كتاب Kinematic and Dynamic Simulation of Multibody Systems
منتدى هندسة الإنتاج والتصميم الميكانيكى
بسم الله الرحمن الرحيم

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 كتاب Kinematic and Dynamic Simulation of Multibody Systems

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عدد المساهمات : 15047
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تاريخ التسجيل : 01/07/2009
العمر : 30
الدولة : مصر
العمل : مدير منتدى هندسة الإنتاج والتصميم الميكانيكى
الجامعة : المنوفية

مُساهمةموضوع: كتاب Kinematic and Dynamic Simulation of Multibody Systems    الخميس 21 يونيو 2012, 9:55 pm

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Kinematic and Dynamic Simulation of Multibody Systems
The Real-Time Challenge
Javier Garcfa de Jalon and Eduardo Bayo
Department of Applied Mechanics
University of Navarra and CEIT
Department of Mechanical and Environmental Engineering
University of California
Santa Barbara


ويتناول الموضوعات الأتية :

Contents
1 Introduction and Basic Concepts 1
1.1 Computer Methods for Multibody Systems 5 .
1.2 Basic Concepts .7
1.2.1 Multibody Systems and Joints 7
1.2.2 Dependent and Independent Coordinates 8 .
1.2.3 Symbolic vs. Numerical Formulations 9 .
1.3 Types of Problems 10
1.3.1 Kinematic Problems 10
1.3.2 Dynamic Problems 11 .
1.3.3 Other Problems: Synthesis or Design 13 .
1.4 Summary 15
References 15 .
2 Dependent Coordinates and Related Constraint Equations 1 6
2.1 Planar Multibody Systems 16 .
2.1.1 Relative Coordinates 19 .
2.1.2 Reference Point Coordinates 24 .
2.1.3 Natural Coordinates .26
2.1.4 Mixed and Two-Stage Coordinates 34 .
2.2 Spatial Multibody Systems 36
2.2.1 Relative Coordinates 36 .
2.2.2 Reference Point Coordinates 38 .
2.2.3 Natural Coordinates .44
2.2.3.1 Rigid Body Constraints 47 .
2.2.3.2 Joint Constraints 52 .
2.2.4 Mixed Coordinates 56
2.3 Comparison Between Reference Point and Natural Coordinates 61
2.4 Concluding Remarks 63 .
References 64 .
Problems 66 3 Kinematic Analysis 7 1 .
3.1 Initial Position Problem 71
3.2 Velocity and Acceleration Analysis 78
3.2.1 Velocity Analysis 78 .
3.2.2 Acceleration Analysis 81
3.3 Finite Displacement Analysis 83 .
3.3.1 Newton-Raphson Iteration 83
3.3.2 Improved Initial Approximation 84
3.3.3 Modified Newton-Raphson Iteration 86 .
3.3.4 Kinematic Simulation 87 .
3.4 Redundant Constraints 88 .
3.5 Subspace of Allowable Motions 93
3.5.1 Scleronomous Systems 94
3.5.2 Rheonomous Systems 97 .
3.5.3 Calculation of Matrix R: Projection Methods . 100
3.5.4 Orthogonalization Methods . 105
3.6 Multibody Systems with Non-Holonomic Joints 107
3.6.1 Wheel Element in the Planar Case: First Method. 107 .
3.6.2 Wheel Element in the Planar Case: Second Method. 110
3.6.3 Wheel Element in the Three-Dimensional Case. 111 .
References 113 .
Problems 114
4 Dynamic Analysis. Mass Matrices and External Forces 1 2 0 .
4.1 Background on Analytical Dynamics 120
4.1.1 Principle of Virtual Displacements . 121
4.1.2 Hamilton's Principle 122 .
4.1.3 Lagrange's Equations 123 .
4.1.4 Virtual Power 126
4.1.5 Canonical Equations 128
4.2 Inertia Forces. Mass Matrix 130
4.2.1 Mass Matrix of Planar Bodies 131 .
4.2.2 Mass Matrix of Three Dimensional Bodies 134
4.2.3 Kinetic Energy of an Element 143 .
4.3 External Forces 144
4.3.1 Concentrated Forces and Torques 144
4.3.2 Forces Exerted by Springs 146
4.3.3 Forces Induced by Known Acceleration Fields 152
References 153 .
Problems 153
5 Dynamic Analysis. Equations of Motion .1 5 6
5.1 Formulations in Dependent Coordinates 157
5.1.1 Method of the Lagrange's Multipliers 159 .
5.1.2 Method Based on the Projection Matrix R 160 .5.1.3 Stabilization of the Constraint Equations 162
5.1.3.1 Integration of a Mixed System of Differential
and Algebraic Equations. 163
5.1.3.2 Baumgarte Stabilization 163 .
5.1.4 Penalty Formulations 164
5.2 Formulations in Independent Coordinates 170
5.2.1 Determination of Independent Coordinates 171 .
5.2.2 Extraction Methods (Coordinate Partitioning) . 173
5.2.3 Methods Based on the Projection Matrix R 175
5.2.4 Comparative Remarks 178 .
5.3 Formulations Based on Velocity Transformations 179 .
5.3.1 Open-Chain Multibody Systems 180
5.3.1.1 Definition of Base Body Motion 182
5.3.1.2 Different Joints in 3-D Multibody Systems 184 .
5.3.2 Closed-Chain Multibody Systems 187
5.4 Formulations Based on the Canonical Equations 189 .
5.4.1 Lagrange Multiplier Formulation . 189
5.4.2 Formulation Based on Independent Coordinates . 191
5.4.3 Augmented Lagrangian Formulation in Canonical Form 192
References 196 .
Problems 198
6 Static Equilibrium Position and Inverse Dynamics 2 0 1
6.1 Static Equilibrium Position 202
6.1.1 Computation of Derivatives of Potential Energy . 202
6.1.1.1 Derivatives of the Potential of External Forces 203 .
6.1.1.2 Derivatives of the Potential of External
Torques . 204
6.1.1.3 Derivatives of the Potential Energy of
Translational Springs 204
6.1.1.4 Derivatives of the Potential Energy of
Rotational Springs 206
6.1.1.5 Derivatives of the Potential Energy of
Gravitational Forces 206
6.1.2 Method of the Lagrange Multipliers 207 .
6.1.3 Penalty Formulation 208 .
6.1.4 Virtual Power Method 209 .
6.1.4.1 Theoretical Development 209 .
6.1.4.2 Practical Computation of Derivatives . 211
6.1.5 Dynamic Relaxation 212
6.2 Inverse Dynamics 213 .
6.2.1 Newton's Method 213
6.2.2 Method of the Lagrange Multipliers 220 .
6.2.2.1 Constraint Forces in Planar Multibody
Systems 221
6.2.2.2 Constraint Forces in Three-Dimensional
Multibody Systems . 227
6.2.2.3 Calculation of Reaction Forces at the Joints 229 6.2.3
Method of the Lagrange Multipliers with Redundant
Constraints 231
6.2.4 Penalty Formulation 233 .
6.2.5 Virtual Power Method 233 .
6.2.5.1 Calculation of Motor Forces 234 .
6.2.5.2 Calculation of Reactions at the Joints . 235
6.2.6 Inverse Dynamics of Open Chain Systems 239
References 242 .
7 Numerical Integration of the Equations of Motion 2 4 3 .
7.1 Integration of Ordinary Differential Equations . 243
7.1.1 General Background . 244
7.1.2 Runge-Kutta Methods 247
7.1.3 Explicit and Implicit Multistep Methods 249 .
7.1.4 Comparison Between the Runge-Kutta and the Multistep
Methods 253
7.1.5 Newmark Method and Related Algorithms 255 .
7.2 Integration of Differential-Algebraic Equations 261 .
7.2.1 Preliminaries 261 .
7.2.2 Solutions by Backward Difference Formulae 263
7.2.3 Solutions by Implicit Runge-Kutta Methods 265
7.3 Considerations for Real-Time Simulation 266
References 268 .
Problems 270
8 Improved Formulations for Real-Time Dynamics .2 7 1
8.1 Survey of Improved Dynamic Formulations . 271
8.1.1 Formulations O(N3): Composite Inertia 273
8.1.2 Formulations O(N): Articulated Inertia 276 .
8.1.3 Extension to Branched and Closed-Chain
Configurations 279 .
8.2 Velocity Transformations for Open-Chain Systems 281 .
8.2.1 Dependent and Independent Coordinates 282 .
8.2.2 Dependent and Independent Velocities: Matrix R 285 .
8.2.3 Equations of Motion 288 .
8.2.4 Position Problem 289 .
8.2.5 Velocity and Acceleration Problems 292 .
8.2.5.1 Formulation A 293 .
8.2.5.2 Formulation B 296 .
8.2.6 Element-by-Element Computation of Matrix R 297
8.2.7 Computation of Mass Matrices Mb 300
8.2.8 Computation of the Matrix Product RTMR 301
8.2.9 Computation of the Matrix Product RTMSc . 302
8.2.10 Computation of the Term RT(Q?C) 302
8.3 Velocity Transformations for Closed-Chain Systems 303 .8.4
Examples Solved by Velocity Transformations . 307
8.4.1 Open-Chain Example: Human Body 308 .
8.4.2 Closed-Chain Example: Heavy Truck 309 .
8.4.3 Numerical Results 313
8.5 Special Implementations Using Dependent Natural Coordinates 314 .
8.5.1 Differential Equations of Motion in the Natural
Coordinates 314 .
8.5.2 Integration Procedure 316 .
8.5.3 Numerical Considerations . 318
References 323 .
9 Linearized Dynamic Analysis .3 2 5
9.1 Linearization of the Differential Equations of Motion 325
9.1.1 Independent Coordinates 326 .
9.1.2 Dependent Coordinates . 331
9.1.3 Canonical Equations 334
9.2 Numerical Computation of Derivatives 335 .
9.3 Numerical Evaluation of the Dynamic Response . 336
References 337 .
10 Special Topics 3 3 8 .
10.1 Coulomb Friction . 338
10.1.1 Review of the Coulomb Friction Hypothesis . 339
10.1.2 Coulomb Friction in Multibody Systems: Sliding
Condition 341
10.1.3 Coulomb Friction in Multibody Systems: Stiction
Condition 343
10.2 Impacts and Collisions 345
10.2.1 Known Impact Forces 346
10.2.2 Impacts Between Bodies 348 .
10.3 Backlash 351 .
10.3.1 Planar Revolute Joint 352
10.3.2 Planar Prismatic Joint 354 .
10.4 Kinematic Synthesis 356 .
10.5 Sensitivity Analysis and Optimization 362
10.6 Singular Positions 366
References 373 .
11 Forward Dynamics of Flexible Multibody Systems .3 7 5
11.1 An Overview 375 .
11.2 The Classical Moving Frame Approach 377
11.2.1 Kinematics of a Flexible Body 378
11.2.2 Derivation of the Kinetic Energy 380 .
11.2.3 Derivation of the Elastic Potential Energy 383 .
11.2.4 Potential of External Forces 38411.2.5 Constraint Equations 384 .
11.2.6 Governing Equations of Motion 386
11.2.7 Numerical Example . 387
11.3 Global Method Based on Large Rotation Theory 389 .
11.3.1 Kinematics of the Beam 389 .
11.3.2 A Nonlinear Beam Finite Element Formulation 390
11.3.3 Derivation of the Kinetic Energy 392 .
11.3.4 Derivation of the Elastic Potential Energy 394 .
11.3.5 Constraint Equations 399 .
11.3.6 Governing Equations of Motion 400
11.3.7 Numerical Examples 401 .
References 407 .
12 Inverse Dynamics of Flexible Multibodies 4 0 9 .
12.1 Inverse Dynamics Equations for Planar Motion 410
12.1.1 Inverse Dynamics Equations of an Individual Link 411
12.1.2 Solution of the Inverse Dynamics for an Individual
Link . 414
12.1.2.1 The Time Invariant Case 414
12.1.2.2 The Time Varying Case . 419
12.2 Recursive Inverse Dynamics for Open-Chain Configurations . 420
12.2.1 The Planar Open-Chain Case 420
12.2.2 The Spatial Open-Chain Case 421 .
12.3 Non-Recursive Inverse Dynamics . 422
12.3.1 A Planar Open-Chain Example 425
12.3.2 A Planar Closed-Chain Example 430
Appendix 431
References 433 .


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عدد المساهمات : 15047
التقييم : 24853
تاريخ التسجيل : 01/07/2009
العمر : 30
الدولة : مصر
العمل : مدير منتدى هندسة الإنتاج والتصميم الميكانيكى
الجامعة : المنوفية

مُساهمةموضوع: رد: كتاب Kinematic and Dynamic Simulation of Multibody Systems    الخميس 03 يناير 2013, 11:01 pm

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