Theory of Machines and Mechanisms

Theory of Machines and Mechanisms, Third Edition, is a comprehensive study of rigid-body mechanical systems and provides background for continued study in stress, strength, fatigue, life, modes of failure, lubrication and other advanced aspects of the design of mechanical systems. This third edition provides the background, notation, and nomenclature essential for students to understand the various and independent technical approaches that exist in the field of mechanisms, kinematics, and dynamics of machines. The authors employ all methods of analysis and development, with balanced use of graphical and analytic methods. New material includes an introduction of kinematic coefficients, which clearly separates kinematic (geometric) effects from speed or dynamic dependence. At the suggestion of users, the authors have included no written computer programs, allowing professors and students to write their own and ensuring that the book does not become obsolete as computers and programming languages change. Part I introduces theory, nomenclature, notation, and methods of analysis.It describes all aspects of a mechanism (its nature, function, classification, and limitations) and covers kinematic analyses (position, velocity, and acceleration). Part II shows the engineering applications involved in the selection, specification, design, and sizing of mechanisms that accomplish specific motion objectives. It includes chapters on cam systems, gears, gear trains, synthesis of linkages, spatial mechanisms, and robotics. Part III presents the dynamics of machines and the consequences of the proposed mechanism design specifications. New dynamic devices whose functions cannot be explained or understood without dynamic analysis are included. This third edition incorporates entirely new chapters on the analysis and design of flywheels, governors, and gyroscopes.

Table of Contents:
Preface; PART 1. KINEMATICS AND MECHANISMS; 1. THE WORLD OF MECHANISMS; 1.1 Introduction; 1.2 Analysis and Synthesis; 1.3 The Science of Mechanics; 1.4 Terminology, Definitions, and Assumptions; 1.5 Planar, Spherical, and Spatial Mechanisms; 1.6 Mobility; 1.7 Classification of Mechanisms; 1.8 Kinematic Inversion; 1.9 Grashof's Law; 1.10 Mechanical Advantage; 1.11 Problems; 2. POSITION 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 The Loop-Closure Equation; 2.7 Graphic Position Analysis; 2.8 Algebraic Position Analysis; 2.9 Complex-Algebra Solutions of Planar Vector Equations; 2.10 Complex Polar Algebra; 2.11 Position Analysis Techniques; 2.12 The Chace Solutions to Planar Vector Equations; 2.13 Coupler Curve Generation; 2.14 Displacement of a Moving Point; 2.15 Displacement Difference between Two Points; 2.16 Rotation and Translation; 2.17 Apparent Displacement; 2.18 Absolute Displacement; 2.19 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 Geometric Methods; Velocity Polygons; 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 Analytic Methods; 3.10 Complex-Algebra Methods; 3.11 The Method of Kinematic Coefficients; 3.12 The Vector Method; 3.13 Instantaneous Center of Velocity; 3.14 The Aronhold-Kennedy Theorem of Three Centers; 3.15 Locating Instant Centers of Velocity; 3.16 Velocity Analysis Using Instant Centers; 3.17 The Angular-Velocity-Ratio Theorem; 3.18 Relationships between First-Order Kinematic Coefficients and Instant Centers; 3.19 Freudenstein's Theorem; 3.20 Indices of Merit; Mechanical Advantage; 3.21 Centrodes; 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 Polygons; 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 Analytic Methods; 4.10 Complex-Algebra Methods; 4.11 The Method of Kinematic Coefficients; 4.12 The Chace Solutions; 4.13 The Instant Center of Acceleration; 4.14 The Euler-Savary Equation; 4.15 The Bobillier Constructions; 4.16 Radius of Curvature of a Point Trajectory Using Kinematic Coefficients; 4.17 The Cubic of Stationary Curvature; 4.18 Problems; PART 2. DESIGN OF MECHANISMS; 5. CAM DESIGN; 5.1 Introduction; 5.2 Classification of Cams and Followers; 5.3 Displacement Diagrams; 5.4 Graphical Layout of Cam Profiles; 5.5 Kinematic Coefficients of the Follower Motion; 5.6 High-Speed Cams; 5.7 Standard Cam Motions; 5.8 Matching Derivatives of the Displacement Diagrams; 5.9 Plate Cam with Reciprocating Flat-Face Follower; 5.10 Plate Cam with Reciprocating Roller Follower; 5.11 Problems; 6. SPUR GEARS; 6.1 Terminology and Definitions; 6.2 Fundamental Law of Toothed Gearing; 6.3 Involute Properties; 6.4 Interchangeable Gears; AGMA Standards; 6.5 Fundamentals of Gear-Tooth Action; 6.6 The Manufacture of Gear Teeth; 6.7 Interference and Undercutting; 6.8 Contact Ratio; 6.9 Varying the Center Distance; 6.10 Involutometry; 6.11 Nonstandard Gear Teeth; 6.12 Problems7. Helical Gears; 7.1 Parallel-Axis Helical Gears; 7.2 Helical Gear Tooth Relations; 7.3 Helical Gear Tooth Proportions; 7.4 Contact of Helical Gear Teeth; 7.5 Replacing Spur Gears With Helical Gears; 7.6 Herringbone Gears; 7.7 Crossed-Axis Helical Gears; 7.8 Problems8. Bevel Gears; 8.1 Straight-Tooth Bevel Gears; 8.2 Tooth Proportions for Bevel Gears; 8.3 Crown and Face Gears; 8.4 Spiral Bevel Gears; 8.5 Hypoid Gears; 8.6 Problems; 9. WORMS AND WORM GEARS; 9.1 Basics; 9.2 Problems; 10. MECHANISM TRAINS; 10.1 Parallel-Axis Gear Trains; 10.2 Examples of Gear Trains; 10.3 Determining Tooth Numbers; 10.4 Epicyclic Gear Trains; 10.5 Bevel Gear Epicyclic Trains; 10.6 Analysis of Planetary Gear Trains by Formula; 10.7 Tabular Analysis of Planetary Gear Trains; 10.8 Adders and Differentials; 10.9 All Wheel Drive Train; 10.10 Problems; 11. SYNTHESIS OF LINKAGES; 11.1 Type, Number, and Dimensional Synthesis; 11.2 Function Generation, Path Generation, and Body Guidance; 11.3 Two-Position Synthesis of Slider-Crank Mechanisms; 11.4 Two-Position Synthesis of Crank-and-Rocker Mechanisms; 11.5 Crank-Rocker Mechanisms with Optimum Transmission Angle; 11.6 Three-Position Synthesis; 11.7 Four-Position Synthesis; Point-Precision Reduction; 11.8 Precision Positions; Structural Error; Chebychev Spacing; 11.9 The Overlay Method; 11.10 Coupler-Curve Synthesis; 11.11 Cognate Linkages; The Roberts-Chebychev Theorem; 11.12 Bloch's Method of Synthesis; 11.13 Freudenstein's Equation; 11.14 Analytic Synthesis Using Complex Algebra; 11.15 Synthesis of Dwell Mechanisms; 11.16 Intermittent Rotary Motion; 11.17 Problems; 12. SPATIAL MECHANISMS; 12.1 Introduction; 12.2 Exceptions in the Mobility of Mechanisms; 12.3 The Position-Analysis Problem; 12.4 Velocity and Acceleration Analyses; 12.5 The Eulerian Angles; 12.6 The Denavit-Hartenberg Parameters; 12.7 Transformation-Matrix Position Analysis; 12.8 Matrix Velocity and Acceleration Analyses; 12.9 Generalized Mechanism Analysis Computer Programs; 12.10 Problems; 13. ROBOTICS; 13.1 Introduction; 13.2 Topological Arrangements of Robotic Arms; 13.3 Forward Kinematics; 13.4 Inverse Position Analysis; 13.5 Inverse Velocity and Acceleration Analyses; 13.6 Robot Actuator Force Analyses; 13.7 Problems; PART 3. DYNAMICS OF MACHINES; 14. STATIC FORCE ANALYSIS; 14.1 Introduction; 14.2 Newton's Laws; 14.3 Systems of Units; 14.4 Applied and Constraint Forces; 14.5 Free-Body Diagrams; 14.6 Conditions for Equilibrium; 14.7 Two- and Three-Force Members; 14.8 Four-Force Members; 14.9 Friction-Force Models; 14.10 Static Force Analysis with Friction; 14.11 Spur- and Helical-Gear Force Analysis; 14.12 Straight-Bevel-Gear Force Analysis; 14.13 The Method of Virtual Work; 14.14 Problems; 15. DYNAMIC FORCE ANALYSIS (PLANAR); 15.1 Introduction; 15.2 Centroid and Center of Mass; 15.3 Mass Moments and Products of Inertia; 15.4 Inertia Forces and D'Alembert's Principle; 15.5 The Principle of Superposition; 15.6 Planar Rotation about a Fixed Center; 15.7 Shaking Forces and Moments; 15.8 Complex Algebra Approach; 15.9 Equations of Motion; 15.10 Problems; 16. DYNAMIC FORCE ANALYSIS (SPATIAL); 16.1 Introduction; 16.2 Measuring Mass Moment of Inertia; 16.3 Transformation of Inertia Axes; 16.4 Euler's Equations of Motion; 16.5 Impulse and Momentum; 16.6 Angular Impulse and Angular Momentum; 16.7 Problems; 17. VIBRATION ANALYSIS; 17.1 Differential Equations of Motion; 17.2 A Vertical Model; 17.3 Solution of the Differential Equation; 17.4 Step-Input Forcing; 17.5 Phase-Plane Representation; 17.6 Phase-Plane Analysis; 17.7 Transient Disturbances; 17.8 Free Vibration with Viscous Damping; 17.9 Damping Obtained by Experiment; 17.10 Phase-Plane Representation of Damped Vibration; 17.11 Response to Periodic Forcing; 17.12 Harmonic Forcing; 17.13 Forcing Caused by Unbalance; 17.14 Relative Motion; 17.15 Isolation; 17.16 Rayleigh's Method; 17.17 First and Second Critical Speeds of a Shaft; 17.18 Torsional Systems; 17.19 Problems; 18. DYNAMICS OF RECIPROCATING ENGINES; 18.1 Engine Types; 18.2 Indicator Diagrams; 18.3 Dynamic Analysis - General; 18.4 Gas Forces; 18.5 Equivalent Masses; 18.6 Inertia Forces; 18.7 Bearing Loads in a Single Cylinder Engine; 18.8 Crankshaft Torque; 18.9 Engine Shaking Forces; 18.10 Computation Hints; 18.11 Problems; 19. BALANCING; 19.1 Static Unbalance; 19.2 Equations of Motion; 19.3 Static Balancing Machines; 19.4 Dynamic Unbalance; 19.5 Analysis of Unbalance; 19.6 Dynamic Balancing; 19.7 Balancing Machines; 19.8 Field Balancing with a Programmable Calculator; 19.9 Balancing a Single-Cylinder Engine; 19.10 Balancing Multi-Cylinder Engines; 19.11 Analytical Technique for Balancing Multi-Cylinder Reciprocating Engines; 19.12 Balancing Linkages; 19.13 Balancing of Machines; 19.14 Problems; 20. CAM DYNAMICS; 20.1 Rigid- and Elastic-Body Cam Systems; 20.2 Analysis of an Eccentric Cam; 20.3 Effect of Sliding Friction; 20.4 Analysis of Disk Cam with Reciprocating Roller Follower; 20.5 Analysis of Elastic Cam Systems; 20.6 Unbalance, Spring Surge, and Windup; 20.7 Problems; 21. FLYWHEELS; 21.1 Dynamic Theory; 21.2 Integration Technique; 21.3 Multi-Cylinder Engine Torque Summation; 21.4 Problems; 22. GOVERNORS; 22.1 Classification; 22.2 Centrifugal Governors; 22.3 The Inertia Governor; 22.4 Mechanical Control Systems; 22.5 Standard Input Functions; 22.6 Solution of Linear Differential Equations; 22.7 Analysis of Proportional-Error Feedback Systems; 23. GYROSCOPES; 23.1 Introduction; 23.2 The Motion of a Gyroscope; 23.3 Steady or Regular Precession; 23.4 Forced Precession; 23.5 Problems; APPENDICES; 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 Properties of Areas; Table 5 Mass Moments of Inertia; Table 6 Involute Function; Answers to Selected Problems