Equations of motion of planar mechanical systems based on particle dynamics and a recursive algorithm

Abstract

In the present study, the equations of motion for planar mechanical systems that consist of interconnected rigid bodies with common types of kinematic joint are derived on the basis of particle dynamics and a recursive approach. The system of rigid bodies is replaced by a dynamically equivalent constrained system of particles. Then, for the resulting equivalent system of particles, the concepts of linear and angular momenta are used to generate the equations of motion without either introducing any rotational coordinates or distributing the external forces and force couples over the particles. For an open-loop system, the equations of motion are generated recursively along the open chains. For a closed-loop system, the system is transformed to open chains by cutting suitable kinematic joints with the addition of cut-joint kinematic constraints. Examples of multibranch closed-loop systems are chosen to demonstrate the generality and simplicity of the proposed method.