Microrobotics for Micromanipulation E-Book

• Herausgeber: John Wiley & Sons
• Kategorie: Wissenschaft und neue Technologien
• Sprache: Englisch

Seitenzahl: 642

Veröffentlichungsjahr: 2013

Beschreibung

Microrobotics is an emerging and booming area with many and various applications, including in fields such as industrial/manufacturing robotics, medical robotics, and laboratory instrumentation. Microrobotics for Micromanipulation presents for the first time, in detail, a treatment of the field of robotics dedicated to handling objects of micrometer dimensions. At these dimensions, the behavior of objects is significantly different from the better known, larger scales, which leads to implementation techniques that can be radically different from the more commonly used solutions. This book details the behaviors of objects at the micrometer scale and provides robotics solutions that are suitable, in terms of actuators, grippers, manipulators, environmental perception, and microtechnology. Worked examples are included in the book - enabling engineers, students and researchers to familiarize themselves with this emerging area and to contribute to its development.

Leseprobe

Table of Contents

Foreword

Introduction

Chapter 1. The Physics of the Microworld

1.1. Introduction

1.2. Details of the microworld

1.3. Surface forces

1.4. Contact forces

1.5. Experimental analysis of forces for micromanipulation

1.6. Forces in liquid media

1.7. Friction and roughness

1.8. Relevant parameters and indicators

1.9. Exercises

1.10. List of symbols

Chapter 2. Actuators for Microrobotics

2.1. Introduction

2.2. Principles of motion and guiding

2.3. Classification of actuators

2.4. Piezoelectric actuators

2.5. Electrostatic actuators

2.6. Thermal actuators

2.7. Electro-active polymers

2.8. Magneto-/electrorheological fluids

2.9. Summary

2.10. Suppliers of active materials

2.11. Exercises

Chapter 3. Microhandling and Micromanipulation Strategies

3.1. Introduction

3.2. Contact-free micromanipulation and positioning

3.3. Contact-based micromanipulation and positioning

3.4. Release strategies

3.5. Summary

3.6. Conclusion

3.7. Exercises

Chapter 4. Architecture of a Micromanipulation Station

4.1. Introduction

4.2. Kimenatics

4.3. Visual perception

4.4. Force sensing

4.5. Introduction to sensor-based linear multivariable control

4.6. Application to automation and remote operation for micromanipulation tasks

4.7. Environmental control

4.8. Applications

4.9. Conclusion

4.10. Exercises

Chapter 5. Microtechnologies and Micromanipulation

5.1. Silicon surface machining processes

5.2. Early demonstrators

5.3. Standard processes and fabrication examples

5.4. Alternative surface machining processes

5.5. Co-integration with electronics

5.6. Consistency of surface micromachining

5.7. Conclusion

Chapter 6. Future Prospects

6.1. Micromachining

6.2. Nanomanipulation

Chapter 7. Solutions to Exercises

7.1. Chapter 1

7.2. Chapter 2

7.3. Chapter 3

7.4. Chapter 4

Bibliography

List of Authors

Index

First published 2010 in Great Britain and the United States by ISTE Ltd and John Wiley & Sons, Inc. Adapted and updated from La microrobotique: applications à la micromanipulation published 2008 in France by Hermes Science/Lavoisier © LAVOISIER 2008

Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act 1988, this publication may only be reproduced, stored or transmitted, in any form or by any means, with the prior permission in writing of the publishers, or in the case of reprographic reproduction in accordance with the terms and licenses issued by the CLA. Enquiries concerning reproduction outside these terms should be sent to the publishers at the undermentioned address:

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The rights of Nicolas Chaillet and Stéphane Régnier to be identified as the authors of this work have been asserted by them in accordance with the Copyright, Designs and Patents Act 1988.

Library of Congress Cataloging-in-Publication Data

Microrobotique. English

Microrobotics for micromanipulation/edited by Nicolas Chaillet, Stéphane Régnier.

p. cm.

Includes bibliographical references and index.

ISBN 978-1-84821-186-5

I. Microrobots. 2. Manipulators (Mechanism) 3. Microelectromechanical systems. I. Chaillet, Nicolas. II. Régnier, Stéphane. III. Title.

TJ211.36.M5313 2010

629.8′933--dc22

2010006763

British Library Cataloguing-in-Publication Data

A CIP record for this book is available from the British Library

ISBN 978-1-84821-186-5

Foreword

Robotics, as established over the last 40 years, has relied on the idea that imitation of manual actions by humans is the best strategy for creating manipulators able to replace the work of humans for highly repetitive tasks in the manufacturing industry. Subsequently, with the advent of mobile robots, it was human and animal locomotion that inspired researchers. Almost anything conceived by nature has been copied in robots, from jumping robots to eel-like robots and robotic coloscopes imitating caterpillars.

As the dimensions of these robots decrease, adhesive problems come to dominate over problems related strictly to mobility. Here again, bio-inspired approaches have flourished. Again, in the context of the exploration of the gastrointestinal tract, for recent endoscopic video capsules ingested by the patient, the challenge has been to understand sliding effects in order to control its movement, or to temporarily attach it to a wall in order to perform a biopsy. Various types of interface have been designed for controlling adhesive effects, based on biomimetic models. One example is the hierarchical lattices of micro- and nanofibers – inspired by those found on the feet of geckos – which exploit van der Waals type forces. Another is that of microfiber lattices covered with a hydrophobic liquid – the secretion of which is triggered by the pressure of a foot resting on the ground, as observed in crickets and cockroaches – an effect that relies on capillary forces. These two examples illustrate the continuity between robotics in the macroworld, whose theoretical and technological underpinnings are well understood in most ways, and robotics in the microworld, where the first steps are only just being taken.

This book reveals the complexities inherent in microrobotics compared to the more familiar macrorobotics. The first difference is the complexity of the theory of the physics of the microworld compared to the macroworld: in the macroworld, gravity and inertial forces behave in a relatively simple manner; the underlying models are within the grasp of any user with a Master’s level university education in mechanics or robotics. In the microworld, on the other hand, the surface forces and contact forces that hold sway require a much more sophisticated understanding of physics – in particular electrostatics, thermodynamics, fluid physics, material science, etc. The behavioral laws for fluids, models of friction and roughness must be translated to these small scales. The sorts of effects seen on this scale cannot be reduced to analytical equations whose coefficients are “easily” identifiable physical parameters. The models used introduce empirical or experimental constants that are difficult to quantify, and depend on the materials involved in the interaction, their shapes, and their environment.

The next difference is in terms of experiments: the measured forces may be tens of nano-Newtons; motion can range from microns to millimeters, with resolutions between 0.1 µm and 25 µm and as small as a microradian in orientation. Under these sorts of constraints, environmental conditions play a strong role. For example, a change in temperature of just 5° leads to an expansion of 15 µm in a 100 mm aluminum rod. Humidity also has a strong effect on these interaction forces. It is thus clear that microrobot design, and that of the associated support structures (from working stations up to microfactories), is a whole new field of research beyond conventional robotics, and one that considerably borrows from microelectronics and microsystems.

The final difference is in the nature and diversity of applications for micromanipulation: these can range from the assembly of mechanical, electronic or optical components for products in everyday use, which are being increasingly miniaturized, to the exploration of the living world through the design of micro-instruments, microprobes, microsensors, etc. for diagnostics, monitoring, therapy, surgery, manipulation of cells in their natural environment, and so on. Microrobotics also contributes to the expansion of scientific and technological frontiers by contributing to the development and characterization of novel actuators, materials and processes. Whatever the objectives, it is clear that between the specified need and the integration of a microrobotic solution, a multidisciplinary approach encapsulating a broad spectrum of skills will be called for.

Microrobotics for Micromanipulation is an ambitious work offering a thorough overview of the field and a detailed discussion of specific problems. It reveals a whole new world, along with its limitations, achievements and future prospects, over the course of a thorough state of the art that includes well over 350 references. The theoretical underpinnings are illustrated with real experiments on platforms such as those developed at the ISIR/SI, Paris (formerly LRP) and the FEMTO-ST AS2M, Besançon (formerly LAB). These are used to give a better understanding of the observed phenomena and their complexity. The presentation is clear, rigorous and well illustrated, with a wide range of examples of prototypes and industrial products. Chapters 1–4 end with a series of exercises and answers, something unusual and which deserves special mention in such books. This adds to the undeniable pedagogical qualities of the book.

It was with great interest that I read this book, and it is with great confidence that I recommend it to the reader. It is the fruit of considerable collective effort that includes contributions from the main players in the field (at ISIR and at FEMTO-ST, but also at CEA/LIST, Fontenay aux Roses, IEMN/ISEN, Lille and the Université Libre de Bruxelles). The effort was led by two French pioneers of microrobotics, Stéphane Régnier and Nicolas Chaillet. It deserves to become a definitive reference for future designers and users of microrobots, whether qualified engineers or students in the course of Master’s-level study, and whether or not they have prior training in robotics. It will also be a mine of information for doctoral students, qualified researchers and industrial researchers, particularly those who have been regular participants in the French GDR Robotique (robotics research group) working on multiscale manipulation.

I also finished the book with a feeling of nostalgia, remembering the late Alain Bourjault, who launched this theme in 1995 and who supported it throughout his life with great determination. This book definitely owes a great deal to him.

Étienne DOMBRE, DR CNRS, LIRMM, Head of the Robotics Research Group, CNRS, France

Introduction

Microrobotics is a recent field that has developed over the last 20 years. Following on from an earlier work published in 2002, La microrobotique [BOU 02], and in light of recent results within the field, we decided to write a new book targeted at engineers, students and researchers. This book would present a specific field of microrobotics in greater detail that is specifically involved with the manipulation of micron-sized objects.

Generally speaking, a microrobot is a robot that performs tasks in the microworld – in other words the world of micron-sized objects, also known as micro-objects. A microrobot can:

– manipulate micro-objects, in which case it is known as a micromanipulator.

Although a micromanipulator is not necessarily itself micron-sized, it is generally preferable that it should be small, in particular for reasons of structural rigidity and position resolution. This resolution must be submicron so that it can manipulate and position micron-sized objects. The effector of a micromanipulator must, on the other hand, necessarily be micron-sized, since it is immersed in the microworld, interacting with micro-robjects. All or part of such a microrobot may be based on deformable structures; this avoids the backlash and friction inherent in articulated mechanisms, which, bearing in mind the scale we are working on, are liable to catastrophically degrade the resolution;

– be totally immersed in the microworld, in which case the microrobot itself is micron-sized.

Such robots are generally mobile, able to move in a confined environment (such as within the human body) in order to carry out a task (which might be the transport of micro-objects).

This book very much focuses on the first type, i.e. the manipulation of micron-sized objects, also known as micromanipulation. Given the increasing miniaturization of everyday consumer products, the need for micromanipulation is growing, and in particular for microassembly. Micromechanisms (watches, medical, etc.), microsystems, optics, microelectronics and biology are increasingly in need of efficient and reliable methods of micromanipulation. This book obviously has a bias towards the manipulation of objects by robotic means: inspired by methods that have been tried and tested on macroscopic scales, microrobotics offer the flexibility required in the fabrication of products that have some degree of variability.

Self-assembly, which involves exploiting forces that can cause several micro-objects to position themselves spontaneously at predetermined positions on a surface (making use of long-range forces such as electrostatic forces, or contact forces such as capillary forces), is not within the scope of the present book. This book will concentrate on manipulation by microrobots (which is by nature serial, in contrast to self-assembly, which is parallel but at present still not very flexible).

It should be noted that a microrobot is not necessarily a “MEMS” (Micro-Electro-Mechanical System), in other words a microsystem mostly fabricated using microfabrication technologies coming from microelectronics. It may, however, make use of microfabrication technologies, integrating one or more MEMSs, especially for its effectors. If the whole robot is micron-sized, it may itself be a MEMS.

The physical scales discussed in this book span a broad range: the microworld covers the range of 1 µm–1 mm, which is three whole orders of magnitude! It is clear that the physical effects underlying the static and dynamic behaviors involved will vary in strength over such a large range of scales. It is thus important to recognize and understand them as much as possible. Furthermore, many micromanipulation solutions have appeared in recent years that make use of phenomena specific to the scales they operate on. Each solution has its own advantages and disadvantages, but to date no one solution has shown enough clear advantages to raise it clearly above the others. As a result, an understanding of the physics of the microworld is a crucial element of microrobotics, both to understand the behavior of objects on this scale and to appreciate the specific effects used in a given microprehensor. The first chapter of this book describes in detail this physics and the forces involved.

In order to achieve very high positioning resolutions, and consequently very high repeatabilities and precisions, specific actuators may be used, and in particular ones based on active materials such as piezoelectric ceramics, which are currently without question the most widely used material for driving micromanipulators. Chapter 2 presents some of these actuator materials, along with a discussion of guiding with the use of compliant structures.

Generally speaking, the change in the balance of forces involved on the macroscopic scale (where volume-based forces such as weight and inertia dominate) and on the microscopic scale (where surface-based forces such as capillary and electrostatic forces dominate) renders the problem of prehension a particularly delicate one. Chapter 3 therefore discusses microprehensors and micromanipulation strategies applicable in this context.

Beyond the crucial issue of prehension, the scale we are working on also introduces requirements on manipulators. In addition, given that a human cannot directly view the workspace, and cannot feel forces on the microscopic scale, a micromanipulation station must incorporate a vision system and suitable force measurement apparatus. Even if the station is not to be fully automatic, these are crucial for remote operation. All this, along with some elements of control theory, is presented in Chapter 4.

Chapter 5 describes fabrication technologies suitable for microsystems and particularly useful for the fabrication of all or part of a microrobot.

Chapter 6 offers two future directions for micromanipulation:

– further reduction in the scale of the objects to be manipulated, extending the manipulation to nanometer-sized objects. This field of nanorobotics, still in its infancy, is likely to prove an extremely useful complement to the growth of nanotechnologies;

– integration of micromanipulators into a more complete miniaturized production system for microproducts. Such a production system, still very much in the early research stages, is commonly referred to as a microfactory.

Throughout this book, a recurring theme is that of scaling effects. Compared to the macroscopic scale, these introduce a very marked evolution in the dynamics of objects, and require a complete rethink of their function and the techniques used to manipulate them. The three scientific principles underlying this development are:

– knowledge of the dynamics of the microworld, in order to understand it and exploit specific phenomena;

– (micro)mechatronics, for the construction of suitable microrobotic components and structures;

– control of microrobotic systems, and associated perception functions.

We hope that this book, with its detailed review of microrobotics in the sense of robotics for micromanipulation, and its exercises to help the reader understand and master the field, will help engineers, students and researchers to become familiar with this recent field, and to contribute to its development through their scientific and technological work.

Nicolas CHAILLET and Stéphane RÉGNIER

Chapter 1

The Physics of the Microworld1

1.1. Introduction

The term “Micromanipulation” refers to the range of techniques available for the manipulation of objects with sizes ranging from 1 mm to 1 µm. The range in which micromanipulation operates is commonly referred to as the microworld.1 This is in contrast to the “macroworld”, which consists of those objects whose size is greater than 1 mm. The workings of this world cannot easily be described using analogies with existing systems in the macroworld, but require a separate description all of their own.

1.1.1. Scale effect

Miniaturization of an object or process can prove complex, because the range of physical phenomena involved may not all change in the same manner as the scale is reduced. If, for example, we were to scale down a guitar, we would obtain a new guitar whose range of notes had become much higher. The resonant frequencies of the strings increase as their dimensions are reduced. In order to obtain a miniaturized guitar with the same range of notes as a conventional guitar, we would need to completely redesign the instrument. The same is true for most behaviors of a system – they will change as the scale is reduced. The impact of the scale change on physical phenomena is commonly known as the “scale effect”.

The physical phenomena which dominate on a human scale, such as weight or inertia, are mostly volumic. In other words, they are directly proportional to the volume of the object under consideration. Thus, if we change between a cube of steel with sides whose lengths l are one centimeter and a cube with sides whose lengths are (ten times smaller), the characteristic dimension l has been reduced by a factor of 10, whereas its mass changes from 7.9 grams to 7.9 milligrams and so has been reduced by a factor of .

Certain physical phenomena, generally ones that are less familiar in everyday life, are not volumic. An example of this is the surface tension force. This is a length-based effect, and so its evolution is proportional to the scale under consideration. Hence the surface tension of a cube with sides of length l is directly proportional to this length. For a cube ten times smaller, with length l′, the surface tension force is also simply divided by . Consequently, this effect decreases in strength much less rapidly during the miniaturization process. The miniaturization of a concept is subject to the scale effect, which modifies the relative strength of one physical effect compared to another. This modification could either render the miniaturized device inoperable or improve its performance.

1.1.2. Illustration of the scale effect

The scale effect can be illustrated in everyday terms by comparing the methods of locomotion and behavior of insects and people as a result of their significant differences in size.

A first insight into the impact of the scale effect can be drawn from observing aquatic insects walking along the surface of a pond. The insects travel on top of the surface without any part of themselves being immersed in the water. They use the surface tension between the liquid surface and the hydrophobic tips of their legs. On the human scale, travel within water is governed by the equilibrium between the Archimedes force and the weight, which requires a significant volume to be immersed in order to be in equilibrium. The scale effect is volumic for the Archimedes force and for weight, whereas it is length-based for surface tension. Consequently, the latter rapidly becomes dominant over the two other effects during the miniaturization process. On the scale of an insect, the use of surface tension to travel across a liquid medium is therefore more effective than the use of the Archimedes force.

A second example inspired by nature is based on observing the motion of a fly on a vertical glass surface. This method of locomotion is based on adhesive forces between small pads on the ends of the feet of the fly and the smooth surface. It is clearly impossible for a person to climb up a perfectly smooth, vertical surface with their bare hands using the simple adhesive effect. Here the adhesive forces involved are also length-based. Once again, a physical effect which is not used on the human scale becomes dominant compared to weight on the scale of an insect, and hence is used as a method of locomotion.

Finally, leaving behind the comparison between insects and humans, we will discuss another example involving phenomena specific to the microworld. It involves the electrostatic forces which occur in the presence of electric charges. A well-known experiment demonstrating this involves bringing a plastic ruler close to some paper confetti after the ruler has been given an electric charge by rubbing it. The confetti is attracted by the charges present on the ruler and sticks to it, with the attraction being effective at fairly considerable distances of the order of a few centimeters. Once again, weight is negligible compared to the electrostatic force we have produced.

An ant also takes glory from the scale effect, since it is often admired for its ability to carry several times its work weight. This is not the result of supernatural muscular abilities, but simply a consequence of the scale effect, which means that the significance of weight on these scales is smaller compared to that in the human environment. Weight is no longer the dominant force on the ant’s scale. On the other, hand the insect, living as it does in a world ruled by adhesive and capillary effects, is undoubtedly regularly amazed by our ability to split the surface of water despite the surface tension that it considers to dominate over weight.

In order to understand the phenomena involved in miniaturization, we must observe the behavior on microscopic scales without making comparisons, which will invariably turn out to be inappropriate, with the world we are familiar with.

1.1.3. Microworlds

Understanding the microworld requires an appreciation of the physical phenomena that dominate it, but also an appreciation of micro-objects and their properties. Understanding micro-objects is not easy. Just as it is easy to understand objects on our own scale (between 1 mm and 1 m), it is hard to achieve a real picture of the nature of micro-objects.

It is obvious that tools of a different nature would be necessary for the manipulation of a grain of rice (2–3 mm) and a soccer ball (200 mm). Does the same apply if we now consider a small biological cell (2–3 µm) and a human ovule (200 µm)? Since the difference in size between the small cell and the ovule is the same as that between the grain of rice and the soccer ball, the methods of manipulating the small cell and the ovule will surely be very different too. All the same, this requirement may not be intuitively obvious.

The microworld is difficult to comprehend. We can much more easily grasp the sizes of objects between 1 mm and 1 m in size. The natural response, then, in order to better understand micro-objects and their relative sizes, is to artificially multiply their dimensions by 1,000. In this way, we will create a new scale which we will refer to as the “kiloworld”.

When we do this, the size of a small biological cell becomes 2 mm in the kiloworld and ovules have a size of 20 cm. In Table 1.1 we list a number of equivalents in the microworld and the kiloworld. Figure 1.1 gives a summary of the relative sizes of various micro-objects and their equivalents in the kiloworld.

Table 1.1.Kiloworld equivalents of various micro-objects

The comparison with the kiloworld must not hide the fact that the ratio between forces in the microworld is different from the ratio between forces in the macroworld and that, as a result, it is much more difficult to manipulate a microscopic object than to manipulate a millimeter-sized object. This concept of the kiloworld helps us to judge the relative sizes of microscopic objects, but does not help us to appreciate the forces of the microworld.

This method of translation between the microworld and the kiloworld is of pedagogical interest in understanding the sizes of micro-objects. It is definitely not a way of analyzing forces in the microworld, but is simply a way of helping future microroboticians and the general public to appreciate this “universe”.

It is clear, using this concept of the kiloworld, that the microworld is an extremely varied place. Micro-objects have a wide variety of scales (from 1 mm to 1 m on the scale of the kiloworld). Micromanipulation methods will thus also be extremely varied on the scale of this world.

1.2. Details of the microworld

Attempts to scale down a manipulation process encounter a number of technological or physical boundaries, which we will discuss below. Taking into account all these new restrictions requires methodological changes in order to adapt to this new paradigm.

Figure 1.1.Examples of microworld objects and their equivalents in the kiloworld

1.2.1. Perception

Measurement of the position of objects being manipulated and/or the position of terminal organs, as well as measurement of the force applied during a micromanipulation task, particularly is a difficult task to carry out in the microworld.

1.2.1.1. Position-sensing

Measurement of the position of micro-objects most commonly involves visual methods, since conventional methods of measurement cannot be used on such small objects. Two methods are commonly used:

– photonic microscope or optical microscope,

– scanning electron microscope (SEM).

These two types of device are used to visualize micro-objects of sizes between 1 micrometer and 1 millimeter. Particular issues with photonic microscopes on these scales include:

– small depth of field,

– very limited field of view,

– strong sensitivity to illumination.

A study of position measurement for micro-objects during a robotic task using a photonic microscope must be carried out with these particular issues in mind.

The use of electron microscopy is an alternative method of measuring the position of micro-objects. It has the advantage of an infinite depth of field, but it has a larger response time of the order of 500 ms. This tool was initially developed for imaging micrometer-sized structures, and was not intended to carry out visual tasks. To date, there have been few works discussing the treatment of video images from SEMs. Automatic measurement of the 3D position of micro-objects remains a significant obstacle to be overcome in the automation of micromanipulation tasks.

The details of these measurement techniques will be discussed in Chapter 4.

1.2.1.2. Force-sensing

As is the case in conventionally sized robotic systems, certain micromanipulation tasks require measurement and/or control of the strength of manipulation.

Force measurement may, for example, be required to:

– ensure a strong enough, but not excessive, grip so as not to risk damaging the manipulator or the object (especially in the case of biological objects);

– control the strength of insertion during an assembly operator;

– detect when a contact is made that may be out of view of the vision system.

The order of magnitude of the forces to be measured clearly depends very much on the type of objects (biological, artifacts, etc.) and their characteristic size. These forces are nevertheless generally of the order of micro-newton to milli-newton. Measurement of the manipulation force applied to a micro-object is made difficult by the absence of reliable measurement techniques for this level of force on a robotic actuator. Indeed, there are not currently multi-axis sensors able to measure forces of this magnitude with good resolution. Technological issues are currently the main problem, and this is holding back the development of piezoresistive, capacitative or other solutions.

In Chapters 4 and 5 of this book we will give some discussion of the measurement of force on these scales, and of technological methods.

1.2.2. Design of microactuators and fabrication technology

The choice of actuator energy, the design of an actuator and the available fabrication techniques are all equally dependent on the characteristic size of the actuator and the desired performance. Actuators using deformable materials (thermal bilayers, shape-memory alloy structures, piezoelectric strips) are particularly suited to microscopic scales since they do not suffer from mechanical friction as in conventional systems. The use of active materials with traditionally nonlinear behavior and strong hysteresis requires specific effort to model their behavior and investigation of tailored and robust control methods.

The second chapter of this book contains an overview of these actuators.

In addition, we also need to take into account the specific fabrication limitations on these scales during the design process. Microactuators cannot be constructed using traditional fabrication processes (shaping by removal of material), and the techniques on these scales, inspired by electronic microfabrication, makes only the creation of structures possible. Problems with connectivity, the lack of reliability of these MEMS techniques and the cost of such processes are also important criteria in the design of microactuators.

Two broad areas have been studied:

– the use of a monolithic structure which includes both actuators and terminal organs in a single indivisible structure. This choice leads to strong microfabrication constraints, but has the advantage of ease of connectivity;

– the use of an assembly structure that enables the use of terminal organs and actuators with mutually incompatible fabrication processes. This more modular method simplifies the fabrication process but can make it difficult to achieve connectivity between the various assembled elements.

The study of microactuators is also made difficult by the absence of “professional experience” in the field. The general design rules on the macroscopic scale are not valid on the microscopic scale. In general terms, such undertakings require a multidisciplinary approach to the interface between material physics, microfabrication and automation.

1.2.3. Micro-object behavior

The behavior of physical objects is also strongly modified by the reduction in scale. Below a limit of the order of a millimeter, weight and intertia become negligible compared to surface forces (adhesion, capillarity, electrostatics, etc.). Objects tend either to stick to the probes (adhesion effects) or to be repelled by strong accelerations (low inertia). Modification of these behaviors requires robotic manipulation methods to be adapted. In this chapter we will study the forces that come into play on these scales.

1.2.4. Environmental control

Since the behavior of active actuators and micro-objects strongly depends on the environmental conditions (temperature and humidity in the air, and temperature and chemical composition in a liquid), environmental control is required in order to ensure the reliability of an automatic micromanipulation process. Control of vibrations is also necessary when carrying out a micromanipulation task.

1.2.5. Repeatability and dexterity of microrobots

Finally, for the manipulation of objects of micrometer scale, the level of repeatability required for a robot is naturally less than a micrometer. Since working environments are strongly constrained by the perception function, which is currently performed using optical systems, the dexterity of manipulation microrobots is also a major issue in implementing micromanipulation and in particular microassembly.

1.2.6. Summary

We have seen that the design of a micromanipulation robot is subject to new constraints that differ from those in conventional robotics. In summary, a micromanipulation robot must:

– integrate innovative perception methods (Chapter 4);

– possess actuators that operate on these scales and which follow fabrication tolerances specific to these scales (Chapter 2);

– implement micromanipulation strategies tailored to the behavior of micro-objects (Chapter 3);

– operate in a controlled environment (Chapter 4);

– have submicrometer repeatability, and a dexterity that is sufficient for carrying out microassembly tasks (Chapter 5).

An investigation of innovative robotic methods and techniques must address these issues. The rest of this chapter will study the forces that we will encounter in the microworld.

1.3. Surface forces

Three large classes of adhesive forces dominate on the microscopic scale. These forces are [ISR 91]:

– van der Waals forces, interaction forces between the molecules of two nearby bodies;

– elastic forces, classical Coulomb forces that depend on charges present on surfaces;2

– capillary forces, whose existence is determined by the environmental humidity conditions.

A classification of forces as a function of separation distance is given in [LEE 91] and is presented in Table 1.2. In general terms, adhesion between solids encompasses all the chemical binding effects which contribute to the cohesion of solids, such as hydrogen bonds and metallic, covalent and ionic bonds. Although the energy of these bonds is not negligible, their effects are not considered [KRU 67]. This is because, aside from extremely specific environments (ultra-vacuum), chemical bonds on object surfaces tend to be saturated by contaminants (oxidation, etc.). They cannot therefore form bonds when they come into contact with another body. The forces we will consider, then, are those listed above and used in a number of reference works [BOW 86, FEA 95, HEC 90].

Table 1.2.Forces present on the microscopic scale

Interaction range

Force

Infinite

gravity

A few nm to 1mm

capillary force

> 0.3nm

electrostatic force

> 0.3nm

van der Waals force

< 0.3nm

molecular interactions

0.1 – 0.2 nm

chemical interactions

1.3.1. Van der Waals forces

Van der Waals forces were studied in the 1930s by Hamaker [HAM 37] and then developed in the 1950s by Lifshitz [LIF 56]. These forces depend on the materials in contact, through the Hamaker constant, and on the interaction distance. Evaluation of this constant, which determines the strength of the force, requires a wide range of physical data on the materials.

1.3.1.1. Origins

On the molecular level, from a general point of view we will consider an interaction potential between two molecules or particles, represented as w(r). The force acting between these two molecules or particles is derived from this potential, and is expressed as

(1.1)

In order to explain the appearance and dependence on the interaction distance of these forces, Israelachvili [ISR 74] proposed a model based on the interaction of two Bohr atoms.

Let a0 be the minimum distance between the electron and the proton for a trajectory of the electron around the proton. This distance is known as the “first Bohr radius” and is expressed as

If at this distance D there is a second Bohr atom, this will be polarized and will acquire an induced dipole moment:

where α is the electronic polarizability3 of the second atom, which is written as

The interaction energy between these two dipoles is

The attractive force present between these two atoms is obtained by differentiating the energy with respect to r. The expression obtained is a function of 1/r7.

1.3.1.2. Intermolecular van der Waals potential

The van der Waals interaction is formed of the sum of three interparticle forces:

– the induction force: this arises from the induced dipole-dipole interaction and is known as the Debye interaction (1920);

– the orientation force: this arises from the dipole-dipole interaction and is known as the Keesom interaction (1921);

– the dispersion force: this interaction exists between all atoms or molecules, even neutral ones, and is known as the London interaction (1937).

The dispersion force provides the largest contribution of the three components of the van der Waals interaction between atoms and molecules. It is unusual in that it is always present, in contrast to the other two, which depend on the properties of the molecules [ISR 91].

Thus, for two polar molecules interacting in a vacuum, the interaction potential is written:

(1.2)

where Cind, Corient and Cdisp represent, respectively, the contributions of the induction, orientation and dispersion effects on the interaction potential. ν is the orbital frequency of the electron, hν is the ionization potential (also written I) and α01, α02, u1, u2 are, respectively, the electronic polarizabilities and the dipole moments for molecules 1 and 2.

This interaction potential between atoms is more generally written as

(1.3)

There are other forms for this interaction potential that can be derived using alternative approaches. It can be obtained by summing all the attractive and repulsive contributions. Its general form as a function of the interaction distance r between the bodies in question is then

(1.4)

with n and m being integers. The first term represents the repulsive part of the interaction, and the second the attractive part. The most well-known form of this potential is the Lennard-Jones potential [FOK 05]:

(1.5)

with ε being the depth of the potential at its minimum and ξ0 the equilibrium inter-atomic spacing. This produces a repulsive force on the scale of a few Angströms that we will not consider in this book. The attractive forces mostly consist of van der Waals forces. Equation (1.3) is therefore equivalent.

1.3.1.3. Integration of the intermolecular potential

The interaction energy between a molecule and a surface consisting of the same molecules will be the sum of the interactions between the molecule and each molecule of the solid body. Figure 1.2 shows the integration modes used to obtain an expression for the interaction potential between surfaces of different geometries.

If ρ is the molecular density, the molecule-surface interaction can be obtained in the following manner:

(1.6)

Figure 1.2.Integration modes

where (ξ, x) are the coordinates of each volume element. The interaction potential Wsp between a sphere and an infinite half-plane can then be calculated by adding, according to a strong additivity hypothesis, the interactions of all the molecules of the sphere with the half-plane, assuming that the sphere is made of a material with the same molecular density ρ. Observing that the sphere can be divided into layers of radius situated at a distance z + ξ from the surface, the interaction potential W between an infinite half-plane and a sphere of radius R can be written as4

(1.7)

If the radius is much greater than the interaction distance, the classical formulation is recovered:

(1.8)

Proceeding in an identical manner, we can obtain the interaction potentials for various surface geometries. Thus, the interaction potential between two plane surfaces can be written:

per unit surface area.

The van der Waals force generated by these potentials is

1.3.1.4. Hamaker constant

The constant A that appears in the potentials introduced in Table 1.3 is known as the Hamaker constant. This is essential to the calculation of van der Waals forces between surfaces. This constant depends on the materials and experimental conditions. It is generally obtained experimentally but can also be calculated theoretically. Two theories exist on this topic. Hamaker [HAM 37] proposed an expression, for two identical solids, of the form

(1.9)

where ρ1 represents the number of atoms per unit volume in body 1 and C is the coefficient of the atom-atom potential. When two different solids interact, the constant becomes

(1.10)

A then takes values in the range [0.4 ~ 4] × 10−19J. This method of calculation provides good approximations for the constant in weakly polar materials, since it takes into account only the dispersion effect and is obtained by assuming additivity of the dispersion forces. In the converse case, it underestimates the value.

1.3.1.5. Lifshitz theory

Lifshitz [LIF 56] developed a more realistic theory which included the influence of neighboring atoms on the pair under consideration. According to this theory, retarded effects due to dispersion forces are less significant. Estimation of the Hamaker constant is more complex. In order to obtain it, we need to know the variations in the dielectric permittivity of the various bodies forming the system as a function of frequency. Then all we need to do is integrate the following equation [KRU 67, ISR 91]:

Table 1.3.Comparison of approximations in the literature (z is the separation distance and R the radius of the sphere)

where are constants and can be found, for example, in [BUT 06].

Thus, the Hamaker constant can be expressed, for two media 1 and 2 interacting in a medium 3 (1-3-2), in the following form:

(1.11)

with k being the Boltzmann constant (1.381 × 10−23J/K); T the temperature (°K); νe the principal electronic absorption frequency (typically of the order of 3.1015s−1); the dielectric permittivity and ni the refractive index.

This complicated expression can be simplified in the case of simpler interactions (e.g. 1-3-1, 1-2 or 1-1 interactions).

1.3.1.6. Combination equations

In certain cases it is possible to obtain approximate values for the Hamaker constant using combination equations. These equations are derived from the expression for A given by McLachlan in 1963 [MCL64]. In this way, for two materials 1 and 2 interacting in a vacuum, it is possible to obtain A12 as a function of the constants Aii for each material:

Similarly, A132, for two materials 1 and 2 interacting through a third medium 3, is approximately

These combination formulae give very good approximations for A, except in the case of strongly polar media such as water. Under these conditions, equation (1.11) gives results closer to experimentally observed values.

Various works such as [ZHO 98] express the van der Waals forces with the help of what is known as the Lifshitz-van der Waals force, written AL. This is expressed in electron-Volts (eV). With this method, the van der Waals force between, for example, a sphere of radius R and a plane surface can be written:

In what follows, the van der Waals forces between microscopic bodies will be described using the Hamaker constant.

Given the strong dependence of the modulus of the van der Waals forces on the Hamaker constant, many research groups have focused on the exact determination of this constant for various experimental environments [BER 96, DZY 60, HOU 80, PAR 81, VAN 78, ZAR 76]. In all these articles, as well as in [ISR 91], physical values for materials and values of the Hamaker constant are given.

1.3.1.7. Retardation effects in van der Waals forces

Experiments, particularly those by Israelachvili [ISR 74], have confirmed the existence of what is known as a retardation effect in van der Waals interactions. In order to explain the origin of this retardation effect, it is necessary to observe the effect on the atomic level. As the separation distance between two atoms 1 and 2 increases, the time required for the field E1 to polarize atom 2 and return to atom 1 is comparable to the lifetime of the instantaneous dipole moment of 1. In this case, the returning field finds a different dipole moment that is less attuned to the attraction.

This retardation phenomenon has an effect on the modulus of the van der Waals forces. Beyond a separation of 50 nm the interparticle van der Waals forces follow a 1/z8 law. To the first approximation, the retarded potentials between macroscopic bodies have a dependence on distance which is that of the non-retarded potentials multiplied by 1/z. [ISR 74] gives as an example several values which allow us to estimate this effect on an interaction between a plane and a sphere, both made of mica:

1.3.1.8. Simplified Derjaguin model

In the previous section van der Waals forces were calculated analytically between a sphere and a half-plane, and between two half-planes. If the interacting bodies do not have a simple geometry, a simple approach is to use the Derjaguin approximation. This consists of assuming that each surface element interacts only with the surface element opposite to it. This method can be applied either at the level of the intermolecular potential or at the level of the van der Waals forces, depending on whether we are considering the molecular potential per unit surface area or the force per unit surface area, in both cases between two plane surfaces. If, for example, we consider the expression for the force, we write

(1.12)

where S is the surface in question, f(r) the force per unit area at a distance r, and z the interfacial distance between the two objects. This integration is then carried out over the whole surface of the body. Often we need to consider problems with symmetric configurations. The most common expression is then:

(1.13)

This approximation is often valid for separation distances that are small compared to the curvature of the surfaces.

In order to better understand this method, we will consider the case of two interacting spheres of radii R1 and R2.

Figure 1.3.Calculation of the van der Waals force for a plane-sphere interaction using the Derjaguin approximation

The surface element associated with a small displacement dx is then

(1.14)

The total force attracting the two spheres is then

(1.15)

with f(r) being the force per unit surface area between two plane surfaces. As can be seen from Figure 1.3, the following equation is satisfied:

We need to find the relationship between r and x. This is given by the equations for the radii of curvature:

(1.16)

Thus we find

Similarly, we can obtain the equation for different distances:

From this we can determine the van der Waals force attracting the two spheres:

with W(r) being the plane-plane interaction potential at distance r, which varies between z and + ∞. We can then determine the van der Waals force:

1.3.1.9. Numerical approach

When the geometry becomes still more complex, analytical techniques are no longer valid. In this section, we discuss an example of numerical integration for interactions between a sphere and another object (such as a parallelepiped) using Gaussian integration methods and the divergence theorem (the study of relative orientations falls into this category).

1) Gaussian integration method: in order to implement the Gaussian method, the domain of integration must be discretized into elementary cubes. Then, the function to be integrated is evaluated at the various vertices of discretized volume and the values are summed with appropriate weightings [ABR 65]. The Gaussian method states that each integral can then be approximated by

(1.17)

Since the function f to be integrated must be evaluated at each vertex, this should preferably be an analytical expression. For example, if the aim is to calculate the force between a sphere S (with radius R) and an elementary volume V separated by a distance z (see Figure 1.4(b)), the interaction potential WdV, s between the sphere and a volume element dV of V can be obtained by integrating equation (1.3) with respect to S, leading to [LAM 04]:

(1.18)

The interaction potential Wsv(z) between a sphere S and a volume V separated by a distance z is given numerically by

(1.19)

The force can be determined from this potential by applying

(1.20)

Figure 1.4.Numerical integration for van der Waals forces. (a) Elementary cube and its various vertices. (b) Interaction between a sphere and another object shape

This approach has previously been applied by Feddema [FED 01] for calculating the interactions between a sphere and a rectangular block, with the aim of devising a manipulation strategy based on van der Waals forces.

2) Integration method based on Green’s function or the divergence theorem.

The van der Waals force can also be evaluated by replacing the volume integral by a surface integral using Green’s function [DEL 01], as can be illustrated with the example of an infinite plane and a paralellepiped separated by a distance z (see Figure 1.5(b)). This problem has an analytic solution which can be used to validate the method.

First, the interaction potential Wp, dV between an infinite half-plane and a volume element dV at a distance d (Figure 1.5(a)) is calculated. Since (see equation (1.6)), the force F between a half-plane and a rectangular block of volume V can be calculated by

– integrating the potential Wp, dV (d) over the volume V lying at a distance z from the half-plane;

– differentiating the result with respect to , giving

(1.21)

where ξ are the coordinates of the element. This integral can be expanded as follows:

(1.22)

Since F depends on A, S (the cross-section of the rectangular block parallel to the plane – see Figure 1.5(b)), L (the depth) and z (the separation distance between a semi-infinite plane and a rectangular block), F takes the form F(A, S, L, z). equation (1.22) is then used in combination with the Green’s function:

We will assume a vector field given by . Its divergence is then div .

Equation (1.21) can now be written in the form

(1.23)

Then, discretizing the surface of the object in question (see Figure 1.5(c)), since the ith element is characterized by a normal vector whose z component is nzi, the integral in equation (1.23) is replaced with a discrete sum:

(1.24)

The case of a parallelepiped with an orientation relative to a half-plane has also been treated using this method (see Figure 1.6(a)). It can be seen in Figure 1.6(b) that the force strongly decreases as soon as the angle is non-zero. A manipulation strategy varying the relative angle by only a few degrees between a probe and an object (in order to relase it) or between an object and the substrate (in order to grasp it) can also be analyzed using this approach, and this will be studied in Chapter 4. We should also note that it is not necessary to orient the probe at an angle of 45° as suggested in [FED 99] in order to reduce this force, although the minimum force does occur for this value.

This current section considers van der Waals forces, and specifically how to calculate them analytically or numerically. The Hamaker constant is crucial to this, and will be discussed in the experimental part of this chapter.

1.3.2. Surface tension effects: capillary forces

The aim of this section is to explain the physical origin of the capillary forces that act between two solids linked by a liquid bridge, known as a meniscus (see Figure 1.7). We will then present two methods for calculating them and some analytical models that allow us to evaluate these forces in a number of specific configurations: plane-plane, sphere-plane and sphere-sphere. Finally, in a series of graphs we will illustrate the effects of the main parameters that govern the capillary force. In the models that we will discuss, we will see that the capillary force depends on the liquid involved through the surface tension γ (N/m), on the materials used that, combined with the chosen liquid, determine the contact angles θ1 and θ2, on the volume of liquid V in the liquid bridge, and on the distance z between the two solids (see Figures 1.7 and 1.8). Finally, the geometry of the solids joined by the liquid bridge also affects the shape of the meniscus and consequently the capillary force.

Figure 1.5.Geometry of the rectangular block

Figure 1.6.(a) Effect of relative orientation of a parallelepiped with a half-plane. (b) Force [N] as a function of separation distance: influence of orientation angle on the van der Waals force for a separation distance of 1 nm

Figure 1.7.Example problem used to describe the capillary force caused by a liquid bridge on the two solids that it links. (Figure reproduced from [LAM 07] with the permission of Springer Science and Business Media)

Figure 1.8.Inputs to a model of equilibrium capillary forces

Figure 1.9.Illustration of the Young-Dupré equation

Another important parameter in the capillary force model is the contact angles formed by the liquid and the object (θ1), and the liquid and the probe (θ2). This angle is determined by the tangent at the liquid-gas interface and the tangent to the solid at the triple interface line (the line defining the intersection of the liquid-gas, liquid-solid and solid-gas interfaces). In Figure 1.9 this triple line reduces to a point that is its intersection with the plane of the figure. This angle characterizes the way the chosen liquid wets the surface in question. Through the Young-Dupré equation this depends on the surface tension γ of the liquid, the surface energy γSL of the solid-liquid interface, and the surface energy γSV of the solid-vapor interface [ADA 97, ISR 92]:

(1.25)

Typical values of the contact angle are given in Table 1.12.

Finally, [OHL 02] gives the following values for γSV:

– nylon (polyamide) 6.6 (41.4 mN m−1),

– high density PE (30.3–35.1 mN m−1),

– low density PE (32.1–33.2 mN m−1),

– PET (40.9–42.4 mN m−1),

– PMMA (44.9–45.8 mN m−1),

– PP (29.7),

– PTFE (20.0–21.8 mN m−1).

To conclude this brief discussion of contact angles, we note that the contact angle depends on the surface roughness and surface impurities [ADA 97].

Finally, the value of the contact angle may vary between a minimum value known as the receding angle θR and a maximum value known as the advancing angle θA, with the terms advancing and receding corresponding to the two limiting situations in which the triple line is on the point of advancing or retreating along the solid. The difference between the advancing and receding angles is known as contact angle hysteresis.

The presence of a surface tension leads to a difference in pressure across a curved interface. Consider a curved surface S in equilibrium5 on which we will lay a grid of curves u and v which intersect at right angles. Consider now a surface element dS bounded by the curves u, v, u + du and v + dv (see Figure 1.10).

Figure 1.10.Surface element defined on the interface between a liquid and a vapor

Considering only the forces normal to the surface S, we require the surface element to be in equilibrium, and this leads to the Laplace equation which links the difference in pressure on either side of the interface to the surface tension with the curvature of the interface at the surface element under consideration [MOU 01]:

(1.26)

The quantity is twice the mean curvature H, which allows us finally to write equation (1.26) in the following form [ADA 97]:

(1.27)

We are now in a better position to understand the physical origin of the capillary forces acting between two solids joined by a liquid bridge. Returning to Figure 1.7, consider an axisymmetric configuration in which the contact line between the meniscus and the object (or the probe) is a circle of radius r1 (or r2). The pressure in the meniscus is denoted pin, and the pressure outside the meniscus pout. θ1 is the contact angle between the object and the meniscus, and θ2 the angle between the probe and the meniscus. z represents the separation distance between the two solids, and h is known as the immersion height. At the pinch point of the meniscus the two principal radii of curvature are ρ′ (in the plane perpendicular to the z axis) and ρ (in the rz plane).

Figure 1.11.Origin of the Laplace force (figure reproduced from [LAM 07] with the permission of Springer Science and Business Media)

The object feels the Laplace force which is caused by the pressure difference pin – pout acting on the area (see Figure 1.11):

(1.28)

and the tension force which is directly exerted by the surface tension along the circumference 2πr1 (see Figure 1.12):

(1.29)

Figure 1.12.Origin of the tension force (reproduced from [LAM 06a] with permission)

The capillary force is formed of these two terms.

Consequently, the capillary force can be written:

(1.30)

Two alternative methods can be used to construct a model of the capillary forces. The first involves determining the force by differentiating the surface energy of the system, and the second involves a separate calculation of the Laplace and tension forces. In both cases, it is helpful to first determine the shape of the meniscus.

In the case of an axisymmetric configuration the total curvature 2H of a surface whose equation is can be written in the following form [LAM 07]:

(1.31)

with and .

Using this, the Laplace equation can be rewritten in the form

(1.32)

Equation (1.32) is a second-order nonlinear differential equation, which requires two initial conditions that are provided by the starting point of the meniscus on one of the solids and an initial slope, which is a function of the contact angle formed by the meniscus. The starting point is generally unknown, and it must initially be selected arbitrarily, and subsequently we iterate until the angle formed by the meniscus with the second solid corresponds to the correct second contact angle. Furthermore, the pressure difference is generally unknown and it is necessary to perform a second round of iteration over Δp until the volume bounded by the meniscus and the two solids corresponds to the fixed liquid volume provided as an input to the model.

Alternatively we can replace a knowledge of the liquid volume by a knowledge of the environmental conditions (temperature and humidity). In this case the liquid in the meniscus is not introduced by the user, but is the result of condensation of the ambient humidity (known as capillary condensation). The curvature of the meniscus (in other words, the difference in pressure) is then fixed by the Kelvin equation

(1.33)

where v is the molar volume of condensed liquid, R is the ideal gas constant, T is the absolute temperature and the ratio p0/p is the relative humidity of the environment. Israelachvili [ISR 92] gives the value for water at 20°C. The details of this method are given in [LAM 07].

In the general case we can use computer code such as Surface Evolver to determine the shape of the meniscus that minimizes the interfacial energy. The energy of the system is then calculated for separation distances z and z + dz. The capillary force is then calculated in the following manner:

(1.34)

The details of this method are discussed in [CHA 07b].

We could also construct a series of approximate models by making assumptions about the shape of the meniscus: a circular profile (valid for small separation distance between solids), a parabolic profile (useful for avoiding numerical discontinuities when the curvature of the meniscus changes sign), a cylindrical shape, etc.

We will illustrate the method using an example based on derivation of the energy combined with the assumption of a cylindrical meniscus, for the case of two parallel plates.

Figure 1.13.Parallel plates

The interfacial energy of the system is given by

(1.35)

which is the sum of the energies of the solid-liquid interface WSL, the solid-vapor interface WSV and the liquid-vapor interface WLV:

In these expressions r0 is an arbitrary constant radius (which disappears during the differentiation) that allows us to write the area of the solid-vapor interface as a function of the radii r1 and r2 that describe the area of the solid-liquid interface. We differentiate this expression in order to obtain the capillary force:

(1.36)

In order to calculate the derivatives of this expression, we must make additional assumptions. The first of these is to assume that the volume of liquid is constant (i.e. we ignore all liquid evaporation). This assumption must be complemented by the following conditions:

1) The separation distance z is assumed to be small compared to the radii r1 or r2, which allows us to ignore the term that depends on the lateral area Σ.