Dynamics and balancing of multibody systems

This book has evolved from the passionate desire of the authors in using the modern concepts of multibody dynamics for the design improvement of the machineries used in the rural sectors of India and The World. In this connection, the first author took up his doctoral research in 2003 whose findings have resulted in this book. It is expected that such developments will lead to a new research direction MuDRA, an acronym given by the authors to "Multibody Dynamics for Rural Applications. " The way Mu- DRA is pronounced it means 'money' in many Indian languages. It is hoped that practicing MuDRA will save or generate money for the rural people either by saving energy consumption of their machines or making their products cheaper to manufacture, hence, generating more money for their livelihood. In this book, the initial focus was to improve the dynamic behavior of carpet scrapping machines used to wash newly woven hand-knotted c- pets of India. However, the concepts and methodologies presented in the book are equally applicable to non-rural machineries, be they robots or - tomobiles or something else. The dynamic modeling used in this book to compute the inertia-induced and constraint forces for the carpet scrapping machine is based on the concept of the decoupled natural orthogonal c- plement (DeNOC) matrices. The concept is originally proposed by the second author for the dynamics modeling and simulation of serial and - rallel-type multibody systems, e. g.

1 Introduction	p. 1
1.1 Dynamics	p. 1
1.2 Formulation of Dynamic Analysis	p. 3
1.2.1 DAE vs. ODE	p. 4
1.2.2 Recursive formulations	p. 6
1.2.3 Velocity transformation methods	p. 7
1.3 Balancing of Mechanisms	p. 10
2 Dynamics of Open-loop Systems	p. 11
2.1 Kinematic Constraints in Serial Systems	p. 11
2.2 Kinematic Constraints in Tree-type Systems	p. 16
2.3 Equations of Motion	p. 19
2.4 Constraint Wrench for Serial Systems	p. 22
2.5 Constraint Wrench in Tree-type Systems	p. 25
2.6 Algorithm for Constraint Wrenches	p. 26
2.7 Applications	p. 29
2.7.1 Two-link manipulator	p. 29
2.7.2 Four link gripper	p. 32
2.7.3 Two six-link manipulators	p. 37
2.8 Summary	p. 40
3 Dynamics of Closed-loop Systems	p. 45
3.1 Equations of Motion	p. 45
3.1.1 Spanning tree	p. 46
3.1.2 Determinate and indeterminate subsystems	p. 48
3.1.3 The DeNOC matrices for the spanning tree	p. 49
3.1.4 Constrained equations of motion for a subsystem	p. 49
3.1.5 Constrained equations of motion for the spanning tree	p. 52
3.2 Algorithm for Constraint Wrenches	p. 52
3.3 Four-bar mechanism	p. 55
3.3.1 Equations of motion	p. 56
3.3.2 Numerical example	p. 60
3.4 Carpet Scrapping Machine	p. 63
3.4.1 Subsystem III	p. 66
3.4.2 Subsystem I	p. 69
3.4.3 Subsystem II	p. 71
3.4.4 Numerical example	p. 72
3.4.5 Computation efficiency	p. 76
3.5 Spatial RSSR Mechanism	p. 76
3.5.1 Subsystem approach	p. 78
3.5.2 Numerical example	p. 83
3.5.3 Computation efficiency	p. 86
3.6 Summary	p. 86
4 Equimomental Systems	p. 87
4.1 Equimomental Systems for Planar Motion	p. 87
4.1.1 Two point-mass model	p. 89
4.1.2 Three point-mass model	p. 90
4.2 Equimomental Systems for Spatial Motion	p. 93
5 Balancing of Planar Mechanisms	p. 99
5.1 Balancing of Shaking Force and Shaking Moment	p. 100
5.1.1 Equimomental system in optimization	p. 101
5.2 Balancing Problem Formulation	p. 102
5.2.1 Equations of motion	p. 102
5.2.2 Equations of motion for a point-mass system	p. 106
5.2.3 Shaking force and shaking moment	p. 110
5.2.4 Optimality criterion	p. 112
5.2.5 Mass redistribution method	p. 113
5.2.6 Counterweighting method	p. 114
5.3 Hoeken's Four-bar Mechanism	p. 118
5.3.1 Balancing of shaking force	p. 119
5.3.2 Optimization of shaking force and shaking moment	p. 121
5.4 Carpet Scrapping Mechanism	p. 130
5.5 Summary	p. 135
6 Balancing of Spatial Mechanisms	p. 137
6.1 Balancing Problem Formulation	p. 138
6.1.1 Dynamic equations of motion	p. 138
6.1.2 Shaking force and shaking moment	p. 141
6.1.3 Optimization problem	p. 142
6.2 Spatial RSSR Mechanism	p. 147
6.3 Summary	p. 157
Appendix A	p. 159
Appendix B	p. 163
References	p. 165
Index	p. 173

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