Nonlinear Modeling of Kinematic and Flexibility Effects in Manipulator Design

Abstract

This paper presents a finite-element-based, nonlinear model to predict the dynamic response of spatial manipulators with flexible links. The methodology takes into account the complete nonlinear coupling effects between the nonlinear gross motion of the links and their deformations due to distributed elasticity. The end-effector performance is predicted for commanded joint motion profiles, when the above nonlinear coupling is taken into account. A simple and efficient finite-element scheme has been developed using a Newton–Euler formulation and Timoshenko Beam Theory. In addition to the spatial manipulators, a particularized methodology is developed for the analysis of planar manipulators. Case studies of both planar and spatial manipulators are presented. Nonlinear kinematic coupling effects are observed to contribute significantly to end-effector positioning errors in flexible manipulator configurations.