Equations of motion of serial chains in spatial motion using a recursive algorithm

Abstract

In the present study, a recursive algorithm for generating the equations of motion of serial chains that undergo spatial motion is presented. The method is based on treating each rigid body as a collection of constrained particles. Then, the force and moment equations are used to generate the rigid body equations of motion in terms of the Cartesian coordinates of the dynamically equivalent constrained system of particles, without introducing any rotational coordinates and the corresponding rotation matrices. For the open loop case, the equations of motion are generated recursively along the serial chains. Closed loop systems are transformed to open loop systems by cutting suitable kinematic joints and introducing cutjoint constraints. The method is simple and suitable for computer implementation. An example is chosen to demonstrate the generality and simplicity of the developed formulation.