Coupling Effects of Kinematics and Flexibility in Manipulators

Abstract

This paper presents a finite, element-based, nonlinear model of flexibility effects in manipulators. The model allows for the coupling effects due to elastic deformations of the manip ulator links and the kinematics at the manipulator joints. The governing equations of motion are derived including the effects of rotatory inertia, shear deformation. and the effects of gross nonlinear motion of each of the links. Using Timo shenko beam theory, a simple and efficient finite element is proposed for the manipulator links. The complete dynamic model is further integrated with a simplistic representation of actuator-servo effects. The model is described in detail for the case of a planar manipulator with revolute joints. The same model can also be extended to spatial manipulators with prismatic pairs.