Dynamic modelling of planar flexible manipulators: Computational and algorithmic efficiency

Abstract

Traditionally, many robot arms are very rigid in construction; this was believed to be necessary for accurate placement and repeatability but led to higher material costs and increased energy consumption. Higher operational speeds and the use of lightweight materials cause elastic deformations to occur during the operation of the manipulator. These deformations degrade the path-tracking performance of the end-effector. The dynamic behaviour of a flexible manipulator is described mathematically by non-linear equations which are difficult to solve analytically. Unfortunately, there is currently no experimental information available with which to compare this design of flexible structure. For design and control purposes, it is suggested in this paper that it is more appropriate to employ approximate solutions with the emphasis on the development of a fast computational algorithm. An analytical study was undertaken to investigate the relevant uncertainties that are either inappropriately described or unavailable in the literature. The purpose of the paper is essentially to include the initial deflections in the simulation, to select the size of the time step, to select the models for emulating the end-effector, payload and joint actuator and, finally, to suppress the uncontrollable off-plane vibrations when encountered. When this knowledge has been obtained, the design and development of the simulation process can begin. In order to demonstrate the practicability of the open-loop simulation proposed and test the software, two representative models were investigated.