Simulation of Flexible-Link Manipulators With Inertial and Geometric Nonlinearities

[+] Author and Article Information
Chris Damaren

Department of Engineering, Royal Roads Military College, FMO Victoria, British Columbia, V0S 1B0

Inna Sharf

Department of Mechanical Engineering, University of Victoria, Victoria, British Columbia, Canada V8W 3P6

J. Dyn. Sys., Meas., Control 117(1), 74-87 (Mar 01, 1995) (14 pages) doi:10.1115/1.2798525 History: Received April 29, 1993; Revised February 11, 1994; Online December 03, 2007


Several important issues relevant to modeling of flexible-link robotic manipulators are addressed in this paper. First, we examine the question of which inertial nonlinearities should be included in the equations of motion for purposes of simulation. A complete model incorporating all inertial terms that couple rigid-body and elastic motions is presented along with a rational scheme for classifying them. Second, the issue of geometric nonlinearities is discussed. These are terms whose origin is the geometrically nonlinear theory of elasticity, as well as the terms arising from the interbody coupling due to the elastic deformation at the link tip. Accordingly, a general way of incorporating the well-known geometric stiffening effect is presented along with several schemes for treating the elastic kinematics at the joint interconnections. In addition, the question of basis function selection for spatial discretization of the elastic displacements is also addressed. The finite element method and an eigenfunction expansion techniques are presented and compared. All issues are examined numerically in the context of a simple beam example and the Space Shuttle Remote Manipulator System. Unlike a single-link system, the results for the latter show that all terms are required for accurate simulation of faster maneuvers. Hence, the conclusions of the paper are contrary to some of the previous findings on the validity of various models for dynamics simulation of flexible-body systems.

Copyright © 1995 by The American Society of Mechanical Engineers
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