DYNAMIC SIMULATION OF CONSTRAINED THREE DIMENSIONAL MULTI-BODY SYSTEMS USING VECTOR NETWORK TECHNIQUES

This thesis presents a significant extension of a new approach to the problem of motion prediction. A comprehensive mathematical model for the systematic formulation of the equations of motion of dynamic three-dimensional constrained multi-body systems is derived. The entire procedure is a basic application of concepts of graph theory in which laws of vector dynamics have been combined.

The method casts simultaneously the three-dimensional inertia equations associated with each rigid body and the geometrical expressions corresponding to the kinematic restrictions into a symmetrical format yielding the differential equations governing the motion of the system. The modelling technique is thoroughly described in this work and its validity is impartially established.

The analytical procedure was successfully implemented within a general-purpose digital simulation program. The computerized algorithm is a "self-formulating" program since from a minimal definition of the mechanism, it will automatically predict the behavior of the system as output, thereby giving the impression that the equations governing the motion of the mechanical system have been completely formulated and solved by the computer. Throughout the dissertation simulations are made of the response of several sample mechanical systems, including a rail vehicle system, which demonstrate the validity, applicability and self-formulating aspect of the automated model.