Kinematic and Dynamic Analysis for Closed-Loop Flexible Manufacturing Systems Using Nonlinear Recursive Method

Abstract

In this paper, a nonlinear recursive method for the dynamic and kinematic analysis of a closed-loop flexible manufacturing system is presented. The kinematic and dynamic models are developed using absolute reference, joint relative, and elastic coordinates as well as joint reaction forces. This recursive method leads to a system of loosely coupled equations of motion. In a closed-loop manufacturing system, cuts are made at selected secondary joints in order to form spanning tree structures. Compatibility conditions and reaction force relationships at the secondary joints are adjoined to the equations of open-loop manufacturing systems in order to form closed-loop kinematic and dynamic equations. Using the sparse matrix structure of these equations and the fact that the joint reaction forces associated with elastic degrees of freedom do not represent independent variables, a method for decoupling the joint and elastic accelerations is developed. Unlike existing recursive formulations, this method does not require inverse or factorization of large nonlinear matrices. The application of nonlinear recursive method in kinematic and dynamic analysis of closed-loop manufacturing systems is also discussed in this paper. The use of the numerical algorithm developed in this investigation is illustrated by a closed-loop flexible four-bar mechanism.