Fundamentals of kinematics and dynamics of machines and mechanisms

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The study of the kinematics and dynamics of machines lies at the very core of a mechanical engineering background. Although tremendous advances have been made in the computational and design tools now available, little has changed in the way the subject is presented, both in the classroom and in professional references.

Fundamentals of Kinematics and Dynamics of Machines and Mechanisms brings the subject alive and current. The author's careful integration of Mathematica software gives readers a chance to perform symbolic analysis, to plot the results, and most importantly, to animate the motion. They get to "play" with the mechanism parameters and immediately see their effects. A CD-ROM packaged with the book contains Mathematica-based programs for suggested design projects.

As useful as Mathematica is, however, a tool should not interfere with but enhance one's grasp of the concepts and the development of analytical skills. The author ensures this with his emphasis on the understanding and application of basic theoretical principles, unified approach to the analysis of planar mechanisms, and introduction to vibrations and rotordynamics.

Author Notes

Oleg Vinogradov is Professor of Mechanical Engineering at the University of Calgary.

Reviews 1

Choice Review

Vinogradov presents his book on kinematics and kinetics of mechanisms and assemblies thereof with a fresh perspective, reflecting his significant teaching experience. Apart from kinematics and force analysis of mechanisms, there are chapters devoted to cams and gears. A welcome new feature is the chapter on linear vibrations, which includes the treatment of rotor dynamics. A unique aspect of the book is the use of Mathematica as a computational tool in solving problems and creating animated graphical displays of mechanism motions. The use of this tool is demonstrated in an appendix with the help of five problems. The solutions include textual explanations and executable commands. The same solutions are included on the accompanying CD-ROM, which also includes instructions regarding the use of Mathematica. All the Mathematica files on the disc were examined easily with the help of Math Reader 4 downloaded from the Mathematica developer's Internet site . At the end of each chapter, there are two sets of useful problems, one for hand calculation and the other for solving with Mathematica. Illustrations are of acceptable quality and the subject index is adequate, but the bibliography is rather scant. Upper-division undergraduates through professionals. P. K. Basu; Vanderbilt University

Chapter 1 Introduction
1.1 The Subject of Kinematics and Dynamics of Machines	p. 1
1.2 Kinematics and Dynamics as Part of the Design Process	p. 1
1.3 Is It a Machine, a Mechanism, or a Structure?	p. 3
1.4 Examples of Mechanisms; Terminology	p. 4
1.5 Mobility of Mechanisms	p. 6
1.6 Kinematic Inversion	p. 10
1.7 Grashof's Law for a Four-Bar Linkage	p. 10
Problems	p. 12
Chapter 2 Kinematic Analysis of Mechanisms
2.1 Introduction	p. 15
2.2 Vector Algebra and Analysis	p. 16
2.3 Position Analysis	p. 18
2.3.1 Kinematic Requirements in Design	p. 18
2.3.2 The Process of Kinematic Analysis	p. 19
2.3.3 Kinematic Analysis of the Slider-Crank Mechanism	p. 20
2.3.4 Solutions of Loop-Closure Equations	p. 22
2.3.5 Applications to Simple Mechanisms	p. 28
2.3.6 Applications to Compound Mechanisms	p. 36
2.3.7 Trajectory of a Point on a Mechanism	p. 39
2.4 Velocity Analysis	p. 41
2.4.1 Velocity Vector	p. 41
2.4.2 Equations for Velocities	p. 42
2.4.3 Applications to Simple Mechanisms	p. 45
2.4.4 Applications to Compound Mechanisms	p. 49
2.5 Acceleration Analysis	p. 51
2.5.1 Acceleration Vector	p. 51
2.5.2 Equations for Accelerations	p. 52
2.5.3 Applications to Simple Mechanisms	p. 55
2.6 Intermittent-Motion Mechanisms: Geneva Wheel	p. 60
Problems and Exercises	p. 64
Chapter 3 Force Analysis of Mechanisms
3.1 Introduction	p. 73
3.2 Force and Moment Vectors	p. 74
3.3 Free-Body Diagram for a Link	p. 75
3.4 Inertial Forces	p. 79
3.5 Application to Simple Mechanisms	p. 80
3.5.1 Slider-Crank Mechanism: The Case of Negligibly Small Inertial Forces	p. 80
3.5.2 Slider-Crank Mechanism: The Case of Significant Inertial Forces	p. 82
3.5.3 Four-Bar Mechanism: The Case of Significant Inertial Forces	p. 88
3.5.4 Five-Bar Mechanism: The Case of Significant Inertial Forces	p. 90
3.5.5 Scotch Yoke Mechanism: The Case of Significant Inertial Forces	p. 95
Problems and Exercises	p. 99
Chapter 4 Cams
4.1 Introduction	p. 103
4.2 Circular Cam Profile	p. 104
4.3 Displacement Diagram	p. 109
4.4 Cycloid, Harmonic, and Four-Spline Cams	p. 110
4.4.1 Cycloid Cams	p. 110
4.4.2 Harmonic Cams	p. 115
4.4.3 Comparison of Two Cams: Cycloid vs. Harmonic	p. 117
4.4.4 Cubic Spline Cams	p. 118
4.4.5 Comparison of Two Cams: Cycloid vs. Four-Spline	p. 124
4.5 Effect of Base Circle	p. 127
4.6 Pressure Angle	p. 127
Problems and Exercises	p. 132
Chapter 5 Gears
5.1 Introduction	p. 135
5.2 Kennedy's Theorem	p. 135
5.3 Involute Profile	p. 137
5.4 Transmission Ratio	p. 138
5.5 Pressure Angle	p. 139
5.6 Involutometry	p. 140
5.7 Gear Standardization	p. 143
5.8 Types of Involute Gears	p. 148
5.8.1 Spur Gears	p. 148
5.8.2 Helical Gears	p. 150
5.8.3 Bevel Gears	p. 153
5.8.4 Worm Gears	p. 157
5.9 Parallel-Axis Gear Trains	p. 160
5.9.1 Train Transmission Ratio	p. 160
5.9.2 Design Considerations	p. 161
5.10 Planetary Gear Trains	p. 162
5.10.1 Transmission Ratio in Planetary Trains	p. 163
5.10.2 Example of a More Complex Planetary Train	p. 165
5.10.3 Differential	p. 166
Problems	p. 167
Chapter 6 Introduction to Linear Vibrations
6.1 Introduction	p. 171
6.2 Solution of Second-Order Nonhomogeneous Equations with Constant Coefficients	p. 175
6.2.1 Solution of the Homogenous Equation	p. 175
6.2.2 Particular Solution of the Nonhomogeneous Equation	p. 177
6.2.3 Complete Solution of the Nonhomogeneous Equation	p. 179
6.3 Free Vibrations of an SDOF System with No Damping	p. 181
6.4 Forced Vibrations of an SDOF System with No Damping	p. 182
6.5 Steady-State Forced Vibrations of an SDOF System with No Damping	p. 184
6.6 Free Vibrations of an SDOF System with Damping	p. 185
6.7 Forced Vibrations of a Damped ([xi] [ 1) SDOF System with Initial Conditions	p. 188
6.8 Forced Vibrations of an SDOF System with Damping ([xi] [ 1) as a Steady-State Process	p. 190
6.9 Coefficient of Damping, Logarithmic Decrement, and Energy Losses	p. 194
6.10 Kinematic Excitation	p. 196
6.11 General Periodic Excitation	p. 197
6.12 Torsional Vibrations	p. 199
6.13 Multidegree-of-Freedom Systems	p. 200
6.13.1 Free Vibrations of a 2DOF System without Damping	p. 202
6.13.2 Free Vibrations of a 2DOF System with Damping	p. 208
6.13.3 Forced Vibrations of a 2DOF System with Damping	p. 212
6.14 Rotordynamics	p. 215
6.14.1 Rigid Rotor on Flexible Supports	p. 215
6.14.2 Flexible Rotor on Rigid Supports	p. 219
6.14.3 Flexible Rotor with Damping on Rigid Supports	p. 220
6.14.4 Two-Disk Flexible Rotor with Damping	p. 224
Problems and Exercises	p. 229
Bibliography	p. 233
Appendix Use of Mathematica as a Tool	p. 235
A.1 Introduction to Mathematica	p. 240
A.2 Vector Algebra	p. 242
A.3 Vector Analysis	p. 242
A.4 Kinematic and Force Analysis of Mechanisms	p. 242
A.4.1 Slider-Crank Mechanism	p. 242
A.4.2 Four-Bar Linkage	p. 254
A.5 Harmonic Cam with Offset Radial and Oscillatory Roller Followers	p. 263
A.6 Vibrations	p. 274
A.6.1 Free Vibrations of a 2DOF System	p. 275
A.6.2 Forced Vibrations of a 2DOF System	p. 283
Index	p. 289

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