Finite difference and finite element simulation of flexible manipulators

Abstract

This chapter presents numerical approaches based on finite difference (FD) and finite element (FE) techniques for dynamic simulation of single-link flexible manipulator systems. A finite-dimensional simulation of the flexible manipulator system is developed using an FD discretisation of the dynamic equation of motion of the manipulator. A methodology is then presented for obtaining the dynamic model of a lightweight flexible manipulator using FE/Lagrangian technique. Structural damping, hub inertia and payload are incorporated in the dynamic model, which is then represented in a state-space form. Simulation results characterising the dynamic behaviour of the manipulator are presented and discussed for both FD and FE methods. A comparative study of the FD and the FE methods of dynamic modelling of flexible manipulators on the basis of computational accuracy, efficiency and demand are then considered. The performance of the algorithms is assessed with experimental results in time and frequency domains.