Non-linear flexibility studies for spatial manipulators

A finite element based, nonlinear model is presented in this paper for revolute jointed spatial manipulators. The model allows for the nonlinear coupling effects between the nonlinear gross motions of the manipulator links and their elastic deformations. The governing equations of motion are derived including the effects of rotatory inertia, shear deformation, and the effects of the gross non-linear motion of each of the links. A simple and efficient finite element has been developed for the manipulator links using Timoshenko Beam Theory. The resulting methodology is shown to identify the effects of the nonlinear interactions on the dynamic positioning characteristics of the manipulator.