اسم المؤلف
PARVIZ E. NIKRAVESH
التاريخ
3 يونيو 2018
المشاهدات
358
التقييم

Computer Aided Analysis of Mechanical Systems
PARVIZ E. NIKRAVESH
Aerospace and Mechanical
Engineering Department
University of Arizona
Contents
Preface ix
Note on Unit System xiii
1 INTRODUCTION 1
1.1 Computers in Design and Manufacturing 1
1.1.1 Computer-Aided Analysis 2
1.2 Multibody Mechanical Systems 3
1.3 Branches of Mechanics 6
1.3.1 Methods of Analysis 6
1.4 Computational Methods 9
1.4.1 Efficiency versus Simplicity 10
1.4.2 A General-Purpose Program 14
2 VECTORS AND MATRICES 19
2.1 Geometric Vectors 19
2.2 Matrix and Algebraic Vectors 21
2.2.1 Matrix Operations 21
2.2.2 Algebraic Vector Operations 24
2.3 Vector and Matrix Differentiation 28
2.3.1 Time Derivatives 28
2.3.2 Partial Derivatives 29
Problems 33
BASIC CONCEPTS AND NUMERICAL METHODS
IN KINEMATICS
3.1 Definitions 35
3.1.1 Classification of Kinematic Pairs 37
3.1.2 Vector of Coordinates 38
3.1.3 Degrees of Freedom 40
3.1.4 Constraint Equations 41
3.1.5 Redundant Constraints 41
3.2 Kinematic Analysis 42
3.2.1 Coordinate Partitioning Method 43
3.2.2 Method of Appended Driving
Constraints 48
3.3 Linear Algebraic Equations 50
3.3.1 Gaussian Methods 51
3.3.2 Pivoting 53
3.3.3 L-U Factorization 56
3.3.4 L-U Factorization with Pivoting 61
3.3.5 Subroutines for Linear Algebraic
Equations 63
3.4 Nonlinear Algebraic Equations 66
3.4.1 Newton-Raphson Method for One Equation
in One Unknown 66
3.4.2 Newton-Raphson Methodfor n Equations in
n Unknowns 67
3.4.3 A Subroutine for Nonlinear Algebraic
Equations 70
Problems 72
PLANAR KINEMATICS
4.1 Cartesian Coordinates 77
4.2 Kinematic Constraints 80
4.2.1 Revolute and Translational Joints
(LP) 81
4.2.2 Composite Joints (LP) 84
4.2.3 Spur Gears and Rack and Pinion (HP) 86
4.2.4 Curve Representation 89
4.2.5 Cam-Followers (HP) 93
4.2.6 Point-Follower (HP) 97
4.2.7 Simplified Constraints 98
4.3 Position, Velocity, and Acceleration Analysis 101
4.3.1 Systematic Generation of Some Basic
Elements 103
4.4 Kinematic Modeling 105
4.4.1 Slider-Crank Mechanism 105
4.4.2 Quick-Return Mechanism 110
Problems 115
Contents
35
775
6
7
Contents
A FORTRAN PROGRAM FOR ANALYSIS
OF PLANAR KINEMATICS
5.1 Kinematic Analysis Program (KAP) 119
5.1.1 Model-Description Subroutines 123
5.1.2 Kinematic Analysis 127
5.1.3 Function Evaluation 130
5.1.4 Input Prompts 134
5.2 Simple Examples 134
5.2.2 Slider-Crank Mechanism 137
5.2.3 Quick-Return Mechanism 139
5.3 Program Expansion 140
Problems 140
EULER PARAMETERS
6.1 Coordinates of A Body 153
6.1.1 Euler’s Theorem on the Motion of a
Body 157
6.1.2 Active and Passive Points of View 157
6.1.3 Euler Parameters 158
6.1.4 Determination of Euler Parameters 160
6.1.5 Determination of the Direction
Cosines 164
6.2 Identities with Euler Parameters 166
6.2.1 Identities with Arbitrary Vectors 170
6.3 The Concept of Angular Velocity 172
6.3.1 Time Derivatives of Euler
Parameters 174
6.4 Semirotating Coordinate Systems 176
6.5 Relative Axis of Rotation 177
6.5.1 Intermediate Axis of Rotation 180
6.6 Finite Rotation 180
Problems 181
SPATIAL KINEMATICS
7.1 Relative Constraints between Two Vectors 186
7.1.1 Two Perpendicular Vectors 188
7.1.2 Two Parallel Vectors 188
7.2 Relative Constraints between Two Bodies 189
7.2.1 Spherical, Universal, and Revolute Joints
(LP) 190
7.2.2 Cylindrical, Translational, and Screw Joints
(LP) 192
7.2.3 Composite Joints 196
7.2.4 Simplified Constraints 199
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119
153
1868
9
10
7.3 Position, Velocity, and Acceleration Analysis 200
7.3.1 Modified Jacobian Matrix and Modified
Vector ‘Y 201
Problems 204
BASIC CONCEPTS IN DYNAMICS
8.1 Dynamics of a Particle 208
8.2 Dynamics of a System of Particles 209
8.3 Dynamics of a Body 211
8.3.1 Moments and Couples 212
8.3.2 Rotational Equations of Motion 215
8.3.3 The Inertia Tensor 217
8.3.4 An Unconstrained Body 219
8.4 Dynamics of a System of Bodies 221
8.4.] A System of Unconstrained Bodies 221
8.4.2 A System of Constrained Bodies 222
8.4.3 Constraint Reaction Forces 223
8.5 Conditions for Planar Motion 224
PLANAR DYNAMICS
9.1 Equations of Motion 227
9.2 Vector of Forces 229
9.2.1 Gravitational Force 229
9.2.2 Single Force or Moment 229
9.2.3 Translational Actuators 231
9.2.4 Translational Springs 232
9.2.5 Translational Dampers 234
9.2 .6 Rotational Springs 236
9.2.7 Rotational Dampers 237
9.3 Constraint Reaction Forces 237
9.3.1 Revolute Joint 237
9.3.2 Revolute-Revolute Joint 240
9.3 .3 Translational Joint 242
9.4 System of Planar Equations of Motion 242
9.5 Static Forces 244
9.6 Static Balance Forces 245
9.7 Kinetostatic Analysis 247
Problems 248
A FORTRAN PROGRAM FOR ANALYSIS
OF PLANAR DYNAMICS
10.1 Solving the Equations of Motion 253
10.2 Dynamic Analysis Program (DAP) 254
10.2.1 Model-Description Subroutines 258
208
227
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12
Contents
10.2.2 Dynamic Analysis 260
10.2.3 Function Evaluation 263
10.2.4 Force Evaluation 263
10.2.5 Reporting 265
10.2.6 Static Analysis 266
10.2.7 Input Prompts 267
10.3 Simple Examples 268
10.3.2 Horizontal Platform 269
10.3.3 Dump Truck 273
10.4 Time Step Selection 277
Problems 281
SPATIAL DYNAMICS
1l.1 Vector of Forces 289
11.1.1 Conversion of Moments 289
11.2 Equations of Motion for an Unconstrained
Body 291
11.3 Equations of Motion for a Constrained Body 292
11.4 System of Equations 293
11.4.1 Unconstrained Bodies 294
11.4.2 Constrained Bodies 296
11.5 Conversion of Kinematic Equations 297
Problems 299
NUMERICAL METHODS FOR ORDINARY
DIFFERENTIAL EQUATIONS
12.1 lnitial-Value Problems 301
12.2 Taylor Series Algorithms 302
12.2.1 Runge-Kutta Algorithms 303
12.2.2 A Subroutine for a Runge-Kutta
Algorithm 304
12.3 Polynomial Approximation 307
12.3.1 Explicit Multistep Algorithms 308
12.3 .2 Implicit Multistep Algorithms 308
12.3.3 Predictor-Corrector Algorithms 309
12.3.4 Methods for Starting Multistep
Algorithms 309
12.4 Algorithms for Stiff Systems 310
12.5 Algorithms for Variable Order and Step Size
Problems 311
311
vii
289
301viii
13 NUMERICAL METHODS IN DYNAMICS
13.1 Integration Arrays 313
13.2 Kinematically Unconstrained Systems 314
13.2.1 Mathematical Constraints 315
13.2.2 Using Angular Velocities 317
13.3 Kinematically Constrained Systems 318
13.3.1 Constraint Violation Stabilization
Method 319
13.3.2 Coordinate Partitioning Method 321
13.3.3 Automatic Partitioning of the
Coordinates 324
13.3.4 Stiff Differential Equation Method 327
13.4 Joint Coordinate Method 330
13.4.1 Open·Chain Systems 331
13 .4.2 Closed·Loop Systems 334
Problems 335
14 STATIC EQUILIBRIUM ANALYSIS
14.1 An Iterative Method 339
14.1.1 Coordinate Partitioning 340
14.2 Potential Energy Function 341
14.2.1 Minimization of Potential Energy 342
14.3 Fictitious Damping Method 344
14.4 Joint Coordinates Method 345
Appendix A. EULER ANGLES AND BRYANT ANGLES
A.I Euler Angles 347
A.1.1 Time Derivatives of Euler Angles 349
A.2 Bryant Angles 351
A.2.1 Time Derivatives of Bryant Angles 352
Appendix B. RELATIONSHIP BETWEEN EULER PARAMETERS
AND EULER ANGLES
B.1 Euler Parameters in Terms of Euler Angles
B.2 Euler Angles in Terms of Euler Parameters
Appendix C. COORDINATE PARTITIONING
WITH L-U FACTORIZATION
REFERENCES
BIBLIOGRAPHY
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