A simplified recursive formulation for the dynamic analysis of planar mechanisms

Abstract

In the present paper, a numerical method for generating the equations of motion of planar mechanisms with only revolute joints is presented. The method rests upon the idea of replacing the rigid body by a dynamically equivalent constrained system of particles. For the open loop case, the equations of motion are generated recursively along the open chains. Geometric constraints that fix the distance between the particles are introduced. For the closed loop case, the system is transformed to open loops by cutting suitable kinematic joints with the addition of kinematic constraints. The method is conceptually easy and suitable for computer implementation. It eliminates the necessity of distributing the external forces and moments over the particles and uses the concepts of linear and angular momentums to generate the rigid body equations of motion without introducing any rotational coordinates. An example with closed loops is chosen to demonstrate the generality and simplicity of the proposed method.