Dynamic Analysis of Geared Robotic Mechanisms Using Graph Theory

Abstract

In this paper, an efficient methodology for the dynamic analysis of geared robotic mechanisms is presented. The approach makes use of the topological structure of mechanical transmission lines to simplify the analysis. The links in a geared robotic mechanism are divided into several levels. Each level contains one primary link and several secondary links. It is shown that the inverse dynamic problem can be solved from the highest level links toward the base link, one or two levels at a time depending on the topological structure of the mechanical transmission lines. Thus, the inverse dynamic problem can be solved without the need of simultaneously solving the entire system of equations. A two degree-of-freedom manipulator is used to illustrate the procedure.