Kinematic and Dynamic Simulation of Multibody Systems

1 Introduction and Basic Concepts.- 1.1 Computer Methods for Multibody Systems.- 1.2 Basic Concepts.- 1.3 Types of Problems.- 1.4 Summary.- References.- 2 Dependent Coordinates and Related Constraint Equations.- 2.1 Planar Multibody Systems.- 2.2 Spatial Multibody Systems.- 2.3 Comparison Between Reference Point and Natural Coordinates.- 2.4 Concluding Remarks.- References.- Problems.- 3 Kinematic Analysis.- 3.1 Initial Position Problem.- 3.2 Velocity and Acceleration Analysis.- 3.3 Finite Displacement Analysis.- 3.4 Redundant Constraints.- 3.5 Subspace of Allowable Motions.- 3.6 Multibody Systems with Non-Holonomic Joints.- References.- Problems.- 4 Dynamic Analysis. Mass Matrices and External Forces.- 4.1 Background on Analytical Dynamics.- 4.2 Inertial Forces. Mass Matrix.- 4.3 External Forces.- References.- Problems.- 5 Dynamic Analysis. Equations of Motion.- 5.1 Formulations in Dependent Coordinates.- 5.2 Formulations in Independent Coordinates.- 5.3 Formulations Based on Velocity Transformations.- 5.4 Formulations Based on the Canonical Equations.- References.- Problems.- 6 Static Equilibrium Position and Inverse Dynamics.- 6.1 Static Equilibrium Position.- 6.2 Inverse Dynamics.- References.- 7 Numerical Integration of the Equations of Motion.- 7.1 Integration of Ordinary Differential Equations.- 7.2 Integration of Differential-Algebraic Equations.- 7.3 Considerations for Real-Time Simulation.- References.- Problems.- 8 Improved Formulations for Real-Time Dynamics.- 8.1 Survey of Improved Dynamic Formulations.- 8.2 Velocity Transformations for Open-Chain Systems.- 8.3 Velocity Transformations for Closed-Chain Systems.- 8.4 Examples Solved by Velocity Transformations.- 8.5 Special Implementations Using Dependent Natural Coordinates.- References.- 9 Linearized Dynamic Analysis.- 9.1 Linearization of the Differential Equations of Motion.- 9.2 Numerical Computation of Derivatives.- 9.3 Numerical Evaluation of the Dynamic Response.- References.- 10 Special Topics.- 10.1 Coulomb Friction.- 10.2 Impacts and Collisions.- 10.3 Backlash.- 10.4 Kinematic Synthesis.- 10.5 Sensitivity Analysis and Optimization.- 10.6 Singular Positions.- References.- 11 Forward Dynamics of Flexible Multibody Systems.- 11.1 An Overview.- 11.2 The Classical Moving Frame Approach.- 11.3 Global Method Based on Large Rotation Theory.- References.- 12 Inverse Dynamics of Flexible Multibodies.- 12.1 Inverse Dynamics Equations for Planar Motion.- 12.2 Recursive Inverse Dynamics for Open-Chain Configurations.- 12.3 Non-Recursive Inverse Dynamics.- References.