A concise survey of compliant mechanisms--from fundamentals to state-of-the-art applications This volume presents the newest and most effective methods for the analysis and design of compliant mechanisms. It provides a detailed review of compliant mechanisms and includes a wealth of useful design examples for engineers, students, and researchers. Concise chapters guide the reader from simple to more challenging concepts- using examples of increasing complexity-eventually leading to real-world applications for specific types of devices. The author focuses on compliant mechanisms that can be designed using both standard linear beam equations and more advanced pseudo-rigid-body models. He describes a number of special-purpose compliant mechanisms that have use across a wide range of applications and discusses compliant mechanisms in microelectromechanical systems (MEMS) with several accompanying MEMS examples. Coverage of essential topics in strength of materials, machine design, and kinematics is provided to allow for a self-contained book that requires little additional reference to solve compliant mechanism problems. This information can be used as a refresher on the basics or as resource material for readers from other disciplines currently working in MEMS. Compliant Mechanisms serves as both an introductory text for students and an up-to-date resource for practitioners and researchers. It provides comprehensive, expert coverage of this growing field. LARRY L. HOWELL is Chair of the Mechanical Engineering Department at Brigham Young University in Provo, Utah. Contents 9 Preface 17 1 Introduction 21 1.1 Advantages of Compliant Mechanisms 22 1.2 Challenges of Compliant Mechanisms 26 1.3 Historical Background 28 1.4 Compliant Mechanisms and Nature 30 1.5 Nomenclature and Diagrams 31 1.6 Compliant MEMS 35 2 Flexibility and Deflection 41 2.1 Linear versus Nonlinear Deflections 41 2.2 Stiffness and Strength 42 2.3 Flexibility 43 2.4 Displacement versus Force Loads 46 2.5 Material Considerations 48 2.6 Linear Elastic Deflections 54 2.7 Energy Storage 58 2.8 Stress Stiffening 61 2.9 Large-Deflection Analysis 62 3 Failure Prevention 81 3.1 Stress 81 3.2 Static Failure 87 3.3 Fatigue Failure 97 4 Rigid-Link Mechanisms 131 4.1 Introduction 131 4.2 Position Analysis 135 4.3 Velocity and Acceleration 143 4.4 Kinematic Coefficients 145 4.5 Mechanism Synthesis 146 5 Pseudo-Rigid-Body Model 155 5.1 Small-Length Flexural Pivots 156 5.2 Cantilever Beam with a Force at the Free End (Fixed-Pinned) 165 5.3 Fixed-Guided Flexible Segment 182 5.4 End-Moment Loading 185 5.5 Initially Curved Cantilever Beam 186 5.6 Pinned-Pinned Segment 190 5.7 Segment with Force and Moment (Fixed-Fixed) 195 5.8 Other Methods of Pin Joint Simulation 200 5.9 Modeling of Mechanisms 214 5.10 Use of Commercial Mechanism Analysis Software 225 6 Force-Deflection Relationships 239 6.1 Free-Body Diagram Approach 240 6.2 Generalized Coordinates 245 6.3 Work and Energy 246 6.4 Virtual Displacements and Virtual Work 248 6.5 Principle of Virtual Work 250 6.6 Application of the Principle of Vi1tual Work 251 6.7 Spring Function for Fixed-Pinned Members 257 6.8 Pseudo-Rigid-Body Four-Bar Mechanism 259 6.9 Pseudo-Rigid-Body Slider Mechanism 268 6.10 Multi-Degree-of-Freedom Mechanisms 274 6.11 Conclusions 276 7 Numerical Methods 279 7.1 Finite Element Analysis 280 7.2 Chain Algorithm 281 8 Compliant Mechanism Synthesis 295 8.1 Rigid-Body Replacement (Kinematic) Synthesis 295 8.2 Synthesis with Compliance: Kinetostatic Synthesis 306 8.3 Other Synthesis Methods 317 8.4 Problems 319 9 Optimal Synthesis with Continuum Models 321 9.1 Introduction 321 9.2 Formulation of the Optimization Problem 326 9.3 Size, Shape, and Topology Optimization 332 9.4 Computational Aspects 343 9.5 Optimality Criteria Methods 347 9.6 Conclusion 352 9.7 Acknowledgments 352 10 Special-Purpose Mechanisms 357 10.1 Compliant Constant-Force Mechanisms 357 10.2 Parallel Mechanisms 366 11 Bistable Mechanisms 375 11.1 Stability 375 11.2 Compliant Bistable Mechanisms 377 11.3 Four-Link Mechanisms 379 11.4 Slider-Crank or Slider-Rocker Mechanisms 392 11.5 Double-Slider Mechanisms 397 11.6 Snap-Through Buckled Beams 402 11.7 Bistable Cam Mechanisms 402 A References 405 B Properties of Sections 419 B.1 Rectangle 419 B.2 Circle 419 B.3 Hollow Circle 420 B.4 Solid Semicircle 420 B.5 Right Triangle 420 B.6 I Beam with Equal Flanges 420 C Material Properties 421 D Linear Elastic Beam Deflections 427 D.I Cantilever Beam with a Force at the Free End 427 D.2 Cantilever Beam with a Force Along the Length 427 D.3 Cantilever Beam with a Uniformly Distributed Load 428 D.4 Cantilever Beam with a Moment at the Free End 428 D.5 Simply Supported Beam with a Force at the Center 428 D.6 Simply Supported Beam with a Force Along the Length 429 D.7 Simply Supported Beam with a Uniformly Distributed Load 429 D.8 Beam with One End Fixed and the Other End Simply Supported 429 D.9 Beam with Fixed Ends and a Center Load 430 D.10 Beam with Fixed Ends and a Uniformly Distributed Load 430 D.11 Beam with One End Fixed and the Other End Guided 430 E Pseudo-Rigid-Body Models 431 E.1 Small-Length Flexural Pivot 431 E.2 Vertical Force at the Free End of a Cantilever Beam 432 E.3 Cantilever Beam with a Force at the Free End 433 E.4 Fixed-Guided Beam 435 E.5 Cantilever Beam with an Applied Moment at the Free End 436 E.6 Initially Curved Cantilever Beam 437 E.7 Pinned-Pinned Segments 438 E.8 Combined Force-Moment End Loading 440 F Evaluation of Elliptic Integrals 441 G Type Synthesis of Compliant Mechanisms 445 G.1 Matrix Representation for Rigid-Link Mechanisms 445 G.2 Compliant Mechanism Matrices 446 G.3 Determination of Isomorphic Mechanisms 449 G.4 Type Synthesis 453 G.5 Determination of Design Requirements 454 G.6 Topological Synthesis of Compliant Mechanisms 455 G.7 Examples 462 Index 471
A concise survey of compliant mechanisms-from fundamentals to state-of-the-art applications This volume presents the newest and most effective methods for the analysis and design of compliant mechanisms. It provides a detailed review of compliant mechanisms and includes a wealth of useful design examples for engineers, students, and researchers.
Concise chapters guide the reader from simple to more challenging concepts-using examples of increasing complexity-eventually leading to real-world applications for specific types of devices. The author focuses on compliant mechanisms that can be designed using both standard linear beam equations and more advanced pseudo-rigid-body models. He describes a number of special-purpose compliant mechanisms that have use across a wide range of applications and discusses compliant mechanisms in microelectromechanical systems (MEMS) with several accompanying MEMS examples.
Coverage of essential topics in strength of materials, machine design, and kinematics is provided to allow for a self-contained book that requires little additional reference to solve compliant mechanism problems. This information can be used as a refresher on the basics or as resource material for readers from other disciplines currently working in MEMS.
Compliant Mechanisms serves as both an introductory text for students and an up-to-date resource for practitioners and researchers. It provides comprehensive, expert coverage of this growing field.
