Dynamic Coupling Between the Joint and Elastic Coordinates in Flexible Mechanism Systems

Abstract

The aim of this investigation is to develop an efficient proce dure for decoupling the joint and elastic accelerations while maintaining the nonlinear inertia coupling between the rigid body motion and the elastic deformation. The inertia projec tion schemes used in most existing recursive methods for the dynamic analysis of flexible robotics and mechanism systems lead to dense coefficient matrices in the acceleration equations, and consequently there is a strong dynamic coupling between the joint and elastic coordinates. When the number of elastic degrees of freedom increases, the size of the coefficient matrix in the acceleration equations becomes large, and consequently the use of these recursive methods for solving for the joint and elastic accelerations becomes less efficient. This investigation discusses the problems associated with the inertia projection schemes used in the existing recursive methods, and it is shown that decoupling the joint and elastic accelerations using these methods requires the factorization of nonlinear matrices whose dimensions depend on the number of elastic degrees of freedom of the system. An amalgamated formulation that can be used to decouple the elastic and joint accelerations is then used to obtain a reduced system of equations whose dimension is in dependent of the number of elastic degrees of freedom of the system. This system can be solved for the joint accelerations as well as the joint reaction forces. The use of the procedure de veloped in this article is demonstrated using a four-bar flexible mechanism.