Dynamic Modeling of Geared Robotic Mechanisms— The Virtual Link Approach

Abstract

In this paper, an efficient and systematic methodology for the formulation of dynamic equations of a general class of geared robotic mechanisms is developed. The concepts of primary links and secondary links of the manipulator are used to organize the analysis. The approach is based on the idea that the contribution to the generalized inertia forces of a secondary link can be divided into two parts. The first part is due to the motion of its associated primary link and the second part is due to the motion relative to its associated primary link. The concept of virtual link is introduced to incorporate the first part of the generalized inertia force contribution with those of primary links. The second part of the generalized inertia force contribution is derived by Lagrangian formulation. It is shown that the coupling effects of secondary links in the dynamic equations of motion can be identified individually and systematically. A 3-dof geared robotic mechanism is used to illustrate the methodology.