Efficient Modelling of Elastic Mechanisms Using Orthogonal Coordinates

Abstract

A systematic method is presented for deriving the equations of motion of mechanisms involving multiple elastic structures connected together by any form of driven or undriven joints. It is assumed that deformations within components are small but there is no restriction on joint motions. Orthogonal coordinates are used to decouple the linear, angular and elastic partitions. The deformation coordinates represent a finite number of the free modes of vibration of each component. Algebraic constraint equations are defined generally for common joints and any new constraints are automatically generated using symbolic techniques. The chosen coordinates and the method of formulating the equations allow efficient numerical solution.