Automatic generation of motion equations for planar mechanical systems using the new set of “branch coordinates”

Abstract

A new set of “branch coordinates” are introduced and used to define the time-varying configuration of a planar multibody system with open and closed kinematic chains. The kinematic and dynamic equations are automatically generated in terms of these coordinates by a formulation procedure that combines graph-theoretic and orthogonal projection methods. A major advantage of this procedure is that the branch coordinates are chosen by the analyst by selecting the spanning trees of the linear graphs representing a given mechanical system. Criteria is given for selecting trees that result in a smaller number of motion equations than would be obtained using traditional absolute or joint coordinate formulations, both of which are special cases of the formulation presented here. Three examples are given to demonstrate this new approach to multibody dynamics.