A recursive method for the dynamic analysis of a system of rigid bodies in plane motion

Abstract

In this study, a recursive method for generating the equations of motion of a system of rigid bodies with all common types of kinematic joints in plane motion is presented. The method rests upon the idea of replacing the rigid body by a dynamically equivalent system of particles with added geometric constraints that fix the distance between the particles. Some kinematic constraints due to common types of kinematic joints are automatically eliminated. The concepts of linear and angular momentums are used to generate the rigid body equations of motion without either introducing any rotational coordinates or distributing the external forces and moments over the particles. For the open loop case, the equations of motion are generated recursively along the open chains. For the closed loop case, the system is transformed to open loops by cutting suitable kinematic joints with the addition of cut-joints kinematic constraints. An example of a multi-branch closed-loop system is chosen to demonstrate the generality and simplicity of the proposed method.