Theory of Machines and Mechanisms

Preface About the Authors PART 1. KINEMATICS AND MECHANISMS 1. The World of Mechanisms 1.1 Introduction 1.2 Analysis and Synthesis 1.3 Science of Mechanics 1.4 Terminology, Definitions, and Assumptions 1.5 Planar, Spheric, and Spatial Mechanisms 1.6 Mobility 1.7 Characteristics of Mechanisms 1.8 Kinematic Inversion 1.9 Grashof's Law 1.10 Mechanical Advantage 1.11 References 1.12 Problems 2. Position, Posture, and Displacement 2.1 Locus of a Moving Point 2.2 Position of a Point 2.3 Position Difference Between Two Points 2.4 Apparent Position of a Point 2.5 Absolute Position of a Point 2.6 Posture of a Rigid Body 2.7 Loop-Closure Equations 2.8 Graphic Posture Analysis 2.9 Algebraic Posture Analysis 2.10 Complex-Algebra Solutions of Planar Vector Equations 2.11 Complex Polar Algebra 2.12 Posture Analysis Techniques 2.13 Coupler-Curve Generation 2.14 Displacement of a Moving Point 2.15 Displacement Difference Between Two Points 2.16 Translation and Rotation 2.17 Apparent Displacement 2.18 Absolute Displacement 2.19 Apparent Angular Displacement 2.20 References 2.21 Problems 3. Velocity 3.1 Definition of Velocity 3.2 Rotation of a Rigid Body 3.3 Velocity Difference Between Points of a Rigid Body 3.4 Velocity Polygons; Velocity Images 3.5 Apparent Velocity of a Point in a Moving Coordinate System 3.6 Apparent-Angular Velocity 3.7 Direct Contact and Rolling Contact 3.8 Systematic Strategy for Velocity Analysis 3.9 Algebraic Velocity Analysis 3.10 Complex-Algebraic Velocity Analysis 3.11 Method of Kinematic Coefficients 3.12 Instantaneous Centers of Velocity 3.13 Aronhold-Kennedy Theorem of Three Centers 3.14 Locating Instantaneous Centers of Velocity 3.15 Velocity Analysis Using Instant Centers 3.16 Angular-Velocity-Ratio Theorem 3.17 Relationships Between First-Order Kinematic Coefficients and Instant Centers 3.18 Freudenstein's Theorem 3.19 Indices of Merit; Mechanical Advantage 3.20 Centrodes 3.21 References 3.22 Problems 4. Acceleration 4.1 Definition of Acceleration 4.2 Angular Acceleration 4.3 Acceleration Difference Between Points of a Rigid Body 4.4 Acceleration Images 4.5 Apparent Acceleration of a Point in a Moving Coordinate System 4.6 Apparent-Angular Acceleration 4.7 Direct Contact and Rolling Contact 4.8 Systematic Strategy for Acceleration Analysis 4.9 Algebraic Acceleration Analysis 4.10 Complex-Algebraic Acceleration Analysis 4.11 Method of Kinematic Coefficients 4.12 Euler-Savary Equation 4.13 Bobillier Constructions 4.14 Instantaneous Center of Acceleration 4.15 Bresse Circle (or de La Hire Circle) 4.16 Radius of Curvature of a Point Trajectory Using Kinematic Coefficients 4.17 Cubic of Stationary Curvature 4.18 References 4.19 Problems 5. Multi-Degree-of-Freedom Planar Linkages 5.1 Introduction 5.2 Posture Analysis; Algebraic Solution 5.3 Velocity Analysis; Velocity Polygons 5.4 Instantaneous Centers of Velocity 5.5 First-Order Kinematic Coefficients 5.6 Method of Superposition 5.7 Acceleration Analysis; Acceleration Polygons 5.8 Second-Order Kinematic Coefficients 5.9 Path Curvature of a Coupler Point Trajectory 5.10 Finite Difference Method 5.11 References 5.12 Problems PART 2. DESIGN OF MECHANISMS 6. Cam Design 6.1 Introduction 6.2 Classification of Cams and Followers 6.3 Displacement Diagrams 6.4 Graphic Layout of Cam Profiles 6.5 Kinematic Coefficients of Follower 6.6 High-Speed Cams 6.7 Standard Cam Motions 6.8 Matching Derivatives of Displacement Diagrams 6.9 Plate Cam with Reciprocating Flat-Face Follower 6.10 Plate Cam with Reciprocating Roller Follower 6.11 Rigid and Elastic Cam Systems 6.12 Dynamics of an Eccentric Cam 6.13 Effect of Sliding Friction 6.14 Dynamics of Disk Cam with Reciprocating Roller Follower 6.15 Dynamics of Elastic Cam Systems 6.16 Unbalance, Spring Surge, and Windup 6.17 References 6.18 Problems 7. Spur Gears 7.1 Terminology and Definitions 7.2 Fundamental Law of Toothed Gearing 7.3 Involute Properties 7.4 Interchangeable Gears; AGMA Standards 7.5 Fundamentals of Gear-Tooth Action 7.6 Manufacture of Gear Teeth 7.7 Interference and Undercutting 7.8 Contact Ratio 7.9 Varying Center Distance 7.10 Involutometry 7.11 Nonstandard Gear Teeth 7.12 Parallel-Axis Gear Trains 7.13 Determining Tooth Numbers 7.14 Epicyclic Gear Trains 7.15 Analysis of Epicyclic Gear Trains by Formula 7.16 Tabular Analysis of Epicyclic Gear Trains 7.17 References 7.18 Problems 8. Helical Gears, Bevel Gears, Worms, and Worm Gears 8.1 Parallel-Axis Helical Gears 8.2 Helical Gear Tooth Relations 8.3 Helical Gear Tooth Proportions 8.4 Contact of Helical Gear Teeth 8.5 Replacing Spur Gears with Helical Gears 8.6 Herringbone Gears 8.7 Crossed-Axis Helical Gears 8.8 Straight-Tooth Bevel Gears 8.9 Tooth Proportions for Bevel Gears 8.10 Bevel Gear Epicyclic Trains 8.11 Crown and Face Gears 8.12 Spiral Bevel Gears 8.13 Hypoid Gears 8.14 Worms and Worm Gears 8.15 Summers and Differentials 8.16 All-Wheel Drive Train 8.17 Note 8.18 Problems 9. Synthesis of Linkages 9.1 Type, Number, and Dimensional Synthesis 9.2 Function Generation, Path Generation, and Body Guidance 9.3 Two Finitely Separated Postures of a Rigid Body (N = 2) 9.4 Three Finitely Separated Postures of a Rigid Body (N = 3) 9.5 Four Finitely Separated Postures of a Rigid Body (N = 4) 9.6 Five Finitely Separated Postures of a Rigid Body (N =5) 9.7 Precision Postures; Structural Error; Chebychev Spacing 9.8 Overlay Method 9.9 Coupler-Curve Synthesis 9.10 Cognate Linkages; Roberts-Chebychev Theorem 9.11 Freudenstein's Equation 9.12 Analytic Synthesis Using Complex Algebra 9.13 Synthesis of Dwell Mechanisms 9.14 Intermittent Rotary Motion 9.15 References 9.16 Problems 10. Spatial Mechanisms and Robotics 10.1 Introduction 10.2 Exceptions to the Mobility Criterion 10.3 Spatial Posture-Analysis Problem 10.4 Spatial Velocity and Acceleration Analyses 10.5 Euler Angles 10.6 Denavit-Hartenberg Parameters 10.7 Transformation-Matrix Posture Analysis 10.8 Matrix Velocity and Acceleration Analyses 10.9 Generalized Mechanism Analysis Computer Programs 10.10 Introduction to Robotics 10.11 Topological Arrangements of Robotic Arms 10.12 Forward Kinematics Problem 10.13 Inverse Kinematics Problem 10.14 Inverse Velocity and Acceleration Analyses 10.15 Robot Actuator Force Analysis 10.16 References 10.17 Problems PART 3. DYNAMICS OF MACHINES 11. Static Force Analysis 11.1 Introduction 11.2 Newton's Laws 11.3 Systems of Units 11.4 Applied and Constraint Forces 11.5 Free-Body Diagrams 11.6 Conditions for Equilibrium 11.7 Two- and Three-Force Members 11.8 Four- and More-Force Members 11.9 Friction-Force Models 11.10 Force Analysis with Friction 11.11 Spur- and Helical-Gear Force Analysis 11.12 Straight-Tooth-Bevel-Gear Force Analysis 11.13 Method of Virtual Work 11.14 Introduction to Buckling 11.15 Euler Column Formula 11.16 Critical Unit Load 11.17 Critical Unit Load and Slenderness Ratio 11.18 Johnson's Parabolic Equation 11.19 References 11.20 Problems 12. Dynamic Force Analysis 12.1 Introduction 12.2 Centroid and Center of Mass 12.3 Mass Moments and Products of Inertia 12.4 Inertia Forces and d'Alembert's Principle 12.5 Principle of Superposition 12.6 Planar Rotation about a Fixed Center 12.7 Shaking Forces and Moments 12.8 Complex Algebra Approach 12.9 Equation of Motion From Power Equation 12.10 Measuring Mass Moments of Inertia 12.11 Transformation of Inertia Axes 12.12 Euler's Equations of Motion 12.13 Impulse and Momentum 12.14 Angular Impulse and Angular Momentum 12.15 References 12.16 Problems 13. Vibration Analysis 13.1 Differential Equations of Motion 13.2 A Vertical Model 13.3 Solution of the Differential Equation 13.4 Step Input Forcing 13.5 Phase-Plane Representation 13.6 Phase-Plane Analysis 13.7 Transient Disturbances 13.8 Free Vibration with Viscous Damping 13.9 Damping Obtained by Experiment 13.10 Phase-Plane Representation of Damped Vibration 13.11 Response to Periodic Forcing 13.12 Harmonic Forcing 13.13 Forcing Caused by Unbalance 13.14 Relative Motion 13.15 Isolation 13.16 Rayleigh's Method 13.17 First and Second Critical Speeds of a Shaft 13.18 Torsional Systems 13.19 References 13.20 Problems 14. Dynamics of Reciprocating Engines 14.1 Engine Types 14.2 Indicator Diagrams 14.3 Dynamic Analysis-General 14.4 Gas Forces 14.5 Equivalent Masses 14.6 Inertia Forces 14.7 Bearing Loads in a Single-Cylinder Engine 14.8 Shaking Forces of Engines 14.9 Computation Hints 14.10 Problems 15. Balancing 15.1 Static Unbalance 15.2 Equations of Motion 15.3 Static Balancing Machines 15.4 Dynamic Unbalance 15.5 Analysis of Unbalance 15.6 Dynamic Balancing 15.7 Dynamic Balancing Machines 15.8 Field Balancing with a Programmable Calculator 15.9 Balancing a Single-Cylinder Engine 15.10 Balancing Multi-Cylinder Engines 15.11 Analytic Technique for Balancing Multi-Cylinder Engines 15.12 Balancing of Linkages 15.13 Balancing of Machines 15.14 References 15.15 Problems 16. Flywheels, Governors, and Gyroscopes 16.1 Dynamic Theory of Flywheels 16.2 Integration Technique 16.3 Multi-Cylinder Engine Torque Summation 16.4 Classification of Governors 16.5 Centrifugal Governors 16.6 Inertia Governors 16.7 Mechanical Control Systems 16.8 Standard Input Functions 16.9 Solution of Linear Differential Equations 16.10 Analysis of Proportional-Error Feedback Systems 16.11 Introduction to Gyroscopes 16.12 Motion of a Gyroscope 16.13 Steady or Regular Precession 16.14 Forced Precession 16.15 References 16.16 Problems APPENDICES Appendix A: Tables Table 1 Standard SI Prefixes Table 2 Conversion from US Customary Units to SI Units Table 3 Conversion from SI Units to US Customary Units Table 4 Areas and Area Moments of Inertia Table 5 Mass and Mass Moments of Inertia Table 6 Involute Function Appendix B: Answers to Selected Problems Index

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