Dynamics of Flexible Manipulator Arms: Alternative Derivation, Verification, and Characteristics for Control

[+] Author and Article Information
B.-S. Yuan

Nikon Precision Research Center, Belmont, CA 94002

W. J. Book, J. D. Huggins

School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA 30332

J. Dyn. Sys., Meas., Control 115(3), 394-404 (Sep 01, 1993) (11 pages) doi:10.1115/1.2899115 History: Received August 22, 1990; Revised July 24, 1992; Online March 17, 2008


This work seeks to provide an effective way for developing the dynamics of a multi-link flexible manipulator consisting of rotary joints connecting two links. Kinematics of both the rotary joint motion and the link deformation are described by 4×4 transformation matrices as proposed in previous works (Book, 1984). The link deflection is assumed small so that the link transformation can be composed of summations of assumed link shapes. To determine the appropriate choice of component mode shapes, two essential techniques employed here are experimental and finite element methods. The resulting equations of motion allow the complete nonlinear model to be recursively derived from the Jacobian matrix and the mass properties via symbolic manipulation. Two prototype models of flexible manipulators are used to verify the dynamics with frequency and time responses. This paper contributes several new results: (1) the velocity terms (Coriolis and centrifugal forces) are related to variations in the mass matrix, (2) the skew symmetry of certain useful terms are shown, (3) the system is theoretically demonstrated to be stable with joint P.D. controllers in addition to an experimental approach, (4) practical and effective incorporation of actuator dynamics (hydraulic cylinder) and structural complexity (non-uniform cross section) is achieved through selection of mode shapes, (5) geometric constraints are incorporated through simplified coordinate transformations and (6) the results are verified on two physical cases.

Copyright © 1993 by The American Society of Mechanical Engineers
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