Page 13 - Dynamics of Mechanical Systems

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4.3 Configuration Graphs........................................................................................................79
4.4 Simple Angular Velocity and Simple Angular Acceleration ......................................83
4.5 General Angular Velocity..................................................................................................85
4.6 Differentiation in Different Reference Frames ..............................................................87
4.7 Addition Theorem for Angular Velocity........................................................................90
4.8 Angular Acceleration.........................................................................................................93
4.9 Relative Velocity and Relative Acceleration of Two Points
on a Rigid Body..................................................................................................................97
4.10 Points Moving on a Rigid Body ....................................................................................103
4.11 Rolling Bodies...................................................................................................................106
4.12 The Rolling Disk and Rolling Wheel............................................................................107
4.13 A Conical Thrust Bearing ...............................................................................................110
4.14 Closure ...............................................................................................................................113
References.....................................................................................................................................113
Problems .......................................................................................................................................114

Chapter 5 Planar Motion of Rigid Bodies — Methods of Analysis ................................125
5.1 Introduction.......................................................................................................................125
5.2 Coordinates, Constraints, Degrees of Freedom ..........................................................125
5.3 Planar Motion of a Rigid Body......................................................................................128
5.3.1 Translation.............................................................................................................129
5.3.2 Rotation..................................................................................................................130
5.3.3 General Plane Motion..........................................................................................130
5.4 Instant Center, Points of Zero Velocity.........................................................................133
5.5 Illustrative Example: A Four-Bar Linkage ...................................................................136
5.6 Chains of Bodies...............................................................................................................142
5.7 Instant Center, Analytical Considerations ...................................................................147
5.8 Instant Center of Zero Acceleration..............................................................................150
Problems .......................................................................................................................................156

Chapter 6 Forces and Force Systems ....................................................................................163
6.1 Introduction.......................................................................................................................163
6.2 Forces and Moments........................................................................................................163
6.3 Systems of Forces.............................................................................................................165
6.4 Zero Force Systems..........................................................................................................170
6.5 Couples ..............................................................................................................................170
6.6 Wrenches............................................................................................................................173
6.7 Physical Forces: Applied (Active) Forces.....................................................................177
6.7.1 Gravitational Forces.............................................................................................177
6.7.2 Spring Forces.........................................................................................................178
6.7.3 Contact Forces.......................................................................................................180
6.7.4 Action–Reaction....................................................................................................181
6.8 First Moments...................................................................................................................182
6.9 Physical Forces: Inertia (Passive) Forces......................................................................184
References.....................................................................................................................................187
Problems .......................................................................................................................................187

Chapter 7 Inertia, Second Moment Vectors, Moments and Products of Inertia,
Inertia Dyadics.......................................................................................................199
7.1 Introduction.......................................................................................................................199
7.2 Second-Moment Vectors..................................................................................................199