Precomputational methods for efficient solution of constrained multibody dynamics.

Abstract

This dissertation is concerned with achieving highly efficient simulation of constrained mechanical systems. The presented techniques may be used to obtain more efficient and general computer based dynamics modeling and simulation algorithms with the potential real-time applications. In order to achieve highly efficient simulation of constrained mechanical systems and to reduce run-time overhead, special off-line precomputation techniques are developed. In this development, the techniques to precompute the trajectory of constrained systems with idealized rigid joints have been extended to precompute the trajectory of constrained systems with deformable joints. Taylor series expansion is applied around the rigid joints to incorporate the joint flexibility into the formulation. The formulations of kinematic analysis of constrained system with deformable joints are developed for off-line precomputing. The special joint subspace projection technique is developed to incorporate relations between a set of equivalent joints and the original deformable joints. This technique can be a powerful tool in the engineering design process. In addition, a QR based special numerical precomputational procedure to determine a suitable set of independent joint variables is extensively discussed and demonstrated by a numerical example. A special kinematic loop decoupling technique is proposed and illustrated by an example of a vehicle suspension system for precomputing the dependent variables and their velocities and acceleration coefficients. These dependent variables and their associated velocities and accelerations may be interpolated as functions of the selected independent quantities. Spatial algebra, which provides the tool to encapsulate detailed information into simple objects due to its homogeneous structure, has been extensively used through this development work. Spatial algebra allows rotational and translational quantities to be combined into single matrix expressions and to be manipulated together as single objects, which can then be abstracted to large-scale systems through block matrix representation. A final example of a vehicle front suspension coupled with the steering system is used to demonstrate the developed precomputational methods.