A Recursive Algorithm for Generating the Equations of Motion of a Chain of Rigid Rods in Spatial Motion

摘要

In this study a recursive algorithm for generating the equations of motion of a chain of rigid rods in spatial motion is presented. The method rests upon the idea of replacing rigid bodies by dynamically equivalent constrained systems of particles. The concepts of linear and angular momenta are used to generate the rigid body equations of motion without either introducing any rotational coordinates or the corresponding rotation matrices. For an open chain, the equations of motion are generated recursively along the serial chains. For a closed chain, the system is transformed to an open chain by cutting suitable kinematic joints and introducing cut-joint kinematic constraints.