Handbook of Compliant Mechanisms

List of Contributors xi Acknowledgments xv Preface xvii Part One Introduction to Compliant Mechanisms 1 Introduction to Compliant Mechanisms 3 1.1 What are Compliant Mechanisms? 3 1.2 What are the Advantages of Compliant Mechanisms? 6 1.3 What Challenges do Compliant Mechanisms Introduce? 6 1.4 Why are Compliant Mechanisms Becoming More Common? 7 1.5 What are the Fundamental Concepts that Help Us Understand Compliance? 8 1.5.1 Stiffness and Strength are NOT the Same Thing 8 1.5.2 It is Possible for Something to be Flexible AND Strong 8 1.5.3 The Basics of Creating Flexibility 10 1.6 Conclusion 13 References 13 2 Using the Handbook to Design Devices 15 2.1 Handbook Outline 16 2.2 Considerations in Designing Compliant Mechanisms 16 2.3 Locating Ideas and Concepts in the Library 19 2.4 Modeling Compliant Mechanisms 20 2.5 Synthesizing Your Own Compliant Mechanisms 21 2.6 Summary of Design Approaches for Compliant Mechanisms 22 Further Reading 24 Part Two Modeling of Compliant Mechanisms 3 Analysis of Flexure Mechanisms in the Intermediate Displacement Range 29 3.1 Introduction 29 3.2 Modeling Geometric Nonlinearities in Beam Flexures 31 3.3 Beam Constraint Model 34 3.4 Case Study: Parallelogram Flexure Mechanism 38 3.5 Conclusions 41 Further Reading 42 4 Modeling of Large Deflection Members 45 4.1 Introduction 45 4.2 Equations of Bending for Large Deflections 46 4.3 Solving the Nonlinear Equations of Bending 47 4.4 Examples 48 4.4.1 Fixed-Pinned Beam 48 4.4.2 Fixed-Guided Beam (Bistable Mechanism) 49 4.5 Conclusions 52 Further Reading 53 References 53 5 Using Pseudo-Rigid Body Models 55 5.1 Introduction 55 5.2 Pseudo-Rigid-Body Models for Planar Beams 57 5.3 Using Pseudo-Rigid-Body Models: A Switch Mechanism Case-Study 60 5.4 Conclusions 65 Acknowledgments 65 References 65 Appendix: Pseudo-Rigid-Body Examples (by Larry L. Howell) 66 A.1.1 Small-Length Flexural Pivot 66 A.1.2 Vertical Force at the Free End of a Cantilever Beam 67 A.1.3 Cantilever Beam with a Force at the Free End 67 A.1.4 Fixed-Guided Beam 69 A.1.5 Cantilever Beam with an Applied Moment at the Free End 70 A.1.6 Initially Curved Cantilever Beam 70 A.1.7 Pinned-Pinned Segments 71 A.1.8 Combined Force-Moment End Loading 73 A.1.9 Combined Force-Moment End Loads – 3R Model 74 A.1.10 Cross-Axis Flexural Pivot 74 A.1.11 Cartwheel Flexure 76 References 76 Part Three Synthesis of Compliant Mechanisms 6 Synthesis through Freedom and Constraint Topologies 79 6.1 Introduction 79 6.2 Fundamental Principles 82 6.2.1 Modeling Motions using Screw Theory 82 6.2.2 Modeling Constraints using Screw Theory 84 6.2.3 Comprehensive Library of Freedom and Constraint Spaces 86 6.2.4 Kinematic Equivalence 86 6.3 FACT Synthesis Process and Case Studies 87 6.3.1 Flexure-Based Ball Joint Probe 87 6.3.2 X-Y-ThetaZ Nanopositioner 88 6.4 Current and Future Extensions of FACT’s Capabilities 89 Acknowledgments 90 References 90 7 Synthesis through Topology Optimization 93 7.1 What is Topology Optimization? 93 7.2 Topology Optimization of Compliant Mechanisms 95 7.3 Ground Structure Approach 98 7.4 Continuum Approach 100 7.4.1 SIMP Method 100 7.4.2 Homogenization Method 103 7.5 Discussion 104 7.6 Optimization Solution Algorithms 105 Acknowledgment 106 References 106 8 Synthesis through Rigid-Body Replacement 109 8.1 Definitions, Motivation, and Limitations 109 8.2 Procedures for Rigid-Body Replacement 111 8.2.1 Starting with a Rigid-Body Mechanism 111 8.2.2 Starting with a Desired Task 114 8.2.3 Starting with a Compliant Mechanism Concept 115 8.2.4 How DoWe Choose the Best Configurations Considering Loads, Strains, and Kinematics? 116 8.3 Simple Bicycle Derailleur Example 116 References 121 9 Synthesis through Use of Building Blocks 123 9.1 Introduction 123 9.2 General Building-Block Synthesis Approach 123 9.3 Fundamental Building Blocks 124 9.3.1 Compliant Dyad 124 9.3.2 Compliant 4-Bar 125 9.4 Elastokinematic Representations to Model Functional Behavior 125 9.4.1 Compliance Ellipses and Instant Centers 126 9.4.2 Compliance Ellipsoids 127 9.4.3 Eigentwist and Eigenwrench Characterization 130 9.5 Decomposition Methods and Design Examples 134 9.5.1 Single-Point Mechanisms 135 9.5.2 Multi-Port Mechanisms using Compliance Ellipsoids 139 9.5.3 Displacement Amplifying Mechanisms using Instant Centers 143 9.6 Conclusions 145 Further Reading 145 References 146 Part Four Library of Compliant Mechanisms 10 Library Organization 149 10.1 Introduction 149 10.1.1 Categorization 149 10.2 Library of Compliant Designs 151 10.3 Conclusion 153 References 153 11 Elements of Mechanisms 155 11.1 Flexible Elements 155 11.1.1 Beams 155 11.1.2 Revolute 161 11.1.3 Translate 179 11.1.4 Universal 181 11.2 Rigid-Link Joints 186 11.2.1 Revolute 186 11.2.2 Prismatic 187 11.2.3 Universal 188 11.2.4 Others 189 References 191 12 Mechanisms 193 12.1 Basic Mechanisms 193 12.1.1 Four-Bar Mechanism 193 12.1.2 Six-Bar Mechanism 195 12.2 Kinematics 197 12.2.1 Translational 197 12.2.2 Rotational 204 12.2.3 Translation—Rotation 209 12.2.4 Parallel Motion 214 12.2.5 Straight Line 218 12.2.6 Unique Motion Path 220 12.2.7 Stroke Amplification 227 12.2.8 Spatial Positioning 230 12.2.9 Metamorphic 233 12.2.10 Ratchet 237 12.2.11 Latch 241 12.2.12 Others 243 12.3 Kinetics 245 12.3.1 Energy Storage 245 12.3.2 Stability 252 12.3.3 Constant Force 262 12.3.4 Force Amplification 263 12.3.5 Dampening 267 12.3.6 Mode 268 12.3.7 Others 269 References 272 13 Example Application 277 13.1 Elements of Mechanisms: Flexible Elements 277 13.2 Mechanisms: Kinematic 282 13.3 Mechanisms: Kinetic 291 References 317 Index 319