A recursive method for the dynamic analysis of mechanical systems in spatial motion

摘要

In the present study, a recursive method for generating the equations of motion of mechanical systems that undergo spatial motion is presented. The method uses the force and moment equations to generate the rigid body equations of motion in terms of the Cartesian coordinates of a 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 cut-joint constraints. The method is simple and suitable for computer implementation. An example is chosen to demonstrate the generality and simplicity of the developed formulation.