Compliant Mechanisms

by Howell, Larry L.

• ISBN13: 9780471384786
• ISBN10: 047138478X
• Edition: 1st
• Format: Hardcover
• Copyright: 2001-08-03
• Publisher: Wiley-Interscience

Summary

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.

Author Biography

LARRY L. HOWELL is Chair of the Mechanical Engineering Department at Brigham Young University in Provo, Utah.

Table of Contents

Preface	xv
Introduction	1	(20)
Advantages of Compliant Mechanisms	2	(4)
Challenges of Compliant Mechanisms	6	(2)
Historical Background	8	(2)
Compliant Mechanisms and Nature	10	(1)
Nomenclature and Diagrams	11	(4)
Compliant Mechanisms versus Compliant Structures	12	(1)
Nomenclature	12	(3)
Diagrams	15	(1)
Compliant MEMS	15	(6)
Problems	18	(3)
Flexibility and Deflection	21	(40)
Linear versus Nonlinear Deflections	21	(1)
Stiffness and Strength	22	(1)
Flexibility	23	(3)
Displacement versus Force Loads	26	(2)
Material Considerations	28	(6)
Maximum Deflection for a Flexible Beam	28	(1)
Ratio of Strength to Young's Modulus	29	(1)
Other Material Selection Criteria	30	(2)
Creep and Stress Relaxation	32	(2)
Linear Elastic Deflections	34	(4)
Energy Storage	38	(3)
Stress Stiffening	41	(1)
Large-Deflection Analysis	42	(19)
Beam with Moment End Load	43	(2)
Elliptic-Integral Solutions	45	(10)
Numerical Methods	55	(1)
Problems	55	(6)
Failure Prevention	61	(50)
Stress	61	(6)
Principal Stresses	62	(5)
Stress Concentrations	67	(1)
Static Failure	67	(10)
Ductile Materials	68	(5)
Brittle Materials	73	(4)
Fatigue Failure	77	(34)
Fatigue Basics	78	(1)
Fatigue Failure Prediction	79	(3)
Estimating Endurance Limit and Fatigue Strength	82	(1)
Endurance Limit and Fatigue Strength Modification Factors	83	(1)
Surface Factor	84	(1)
Size Factor	84	(1)
Load Factor	85	(1)
Reliability	86	(1)
Miscellaneous Effects	86	(2)
Completely Reversed Loading	88	(5)
Fluctuating Stresses	93	(5)
Fatigue of Polymers	98	(4)
Testing	102	(2)
Problems	104	(7)
Rigid-Link Mechanisms	111	(24)
Introduction	111	(4)
Mobility	111	(1)
Kinematic Chains and Inversions	112	(1)
Classification of Four-Bar Mechanisms	113	(1)
Mechanical Advantage	113	(2)
Position Analysis	115	(8)
Four-Bar Mechanisms: Closed-Form Equations	116	(1)
Slider-Crank Mechanisms: Closed-Form Equations	117	(1)
Complex Number Method	118	(5)
Velocity and Acceleration	123	(2)
Kinematic Coefficients	125	(1)
Four-Bar Kinematic Coefficients	125	(1)
Slider-Crank Kinematic Coefficients	126	(1)
Mechanism Synthesis	126	(9)
Function Generation	127	(2)
Path Generation	129	(1)
Motion Generation	130	(1)
Problems	131	(4)
Pseudo-Rigid-Body Model	135	(84)
Small-Length Flexural Pivots	136	(9)
Active and Passive Forces	140	(1)
Stress	141	(3)
Living Hinges	144	(1)
Cantilever Beam with a Force at the Free End (Fixed-Pinned)	145	(17)
Parametric Approximation of the Beam's Deflection Path	147	(1)
Characteristic Radius Factor	148	(2)
Coordinates of Beam End	150	(1)
Rule of Thumb for Characteristic Radius Factor	151	(1)
Angular Deflection Approximation	152	(1)
Stiffness Coefficient	152	(4)
Torsional Spring Constant	156	(1)
Stress	157	(3)
Practical Implementation of Fixed-Pinned Segments	160	(2)
Fixed-Guided Flexible Segment	162	(3)
End-Moment Loading	165	(1)
Initially Curved Cantilever Beam	166	(4)
Stiffness Coefficient for Initially Curved Beams	169	(1)
Stress for Initially Curved Beams	170	(1)
Pinned-Pinned Segment	170	(5)
Initially Curved Pinned-Pinned Segments	172	(3)
Segment with Force and Moment (Fixed-Fixed)	175	(5)
Loading Cases	175	(5)
Other Methods of Pin Joint Simulation	180	(14)
Living Hinges	181	(2)
Passive Joints	183	(2)
Q-Joints	185	(4)
Cross-Axis Flexural Pivots	189	(1)
Torsional Hinges	190	(3)
Split-Tube Flexures	193	(1)
Modelling of Mechanisms	194	(11)
Examples	195	(10)
Use of Commercial Mechanism Analysis Software	205	(14)
Problems	209	(10)
Force-Deflection Relationships	219	(40)
Free-Body Diagram Approach	220	(5)
Generalized Coordinates	225	(1)
Work and Energy	226	(2)
Virtual Displacements and Virtual Work	228	(2)
Principle of Virtual Work	230	(1)
Application of the Principle of Virtual Work	231	(6)
Spring Function for Fixed-Pinned Members	237	(2)
Pseudo-Rigid-Body Four-Bar Mechanism	239	(9)
Pseudo-Rigid-Body Slider Mechanism	248	(6)
Multi-Degree-of-Freedom Mechanisms	254	(2)
Conclusions	256	(3)
Problems	256	(3)
Numerical Methods	259	(16)
Finite Elements Analysis	260	(1)
Chain Algorithm	261	(14)
Shooting Method	268	(7)
Compliant Mechanism Synthesis	275	(26)
Rigid-Body Replacement (Kinematic) Synthesis	275	(11)
Loop Closure Equations	280	(6)
Synthesis with Compliance: Kinetostatic Synthesis	286	(11)
Additional Equations and Unknowns	287	(1)
Coupling of Equations	288	(2)
Design Constraints	290	(2)
Special Case of &thetas;o = &thetas;j	292	(5)
Other Synthesis Methods	297	(2)
Burmester Theory for Finite Displacements	297	(1)
Infinitesimal Displacement	298	(1)
Optimization of Pseudo-Rigid-Body Model	298	(1)
Optimization	299	(1)
Problems	299	(2)
Optimal Synthesis With Continuum Models	301	(36)
Ananthasuresh, G.K.
Frecker, M.I.
Introduction	301	(5)
Distributed Compliance	303	(1)
Continuum Models	303	(1)
Elastostatic Analysis Using the Finite Element Method	304	(1)
Structural Optimization	305	(1)
Formulation of the Optimization Problem	306	(6)
Objective Function, Constraints, and Design Variables	306	(2)
Measures of Stiffness and Flexibility	308	(2)
Multicriteria Formulations	310	(2)
Size, Shape, and Topology Optimization	312	(11)
Size Optimization	312	(7)
Shape Optimization	319	(1)
Topology Optimization	319	(4)
Computational Aspects	323	(4)
Optimization Algorithms	324	(1)
Sensitivity Analysis	325	(2)
Optimality Criteria Methods	327	(5)
Derivation of the Optimality Criterion	327	(2)
Solution Procedure	329	(1)
Examples	329	(3)
Conclusions	332	(1)
Acknowledgments	332	(5)
Problems	332	(5)
Special-Purpose Mechanisms	337	(18)
Compliant Constant-Force Mechanisms	337	(9)
Pseudo-Rigid-Body Model of Compliant Slider Mechanisms	338	(1)
Dimensional Synthesis	339	(3)
Determination of Force Magnitude	342	(1)
Examples	343	(1)
Estimation of Flexural Pivot Stress	344	(1)
Examples	345	(1)
Parallel Mechanisms	346	(9)
Compliant Parallel-Guiding Mechanisms	347	(1)
Applications	347	(3)
Pseudo-Rigid-Body Model	350	(2)
Additional Design Considerations	352	(1)
Problems	353	(2)
Bistable Mechanisms	355	(30)
Stability	355	(2)
Compliant Bistable Mechanisms	357	(2)
Four-Link Mechanisms	359	(13)
Energy Equations	360	(2)
Requirements for Bistable Behavior	362	(5)
Young Bistable Mechanisms	367	(5)
Slider-Crank or Slider-Rocker Mechanisms	372	(5)
Energy Equations	373	(1)
Requirements for Bistable Behavior	374	(1)
Examples for Various Spring Positions	374	(3)
Double-Slider Mechanisms	377	(5)
Double-Slider Mechanisms with a Pin Joining the Sliders	377	(2)
Double-Slider Mechanisms with a Link Joining the Sliders	379	(2)
Requirements for Bistable Behavior	381	(1)
Snap-Through Buckled Beams	382	(1)
Bistable Cam Mechanisms	382	(3)
Problems	383	(2)
A REFERENCES	385	(14)
B PROPERTIES OF SECTIONS	399	(2)
B.1 Rectangle	399	(1)
B.2 Circle	399	(1)
B.3 Hollow Circle	400	(1)
B.4 Solid Semicircle	400	(1)
B.5 Right Triangle	400	(1)
B.6 I Beam with Equal Flanges	400	(1)
C MATERIAL PROPERTIES	401	(6)
D LINEAR ELASTIC BEAM DEFLECTIONS	407	(4)
D.1 Cantilever Beam with a Force at the Free End	407	(1)
D.2 Cantilever Beam with a Force Along the Length	407	(1)
D.3 Cantilever Beam with a Uniformly Distributed Load	408	(1)
D.4 Cantilever Beam with a Moment at the Free End	408	(1)
D.5 Simply Supported Beam with a Force at the Center	408	(1)
D.6 Simply Supported Beam with a Force Along the Length	409	(1)
D.7 Simply Supported Beam with a Uniformly Distributed Load	409	(1)
D.8 Beam with One End Fixed and the Other End Simply Supported	409	(1)
D.9 Beam with Fixed Ends and a Center Load	410	(1)
D.10 Beam with Fixed Ends and a Uniformly Distributed Load	410	(1)
D.11 Beam with One End Fixed and the Other End Guided	410	(1)
E PSEUDO-RIGID-BODY MODELS	411	(10)
E.1 Small-Length Flexural Pivot	411	(1)
E.2 Vertical Force at the Free End of a Cantilever Beam	412	(1)
E.3 Cantilever Beam with a Force at the Free End	413	(2)
E.4 Fixed-Guided Beam	415	(1)
E.5 Cantilever Beam with an Applied Moment at the Free End	416	(1)
E.6 Initially Curved Cantilever Beam	417	(1)
E.7 Pinned-Pinned Segments	418	(2)
E.7.1 Initially Curved Pinned-Pinned Segments	418	(2)
E.8 Combined Force-Moment End Loading	420	(1)
F EVALUATION OF ELLIPTIC INTEGRALS	421	(4)
G TYPE SYNTHESIS OF COMPLIANT MECHANISMS	425	(26)
Murphy, M.D.
G.1 Matrix Representation for Rigid-Link Mechanisms	425	(1)
G.2 Compliant Mechanisms Matrices	426	(3)
G.2.1 Segment-Type Designation	428	(1)
G.2.2 Connection-Type Designation	428	(1)
G.2.3 Examples	429	(1)
G.3 Determination of Isomorphic Mechanisms	429	(4)
G.3.1 Rigid-Body Isomorphic Detection Techniques	431	(1)
G.3.2 Isomorphism Detection for Compliant Mechanisms	431	(2)
G.4 Type Synthesis	433	(1)
G.5 Determination of Design Requirements	434	(1)
G.6 Topological Synthesis of Compliant Mechanisms	435	(7)
G.6.1 Segment-Type Enumeration	436	(1)
G.6.2 Connection-Type Enumeration	437	(1)
G.6.3 Combined Segment and Connection-Type Results	438	(3)
G.6.4 Formation of Compliant Mechanisms	441	(1)
G.7 Examples	442	(9)
G.7.1 Discussions	449	(2)
Index	451