Inverse dynamic analysis of mechanical systems in joint coordinate space

Abstract

An inverse dynamic analysis algorithm for spatial flexible mechanical systems with closed loops is developed in the relative joint coordinate space. System equations of motion and constraint acceleration equations are derived using the velocity transformation technique. An inverse velocity transformation operator, which transforms the Cartesian velocities to the relative velocities, is derived systematically, corresponding to the types of kinematic joint connecting the bodies. Using the resulting matrix, the joint reaction forces and moments are analysed in the Cartesian coordinate space. The joint coordinates and the deformation modal coordinates are used as the generalized coordinates of a flexible mechanical system. The algorithm is verified by means of two numerical examples.