding results in a seam around the channel where the lid film is welded onto the structure. Two different mixers were produced and tested: A mixer with a smooth channel and a mixer with a channel with diagonal ridges. The resulting mixing of fluids is shown in Fig. 8. Phenolphtalein and NaOH are fed into the T-mixer and flow through the mixer channel. The mixture of these colourless fluids has a bright pink colour which makes the mixed volume visible. In the smooth channel, mixing is incomplete over the whole mixing length of 2.5 cm, whereas the mixer with the ridges achieves complete mixing of the fluids proved by the pink area which covers the whole width of the channel. The second method of sealing embossed structures is the fabrication of energy directors in the polymer around the embossed structure. This method was used for the production of micro whistles for signal generation [4] and multilayered micro channels for a polymer micro counter flow heat exchanger. The production of the micro whistles is illustrated in Fig. 9. First, a pyramidal structure is embossed into films which are then placed on an embossing tool which creates the resonating cavity of the whistle. In the last step a lid film with punched-out holes for the airflow

a)

b)

2,5 cm

Fig. 8 Mixing results for phenolphtalein and NaHO in a T-mixer with a) smooth channel and b) channel with diagonal ridges 50 μm wide [2]

a)

b)

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Fig. 9 Production process of polymer micro whistles by ultrasonic hot embossing and welding

Fig. 10 Two micro whistles with attached silicone bellows for signal production in a keypad [4]

Micro whistles

Silicone bellows

through the whistle is welded on top of the whistle by melting the remaining pyramidal structure around the cavity using a flat tool. Compared to producing whistles by milling, ultrasonic hot embossing is extremely time-saving, taking only about 5 minutes for completing a whistle instead of about 20 minutes. The whistles were developed for a battery-less ultrasonic remote control. Ultrasonic signals, which consist of two frequencies each for unambiguous signal identification, are emitted by pressing down two bellows at once. The prototype created at KEmikro was built into the housing of a numeric keypad of a standard PC keyboard. The signals were emitted by normal typing on the keypad and received with a standard microphone. [4] For the production of multi layered micro channels, energy directors were embossed on top of the walls between the channels (Fig. 11).

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Fig. 11 Section of a channel with surrounding energy directors on top of the channel walls embossed in polyvinyl chloride —100 µm

Fig. 12 Sealed channel manufactured by welding a layer of polyvinyl chloride on top of the structure in Fig. 11 —100 µm

Fig. 13 Photo of a cut through multi layered micro channels

A channel can be sealed by welding an additional film on top (Fig. 12). Also, by using this technique channel structures can be welded on top of each other, creating a multi layered structure (Fig. 13) which can be used for a counter flow heat exchanger. Currently, further work is being done to optimize size and design of the ridges to avoid the flow of molten polymer into the channels which is visible in Figs. 12 and 13.

4 Ultrasonic Hot Embossing of Moulded Interconnect Devices Our investigations show that moulded interconnect devices (MID) can be manufactured by ultrasonic hot embossing, similar to the procedure with conventional hot embossing. It appears to be advantageous that only the part of the polymer which is in mechanical contact to the protruding structures on the tool is heated and the rest of the polymer substrate remains unchanged. A 10 mm long, 700 μm wide,

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and 500 μm high bar was milled into the surface of the tool. In the middle of the bar a 100 μm deep and 500 μm wide chamfer was milled, thus creating a sharp cutting edge, 100 μm in width and 100 μm in height. On an aluminium film, 10 μm in thickness, a liquid thermoplastic resin was spincoated approximately 50 to 80 μm in thickness. The aluminium film was put on the tool with the polymer layer on the upper side (Fig. 14a). A 250 μm thick polypropylene sheet was placed above. Both films were fixed against lateral movement and ultrasonic hot embossing was performed (Fig. 14b). The fabrication of conductor lines with a width of 50 μm was also possible, however with the available milling machine it was not possible to generate cutting edges in this case. Therefore, just a bar was milled with 50 μm width at the top and a chamfer of 30◦ .

Fig. 14 Ultrasonic hot embossing of MID: (a) metal film and thermoplastic substrate are placed between tool and horn, (b) pressure and ultrasonic energy are applied cutting out and welding metal lines, (c) not welded metal is mechanically removed, (d) the desired metal pattern remains on the polymer substrate

Fig. 15 Aluminium conductor line with a width of 500 μm embossed onto polypropylene [5]

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This manufacturing method was used for a transponder with 4 windings and an overall diameter of 2.5 cm (Fig. 16) [5]. The width of the conductor path (Fig. 15) and the distance between two paths of the coil were 250 and 700 μm, respectively. The ends of the coil were soldered to an SMD capacitor with 6.8 μF. The resonance frequency of the transducer was measured to be 2.5 MHz.

5 Tools for Ultrasonic Hot Embossing The moulding tools needed for ultrasonic hot embossing can be manufactured in various ways and from a wide range of materials. The moulding tool has to withstand the embossing force and the temperatures generated during the process. It can be made by wet or dry etching of silicon or glass, from metals by milling or electroplating into a photoresist or even from polymers with a high glass transition temperature. With the exception of the LIGA mould used for the structures shown in Fig. 3, which was manufactured by x-ray lithography and electroplating at Forschungszentrum Karlsruhe, the tools for the products described in this paper were manufactured by milling microstructures into aluminium panels with a thickness of 4 mm. The milling machine used was the KOSY3 manufactured by the Max Computer GmbH, Schömberg-Schwarzenberg, Germany.

6 Process Parameters for Ultrasonic Hot Embossing The parameters with the highest influence on the embossing or welding results are ultrasonic frequency, amplitude, vibration time and compressive force. The frequency is fixed for each ultrasonic machine, all other parameters can be set within

Fig. 16 Transponder with 4 windings moulded with aluminium film by ultrasonic hot embossing [5]

Fig. 17 Embossing depth into polypropylene as a function of welding time and pressure at 4 μm amplitude and 70 kHz [1]

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50 N

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certain limits. For the workpieces described in this paper, a 35 kHz machine with a maximum power of 900 W, a maximal amplitude of 12 μm and a maximal contact force of 745 N was used. The amplitude was set to the maximum value while vibration time and contact force were adjusted to the respective requirements of the workpiece. The influence of vibration time and embossing force on the embossing depth is exemplified in Fig. 17 for embossing a bar with a height and width of 0.5 mm into polypropylene films with a 70 kHz machine. At higher embossing forces, the depth limit is higher and reached after a shorter ultrasonic vibration time than with a lower force. Further ultrasonic time after reaching the depth limit can result in cracking of the polymer and should be avoided. The optimal value for the vibration time is largely dependent on the polymer and the required embossing depth while the optimal value for the embossing force mainly depends on the surface area of the embossing tool. For example, a channel with a length of 14 mm, a height of 300 μm and width of 600 μm as shown in Fig. 2 was embossed into polyvinylchloride (PVC) at a force of 55 N and a vibration time of 330 ms. The same channel was embossed into polyetheretherketone (PEEK) at a force of 50 N and an ultrasonic time of 1 s. An array with 6 parallel channels requires a force of 250 N and an ultrasonic time of 255 ms (PVC) or 700 ms (PEEK) respectively. Finding the right parameters for embossing is an iterative process, starting with values which were found to be appropriate for a similar task.

7 Conclusion Ultrasonic hot embossing is a promising manufacturing method for a wide range of thermoplastic components. It has been shown that channels and projections, open and sealed structures, multi layered structures and MID can be manufactured by ultrasonic hot embossing and welding. The main advantages of ultrasonic hot embossing compared to conventional hot embossing with heated moulds are the low investment costs for the machines (20,000 C as compared to over 100,000 C) and the shorter cycle times (few seconds compared to several minutes) which are due to the fact that heating and cooling times of the mould are omitted.

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References 1. Khuntontong, P.: Fabrication of Polymer Micro Devices by Ultrasonic Hot Embossing, 2008 2. Khuntontong, P.; Blaser, T.; Schomburg, W.K.: Ultrasonic hot embossing of thermoplastic polymers Proceedings of the Polymer Processing Society 24th Annual Meeting ∼ PPS-24 ∼ June 15-19, 2008 Salerno, Italy, II 364. 3. Khuntontong, P.; Blaser, T.; Maas, D.; Schomburg, W.K.: Fabrication of a polymer micro mixer by ultrasonic hot embossing Proc. 19th MicroMechanics Europe Workshop, MME 2008, 28. - 30. September (2008) 259 - 262, ISBN 978-3-00-025529. 4. Gerhardy, C., Burlage, K., Schomburg, W.K.: Coded ultrasonic remote control without batteries JMM 19 (2009) 074002. 5. Khuntontong, P.; Blaser, T.; Schomburg, W.K.: Fabrication of Molded Interconnection Devices by Ultrasonic Hot Embossing on Thin Polymer Films IEEE Transactions on Electronics Packaging Manufacturing 32 (2009) 152 – 156.

On Binary Topology Design of Electro-Thermally-Compliant MEMS Pranay Sharma and Anupam Saxena

Abstract We demonstrate a method for topology design of Electro- ThermallyCompliant Micro- Electro- Mechanical Systems (MEMS). The method ensures well connected perfectly binary solutions for which only nominal post processing is needed. The Adaptive Material Mask Overlay (AMOM) topology design algorithm is stochastic and is based on the very principle used to fabricate micro- devices and IC circuits. The method employs negative circular masks that act as local material sinks. The center coordinates, radii and the number of masks are all systematically determined to obtain the final topologies for a given computational effort. Three examples, presented elsewhere, are re- solved using the proposed scheme and the solutions are compared with those obtained using the classical gradient based methods. The proposed method shows promise in yielding multiple and large deformation solutions. Keywords MEMS · AMOM · Topology design · ETC micro mechanisms

1 Introduction Microactuation in a Micro- Electro- Mechanical- System (MEMS) can be a result of either electrostatic or electro- thermal transduction. In an electrostatic microactuator, the change in capacitance between two charged parallel plates causes a variation in the distance between them. Alternatively, Electro- Thermally Compliant MEMS (or ETC MEMS) are designed such that an applied voltage produces a non-uniform current density throughout the continuum. This results in differential Joule heating further resulting in some parts of the continuum to expand more than others. If the structure is mechanically constrained, this deformation can be used for actuation. Thus, proper selection of the continuum topology becomes essential to obtain the desired actuation.

P. Sharma (B) Indian Institute of Technology, Kanpur, UP 208016, India e-mail: [email protected]

G.K. Ananthasuresh et al. (eds.), Micromechanics and Microactuators, Mechanisms and Machine Science 2, DOI 10.1007/978-94-007-2721-2_12, C Springer Science+Business Media B.V. 2012

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An ETC micro- actuator can be fabricated indistinguishable with the microsystem unlike other actuation systems requiring special materials such as piezoelectric, electro-active etc. With different topology, shape, voltage, thermal and mechanical boundary conditions, material and selective doping, a wide variety of motions and configurations can be developed. Here, we present a method to design Electro- Thermally- Compliant topologies which are perfectly binary and devoid of continuum singularities so that solution interpretations can be avoided and the latter can be directly fabricated.

1.1 Problem Formulation We design the ETC MEMS continua for desired deflection and strength. These micro- mechanisms may fail because of local temperatures exceeding the melting point or local stresses exceeding the allowable limit. The optimization problem in standard form is posed as Maximize: Desired output displacement Subjected to 1. inequality constraints: a. Local stresses, b. Local temperatures and c. Material resources, and 2. equality constraints which are the equilibrium equations pertaining to voltage, temperature and displacement fields. Consider Fig. 1. V is the applied voltage between regions eE which are also mechanically secured. The output displacement is desired to be maximized along vector n. The governing differential equation for voltage boundary value problem is given by ∂ ∂v ∂v ∂ kc + kc = 0 in ∂x ∂x ∂y ∂y v = vc

Fig. 1 A typical design domain of an ETC microactuator

in eE

(1)

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ν is the electric potential field in the domain, kc is the electrical conductivity and ν c is the voltage difference imposed across the boundary eE . The temperature distribution is obtained by solving ∂ ∂ ∂T ∂T kt + kt + Q − Qc = 0 in ∂x ∂x ∂y ∂y Q = kc T = Te

in eT ;

∂v ∂x

−kt

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∂T = hi (T − T∞ ) ∂n

Qc = h0 (T − T∞ ) /t

in nT

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T: temperature; Qc : heat convected out-of-plane/volume; kt : thermal conductivity; Q: volumetric heat generation rate; Te : specified temperature on eT ; n: unit normal to nT ; t: thickness; hi and h0 : in-plane and out-of plane convective heat transfer coefficients; T∞ is the ambient temperature. Finally, the elastic boundary value problem is given by ∇ · σ = 0 in σ = E (ε − α (T − T0 ) · I) ε = 1/2 ∇u + ∇uT u = ue σ n = fM

in

in

(3)

in eM in eM

σ , ε, I and E: stress, strain, identity and elastic tensors respectively; α: coefficient of linear thermal expansion; T0 : initial temperature; u: displacement field; ue : specified displacement boundary condition, and fM : surface traction.

1.2 Prior Work on ETC Mechanism Topology Design Silicon-based micro- actuators have received significant attention as their fabrication methods are similar to those used for the integrated circuits. Parallel plate, comb-drive and scratch drive electrostatic micro- actuators have been used widely [1]. Using laminates of materials with different expansion coefficients, out-of-plane bimorph micro actuation can be accomplished [2]. The simplest shape of a Guckle

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heatuator [3] is used as ETC building blocks to design more involved micro- actuators [4]. Mankame and Ananthasuresh [5] emphasize detailed thermal modeling for ETC micro- actuators taking convection and radiation into account. A bend-beam electro-thermal actuator is suggested by Que et al [6] to generate rectilinear displacements and forces using cascaded devices. These actuators have been employed to generate rotary and long- throw rectilinear displacements in linear and rotary micro- engines [7]. Within systematic design procedures, Yin and Ananthasuresh [8] formulate the ETC micro- actuator design problem with a single objective of maximizing output deflection subjected to electrical, thermal and elasticity equilibrium equations. The formulation uses the PEAK material assignment function and can be applied to ETC micro-actuator design with multiple materials. The pioneering work by Bendsoe and Kikuchi [9] has led to the development of many gradient [10-13] and function based topology optimization techniques. In classical gradient based methods, every element of the discretized continuum is assigned a material density variable xi . xi can vary from ε to 1, ε ∼ 0.001, say and 1 represents a solid element. The properties of that element, e.g., kc , kt , α and E (all defined in section 1.1) are modeled as functions of xi as: { kc kt α E}a = f (xi ) { kc kt α E}s . The subscripts ‘a’ and ‘s’ represent an arbitrary and a solid element respectively. f (xi ) is a material assignment function. Saxena and Saxena [14] investigated three continuous functions for f (xi ), namely Solid Isotropic Material with Penalization (SIMP) [15], PEAK [16] and SIGMOID [17]. The SIMP function is given by: f (xi ) = (xi )η . Here, η is the penalization exponent. A higher value of η (≥ 5 or more) tends to yield binary but disconnected solutions. A moderate value (η∼3-4) results in properly connected but gray solutions. The PEAK function is given by:

− (xi − 1)2 f (xi ) = exp . 2σ 2 This function encourages binary solutions when the standard deviation σ is reduced gradually during optimization [8]. However, for very small values of σ , obtained solutions are binary but disconnected. For the SIGMOID function 1 exp −γ (p − xi ) ε ≤ xi ≤ p 2 1 1 − exp γ (p − xi ) p ≤ xi ≤ 1 2

f (xi ) =

Saxena and Saxena [14] employ two parameters, p (the threshold) and γ (measure of steepness of the SIGMOID function near xi = p). They recommend that γ should be

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large (∼100) and p should be very small (∼0.1). The SIGMOID function favors full material assignment even if the cell density xi is only slightly larger than the threshold which itself is negligible. Still none of the abovementioned functions ensures a perfectly binary solution and gray/disconnected cells do appear in the synthesized topologies. A function based methodology called Material Mask Overlay Strategy [18] is proposed which gives perfectly binary solutions devoid of any gray regions. The method is based on the concept similar to the photolithographic fabrication technique popularly used to design IC circuits and MEMS themselves. Circular masks are placed over the domain. These masks act as material sinks removing the material beneath them. Thus, voids of various shapes can be obtained by varying the positions and sizes of these masks. The center coordinates of the masks and their radii constitute the design variables in the solution vector. A genetic algorithm, that uses a large number of candidate solutions, is employed. This method is observed to be cumbersome owing to its large population size. An Improved Material Mask Overlay Strategy (IMMOS [19]) uses the Random Mutation Hill Climber (RMHC) that employs very few candidate solutions and does not keep the number of masks constant. Instead, the number of masks is increased after every sub- search is accomplished. Due to a number of sub- searches involved, and due to consistent increase in the number of masks, the overall search becomes temporally and computationally expensive. An Adaptive Material Mask Overlay Method (AMOM [20]) overcomes this drawback by judiciously varying the number of masks after every iteration. The number of masks may increase or decrease. All Material Mask Overlay Methods employ hexagonal cells/finite elements as opposed to rectangular four- node ones. This is because use of rectangular cells often results in checkerboard patterns and point flexures. Regions occupied by checkerboard patterns are associated with high artificial stiffness while point flexures are local hinges with no strain energy. Use of high order elements [21] is partially helpful in removing checkerboard patterns. Direct use of filtering techniques [22] to suppress connectivity singularities has been extensively studied. While checkerboard patterns can be removed completely, point connections can still prevail. The root cause behind both these singularities is geometric as rectangular parameterization permits single node connections between neighboring filled cells. Hexagonal parameterization ensures edge connectivity between any two adjacent cells [23]. Thus both anomalies, checkerboard patterns and point connections, get eliminated inherently. Furthermore, a hexagonal cell can be discretised into two four- noded bilinear elements, the analysis procedure for which is well known. Previously, AMOM has been used to synthesize small deformation monolithic compliant mechanisms with mechanical actuation. Use of mask shapes other than circular has also been investigated [24]. This work applies AMOM to realize binary topologies of Electro- Thermally Compliant MEMS devices. Working of the AMOM is briefly discussed next.

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2 Adaptive Material Mask Overlay Method (AMOM) AMOM is a hill climber search based method that yields perfectly binary and well connected multiple topologies. Negative circular masks are placed over the domain and their sizes and positions are mutated stochastically. Also, their quantity is varied judiciously, which is a significant improvement over MMOS [18] and IMMOS [19]. This process is continued till the permitted number of iterations/generations is exhausted. A general solution vector is given by: {xi , yi , ri . . .}

i = 1 to N

where N is the number of masks in the domain. We start by specifying the maximum number of function evaluations, thus imposing a limit on the applied computational effort. An initial number of masks is also specified. These equally sized negative circular masks are placed uniformly over the domain. This is followed by four mutation schemes explained below and shown pictorially in Fig. 2.

2.1 First Mutation Scheme Each design variable in the solution vector is assigned a random number, say R. If for any design variable, R isless than Rallowed (≈ 0.08), the variable undergoes a Gaussian mutation given by ± exp (a + rb) (u − l). Here, a and b are pre-specified numbers, −8 and 9 respectively, r is a random number while u and l are upper and lower bounds respectively, on the value of the design variable under consideration. Such a mutation scheme permits both small and large mutations about the current value. Fitness of the new solution is evaluated and if found better than its previous value, the solution vector is updated. Otherwise, the old solution is retained.

2.2 Second Mutation Scheme A random number R is assigned to each mask, as opposed to each design variable. If for a mask, R is less than Rallowed , then all its parameters, namely the abscissa and ordinate of its centre, and its radius are altered using Gaussian mutation. Again, if on analysis, the mutated solution is found to be fitter than the previous one, the solution vector is updated.

2.3 Third Mutation Scheme As in the second mutation type, a random number R is assigned to each mask. But this time, the value of Rallowed is increased (≈ 0.2). As a result, more masks are expected to satisfy the criterion of R < Rallowed . All parameters of these masks mutate marginally by the circumscribing radius of the hexagonal cell. If an improvement in the fitness value is noticed, then the solution vector is updated.

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(c)

(f)

(d)

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Fig. 2 (a) Initially, equal sized masks are placed uniformly over the domain. All mutated masks in latter figures are shaded in blue. (b) First mutation scheme: Random design variables are selected and made to undergo Gaussian mutation. (c) Second mutation scheme: Random masks are chosen and all their parameters (x, y, and r) are altered (d) Third mutation scheme: More random masks, shown as dotted, are selected and slightly mutated. (e) One new mask is precisely laid over a set of chosen masks (here, three; the new masks are shown in blue). (f) Fourth mutation scheme: Positions of new masks are marginally altered. (g) Redundant masks (shown dotted and dashed) are removed

2.4 Fourth Mutation Scheme The first three mutation schemes are such that they encompass nearly all possible ways in which the masks can be mutated. However, by this time, the number of masks does not change. In the fourth mutation type, m new masks (m ≤ 10) are introduced into the system without affecting the prevailing topology. There are two ways to achieve this. One method involves placement of these masks outside the domain. But this may result in expenditure of a significant amount of computational effort before these additional masks enter the domain and start affecting the topology. Another method involves random selection of m masks from the current set and placing a new mask over each of these masks. The positions and sizes of the new masks are altered

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marginally and stochastically via the circumscribing radius of the hexagonal cell. The fitness associated with the new solution is compared to its previous value and the solution vector is updated accordingly. Masks are now checked for redundancy. All those masks that are completely enclosed within some other mask are identified and deleted. This is because they do not contribute in topology design as masks enclosing these have already removed the material. Secondly, a few masks may exactly overlap some other masks. A few of these overlapping masks are stochastically chosen and deleted. Thirdly, there may exist a mask that does not contribute in material removal. This is because the cells enclosed within it lose material due to the masks processed prior to this mask. Such masks are also rendered redundant and flagged for deletion. This feature of intelligent mask deletion makes AMOM computationally advantageous over its predecessors.

3 Preprocessing Before any candidate solution suggested by AMOM is analyzed, it undergoes the following pre- processing steps. As mentioned previously, hexagonal cells prevent the existence of checkerboards and point flexures in a topology. However, the continuum has V-notches at its inner and outer contour boundaries. Such regions act as zones of stress concentration and can be particularly harmful in case of multi- axial and/or cyclic loading. To overcome this drawback, the inner and outer boundaries are made to undergo boundary smoothening. First, the edges of all hexagonal cells constituting an inner/outer boundary are identified and their mid points are connected by line segments. Next, all the nodes at the boundary are recognized and are shifted to lie on the nearest line segment. This shifting is along the perpendicular to the line segment to ensure minimum nodal movement. The notch angle thus increases delivering a smoother boundary. The process may be repeated to moderate the notch- effect more. Other preprocessing steps are essential for two reasons, (i) to save computational effort and (ii) to ensure that that candidate continuum is well connected. First, the void cells in a candidate solution are temporarily eliminated. This reduces the mesh size during finite element analysis. The nodes and elements are renumbered and the boundary conditions are updated appropriately. Next, the candidate design undergoes a series of checks. The first two conditions for the design to be rejected via penalization are: (i) At least one of the input nodes has been eclipsed by a mask and thus eliminated. (ii) The output port has been eliminated by some other mask. Another criterion for an intermediate design to be rejected via penalization is that there exists no node in the continuum that is fixed. This allows rigid body translation or rotation of the structure. In case of electro- thermally compliant MEMS, along with the presence of at least one fixed node, it is also ensured that there exists at least one node that is connected to the positive terminal and one that is linked to the negative terminal of the electric supply. This is to ensure that there always exists a potential difference across the continuum causing the flow of electrical current.

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Further, Cholesky decomposition [25] is performed to check if the global finite element stiffness matrix is non- singular. If it is found that the matrix is not positive definite, the input, output and fixed nodes are disconnected and the design is again rejected by penalization. Finally, there may exist some regions in the domain that are not connected to the primary topology. Such dangling regions are identified by noting that they do not include the output port, and are then deleted followed by renumbering of nodes and elements.

4 Synthesis of Electro- Thermally Compliant MEMS Previously, Saxena and Saxena [14] employed classical gradient based optimization methods, using SIMP, PEAK and SIGMOID material functions, with local stress and temperature constraints, to generate optimal topologies for three examples: (i) a simple ETC actuator, (ii) Guckle micro- actuator and (iii) an ETC microgripper. Here, AMOM is employed to solve the same examples for comparison and contrast. For all examples, the following material properties for polysilicon are considered: electrical conductivity (kc ) = 500 mho/m; thermal conductivity (kt ) = 150W/ (m.K); coefficient of thermal expansion (α) = 2.5 × 10−6 /K; Elastic modulus (E) = 169 GPa; Poisson’s ratio (v) = 0.22. For SIMP and SIGMOID, both the out of plane convection coefficient (h0 ) and in-plane convection coefficient (hi ) are taken as 250 W/m2 K. For AMOM, while the in-plane convection has been neglected, the out of plane convection coefficient (h0 ) is considered to be 50 W/m2 K. The maximum allowable stress in any cell is taken as 250 MPa and the temperature is limited to a maximum of 900 K. Finally, at every node that is partially or completely mechanically constrained, a thermal boundary condition of 300 K is assigned.

4.1 Simple ETC Actuator The design domain and boundary conditions for its symmetric half are shown in Fig. 3. The symmetric upper half has overall dimensions of 3 mm × 1 mm.

Desired direction of output displacement

Fig. 3 Design domain of simple ETC actuator

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(a)

(b)

(c)

(d)

Fig. 4 (a) Topology obtained using AMOM (b) Deformation magnified 100 times (c) Temperature profile, (d) Von Mises Stress profile

A voltage of 30 V is supplied across the ends. Figure 4 (a) illustrates how a group of 100 masks (dashed circles) identifies an optimal topology after 10000 function evaluations. The output deformation obtained is 2.23 μm which is depicted in Fig. 4 (b). The solid black topology depicts the preprocessed undeformed state and the red topology shows the deformation due to expansion caused by the applied potential difference. The maximum temperature observed is 674.8 K (Fig. 4c) while the maximum von Mises stress is 202.7 MPa (Fig. 4d). The solution in Fig. 4 is compared with those obtained using the SIMP and SIGMOID gradient based models. Both solutions in Fig. 5 (a) and (b) are obtained using a voltage drop of 20 V. An output deformation of 3.9 μm is obtained for the SIMP solution with the maximum temperature as 797 K and maximum stress as 250 MPa, the limiting value. For the SIGMOID solution, maximum temperature of 578.4 K and maximum stress of 123.4 MPa are observed.

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(b)

Fig. 5 Optimal solutions for ETC actuator using gradient based methods (Saxena and Saxena [14]) (a) using SIMP material model, (b) using SIGMOID material model

4.2 Guckle Micro-Actuator Guckle micro- actuator is studied as the second example. The design domain has dimensions of approximately 3 mm × 0.4 mm. A potential drop of 30 V is provided while using AMOM. The number of function evaluations used is about 10,000. In Fig. 7 (a), a relatively thinner upper member is observed. This results in more electrical resistance in the upper part of the actuator compared to the lower part. Consequently, there is more thermal expansion in this part resulting in the desired downward displacement. The deformation obtained is 3.60 μm. The highest temperature recorded is 625.4785 K and maximum stress is much below the allowable limit at 175.4 MPa. Figure 8 (a) shows the optimal topology with SIMP and its deformed state when 50 V is supplied to the continuum. The output displacement is 3.26 μm and the maximum temperature and stress in the actuator are 608 K and 151 MPa respectively. For the same potential, the SIGMOID solution is shown in Fig. 8 (b). An output displacement of 3.6 μm is achieved. A maximum temperature of 583.87 K and maximum stress of 152.1 MPa are observed in the continuum.

Desired direction of output displacement

Fig. 6 Design domain of the Guckle micro-actuator

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Fig. 7 (a) Resultant topology of the Guckle heatuator with masks (dashed circles) (b) Preprocessed solution with deformation magnified 100 times (c) Temperature profile (d) Stress profile

(a)

(b) Fig. 8 (a) Resultant topology of the Guckle heatuator with SIMP and (b) with SIGMOID material functions (Saxena and Saxena [14])

On Binary Topology Design of Electro-Thermally-Compliant MEMS Fig. 9 Design domain of ETC micro-gripper

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Desired direction of output displacement

4.3 ETC Microgripper The last example is of an electro- thermally- compliant micro- gripper. Its symmetric half has a design domain of 3 mm × 1 mm. A potential drop of 30 V is supplied. Figure 10 (a) illustrates the optimal topology obtained after 7000 function evaluations. A deformation of 3.73 μm is

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Fig. 10 (a) Optimal topology with circular masks, (b) Output deformation magnified 100 times (c) Temperature profile, (d) Stress profile

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Fig. 11 (a) SIMP generated optimal topology, (b) that obtained with the SIGMOID function functions (Saxena and Saxena [14])

obtained while the maximum temperature and stress are 670.2 K and 204.4 MPa respectively. The SIMP material model (Fig. 11a) when used with a voltage value of 30 V delivers an output deformation of 22 μm. The maximum temperature is 806.26 K which is notably higher as compared to previous cases, but well within the upper limit. Maximum stress is 248.3 MPa that is also considerably high but within limits. For the solution with the SIGMOID material function, a small output displacement of 1.9 μm is achieved. The temperature (1235.22 K) and stress (372 MPa) in this case exceed the limiting values.

5 Discussion and Closure Here, we illustrate the use of Adaptive Material Mask Overlay Method to design well- connected, singularity- free binary topologies for Electro- ThermallyCompliant MEMS. The solutions obtained using classical gradient based searches are shown to contain ficticious gray cells that require material interpretation. Further, the altered solutions may behave quantitatively differently compared to the respective optimal solutions, both in terms of the displacement objective and failure constraints. With binary topologies obtained using AMOM, true solution evaluations are performed and fabricated devices are expected to deliver deformations close to those predicted. A disadvantage, however, is the comparitively large computational effort required by AMOM. Future efforts will focus on developing better stochastic methods that yield singularity- free honest solutions more efficiently.

References 1. Jaecklin, V. P., Linder, C., de Rooij, N. F., and Moret, J. M., 1992, “Micromechanical Comb Actuators With Low Driving Voltage”, J. Micromech. Microeng., 2, pp. 250–255. 2. Chu, W. H., and Mehregany, M., 1994, “Microfabricated Tweezers With a Large Gripping Force and a Large Range of Motion”, Technical Digest, IEEE Solid-State Sensors and Actuator Workshop, Hilton Head, SC, Jun., pp. 107–110.

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3. Guckle, H., Klein, J., Christenson, T., Skrobis, K., Laudon, M., and Lowell, E.G., 1992, “Thermomagnetic Metal Flexure Actuators”, Technical Digest, Solid-State Sensor and ActuatorWorkshop, Hilton Head Island, SC, pp. 73–76. 4. Moulton, T., and Ananthasuresh, G. K., 2001, “Micromechanical Devices With Embedded Electro-Thermal-Compliant Actuation”, Sens. Actuators, A, 90, pp. 38–48. 5. Mankame, N. D., and Ananthasuresh, G. K., 2000, “Effect of Thermal Boundary Conditions and Scale on the Behaviour of Electro-Thermal-Compliant Micromechanisms”, Proceedings of Modeling and Simulation of Microsystems MSM2000, San Diego, CA, pp. 609–612. 6. Que, L., Park, J. S., and Gianchandani, Y. B., 2001, “Bent-Beam Electrothermal ActuatorsPart I: Single Beam and Cascades Devices”, J. Microelectromech. Syst., 10_2_, pp. 247–254. 7. Park, J. S., Chu, L. L., Oliver, A. D., and Gianchandani, Y. B., 2001, “Bent-Beam Electrothermal Actuators-Part II: Linear and Rotary Microengines”, J. Microelectromech. Syst., pp. 255–262. 8. Yin, L., and Ananthasuresh, G. K., 2002, “A Novel Topology Design Scheme for the Multi-Physics Problems of Electro-Thermally Actuated Compliant Micromechanisms”, Sens. Actuators, A, 97–98, pp. 599–609. 9. Bendsøe and Kikuchi, 1998, “Generating optimal topologies in structural design using a homogenization method”, Computer Methods in Applied Mechanics and Engineering, 71 (2), pp. 197 – 224. 10. Du, Y., Chen, L., Tian, Q., and Wu, Z., 2009, “Topology synthesis of thermomechanical compliant mechanisms with geometrical nonlinearities using meshless method”, Advances in Engineering Software, Volume 40, Issue 5, May 2009. 11. Tcherniak, D., “Topology optimization of resonating structures using SIMP method,” International Journal for Numerical Methods in Engineering, Volume 54, Issue 11, pages 1605–1622, 20 August 2002. 12. Yulin, M., Xiaoming, W., “A level set method for structural topology optimization and its applications”, Advances in Engineering Software, v.35 n.7, p.415-441, July 2004. 13. Luo, Z. and Tong, L.Y., 2008, “A level set method for shape and topology optimization of large-displacement compliant mechanisms”, International Journal for Numerical Methods in Engineering. v76. 862-892. 14. Saxena, R. and Saxena, A., 2007, “Design of Electrothermally Compliant MEMS With Hexagonal Cells Using Local Temperature and Stress Constraints”, ASME Journal of Mechanical Design, April 2009, Volume 131. 15. Bendsøe, M. P., 1995, “Optimization of Structural topology, shape and material”, Springer, Berlin. 16. Yin, L. and Ananthasuresh, G. K., 2001, “Topology Optimization of Compliant Mechanisms with Multiple Materials using a Peak function Material Interpolation Scheme”, Structural and Multidisciplinary Optimization, 23, pp 49–62. 17. Saxena, R. and Saxena, A., 2007, “On honeycomb representation and SIGMOID material assignment in optimal topology synthesis of compliant mechanisms”, Finite Elem. Anal. Des. (2007), Volume 43, Issue 14, 1082-1098. 18. Saxena A., 2009, “A Material-Mask Overlay Strategy for Continuum Topology Optimization of Compliant Mechanisms using Honeycomb Discretization”, ASME Journal of Mechanism Design, 130 (8), DOI:10.1115/1.2936891. 19. Jain, C., and Saxena, A., 2009, “An improved material-mask overlay strategy for topology optimization of structures and compliant mechanisms”, ASME Journal of Mechanical Design. 20. Saxena, A., 2010, “On an Adaptive Mask Overlay Topology Synthesis Method”, ASME Design Engineering Technical conferences, Aug 15th- Aug 18th, 2010, Montréal, CA, IDETC-2010/29113. 21. Diaz, A., and Sigmund, O., 1995, “Checkerboard patterns in Layout Optimization”, Structural Optimization, 10, pp 40-45. 22. Sigmund, O, 2007, “Morphology-based black and white filters for topology optimization”, Structural and Multidisciplinary Optimization, 33, 401-424.

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23. Saxena, R. and Saxena, A., 2003b, "On Honeycomb Parameterization for Topology Optimization of Compliant Mechanisms”, ASME Design Engineering Technical Conferences, Design Automation Conference, Chicago, IL, Sep. 2-Sept. 6, 2003, paper #. DETC2002/DAC48806. 24. Sharma, P., and Saxena, A., 2010, “On Evaluation of Adaptive Mask Overlay Topology Synthesis Method using Different Mask Shapes”, ASME Design Engineering Technical conferences, Aug 15th- Aug 18th, 2010, Montréal, CA, IDETC-2010/29113. 25. Kreyszig, Erwin, 1999, “Advanced Engineering Mathematics”, 8th Ed., Wiley.

Author Index

A Ananthasuresh, G. K., 61–70, 128

L Lovasz, E. Ch., 101–110

B Becker, F., 1–9 Bhargav, D. B. S., 61–70 Burlage, K., 113–122

M Minchenya, V., 1–9

C Corves, B., 49–60 D Dehelean, L. M., 101–110 Dehelean, N. M., 101–110 Diez, M., 85–98 G Gerhardy, C., 113–122 H Hayashi, T., 11–22 Hernández, A., 85–98 Horie, M., 31–39 Hoshikawa, Y., 31–39 I Ishimori, S., 11–22 Ito, T., 11–22 Ivanov, I., 49–60 K Kamiya, D., 31–39 Kito, Y., 11–22

N Nakazato, Y., 23–29 P Petuya, V., 85–98 Phunopas, A., 11–22 S Saxena, A., 125–138 Sharma, P., 125–138 Schomburg, W. K., 113–122 Sonobe, Y., 23–29 T Terada, H., 73–84 Toyama, S., 23–29 U Urizar, M., 85–98 Y Yamagata, T., 73–84 Z Zeidis, I., 1–9 Zentner, L., 41–47 Zimmermann, K., 1–9

G.K. Ananthasuresh et al. (eds.), Micromechanics and Microactuators, Mechanisms and Machine Science 2, DOI 10.1007/978-94-007-2721-2, C Springer Science+Business Media B.V. 2012

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Subject Index

A AMOM, 129–135, 138 B Bimorph actuator, 74–78, 81 Blood vessel, 23–24, 26–29 C Capsule, 11–22, 108 Cell-manipulation, 62, 68 Changing the shape and dimension of the links, 36 Cochlear implant, 41–47 Compliant mechanism, 41–47, 61–70, 129 Conducting polymer, 73–84 E Elastodynamic locomotion, 1 ETC micro mechanisms, 126, 128, 133, 136–138

K Kinematics, 49–51, 54, 56, 85–98, 104–105

M Magnetic force, 12–14, 17–20 Mathematical modelling, 73 Matrix, 45, 53, 101–110, 133 MEMS, 125–138 Micromechanism, 11–22 Micro robot, 1–9, 63 Miniature gripper, 62, 67

O Optimum design, 31–39

H Hydraulic device, 41–47 Hydraulic pressure, 23–29

P Pad, 101–110, 118 Parallel manipulators, 49–60 Peristalsis motion, 23–29 Piezoelectric actuator, 1, 9 Polymer microstructures, 114 Polypyrrole, 74–78, 80 Positioning, 37–38, 49–50, 61, 63, 67, 74, 78–83, 114 Pressure sensor, 102, 106–107 Proteins, 85–98 PWM control, 78

I Injection molding pantograph mechanism, 31–39 In-pipe robot, 23–29 Intracytoplasmic injection, 61–70

R Recognition, 101–104, 107 Reduction of joint forces, 32 Remote-haptics, 68

F Friction force, 5, 11–14, 16, 18–19 Flexure hinge-based parallel manipulators, 49–60 Flexure hinges, 49–60

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144 S Scale effect, 23–24

T Topology design, 125–138 Transducer, 3, 101–110, 121

Subject Index U Ultrasonic hot embossing, 113–122 welding, 113–114, 116–117 V Vibration of continua, 1