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Loading...Mechanical Simulation with MATLAB
Springer Tracts in Mechanical Engineering
Dan B. Marghitu, Hamid Ghaednia, Jing Zhao
Contents
1 Introduction . 1
1.1 Kinematic Pairs 1
1.2 Degrees of Freedom 3
1.3 Kinematic Chains 4
1.4 Type of Dyads . 6
1.5 Position Analysis for Links 9
1.6 Velocity and Acceleration Analysis for Rigid Body 15
1.7 Planar Dynamics Analysis . 22
1.8 Problems 28
References . 28
2 Classical Analysis of a Mechanism with One Dyad . 31
2.1 Position Analysis . 31
2.2 Velocity and Acceleration Analysis . 38
2.3 Dynamic Force Analysis 44
2.4 Problems 52
References . 54
3 Contour Analysis of a Mechanism with One Dyad . 57
3.1 Closed Contour Equations . 57
3.2 Closed Contour Equations for R-RTR Mechanism . 61
3.3 Force Analysis for R-RTR Mechanism 65
3.4 Problems 70
References . 70
4 Classical Analysis of a Mechanism with Two Dyads 73
4.1 Position Analysis . 73
4.2 Velocity and Acceleration Analysis . 78
4.3 Dynamic Force Analysis 85
4.4 Problems 95
References . 98
viiviii Contents
5 Contour Analysis of a Mechanism with Two Dyads 101
5.1 Velocity and Acceleration Analysis . 102
5.2 Contour Dynamic Force Analysis with D’Alembert Principle . 107
5.2.1 Reaction Force F24 . 107
5.2.2 Reaction Force F23 . 109
5.2.3 Reaction Force F12 . 110
5.2.4 Reaction Force F03 . 112
5.2.5 Reaction Force F05 . 113
5.2.6 Reaction Force F54 and Reaction Moment M54 . 115
5.2.7 Reaction Force F01 and Moment Mm . 117
5.3 Problems 119
References . 119
6 Dyad Routines for Mechanisms 123
6.1 Driver Link 123
6.2 Position Analysis . 124
6.3 Velocity Analysis . 127
6.4 Force Analysis . 132
6.4.1 R-RRR Mechanism 139
6.4.2 R-RTR Mechanism . 146
6.4.3 R-RRT-RTR Mechanism 151
6.4.4 Problems . 161
References . 162
7 Epicyclic Gear Trains . 165
7.1 Introduction . 165
7.2 Epicyclic Gear Train with One Planet . 167
7.2.1 Classical Method 168
7.2.2 Contour Method . 170
7.3 Mechanism with Epicyclic Gears . 172
7.3.1 Classical Method—Velocity Analysis . 174
7.3.2 Contour Method—Velocity Analysis 175
7.4 Epicyclic Gear Train with Multiple Planets . 177
7.4.1 Classical Method—Velocity Analysis . 179
7.4.2 Contour Method—Velocity Analysis 181
7.5 Problems 183
References . 186
8 Cam and Follower Mechanism 189
8.1 Kinematics Analysis 190
8.2 Force Analysis . 195
8.3 Equivalent Linkages 197
8.4 Differential Method . 200
8.5 Problems 201
References . 203Contents ix
9 Direct Dynamics . 207
9.1 Equations of Motion—Sphere on a Spring . 207
9.2 Dynamics of a Rotating Link with an Elastic Force 215
9.3 Impact of a Free Link with MATLAB . 228
9.4 Problems 242
References . 243
Index . 247
Index
B
Body-fixed reference frame, 16
C
Cam, 189, 190, 192–194
Circular pitch, 165
Contour diagram, 4, 6, 61, 101
Coriolis, 41, 57, 60, 64, 83, 194
D
D’Alembert, 24, 25, 57, 101, 107, 123, 134
Degrees of freedom, 3, 6, 7, 24
Diametral pitch, 165
Direct dynamics, 24, 207
Dyad, 6, 31, 73, 125
E
Elastic force, 207, 208, 211, 215
Epicyclic gear, 165, 167
Equivalent linkages, 198
External moment, 31, 73, 108
F
Follower, 9, 189
G
Generalized active force, 25, 224, 225
Generalized coordinates, 25, 229
Generalized inertia force, 25
I
Independent contours, 1, 5, 170, 181
Inertia force, 24, 87–89
Inertia moment, 24
Initial conditions, 208, 209, 219
Inverse dynamics, 24, 31, 57
J
Joint forces, 46, 101, 150
K
Kane’s dynamical equations, 25
Kinematic pair, 1
Kinetic energy, 25, 224, 233, 234
L
Lagrange, 24, 26, 207, 224, 234, 235, 237,
238
M
MatlabFunction, 212
Module, 166, 183
Monoloop, 58
Motor moment, 31, 68, 73
N
Newton-Euler, 24, 46, 47, 73, 91, 93, 207,
230
O
Ode
P
Pitch circle, 165
Pitch point, 165, 168, 173
Planet gear, 167, 169, 170, 179, 183
Poisson, 17, 20
R
Reference frame, 3, 4, 15
Routine, 126, 131, 140
S
Slider, 4, 5, 31, 35, 53, 68, 79, 81, 85–89, 93,
94, 107, 110, 113, 114
Slider-crank, 10
Sun gear, 167, 168, 170
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