A Lagrangian Formulation of the Dynamic Model for Flexible Manipulator Systems

[+] Author and Article Information
K. H. Low, M. Vidyasagar

Department of Electrical Engineering, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1

J. Dyn. Sys., Meas., Control 110(2), 175-181 (Jun 01, 1988) (7 pages) doi:10.1115/1.3152668 History: Received October 10, 1987; Online July 21, 2009


This paper presents a procedure for deriving dynamic equations for manipulators containing both rigid and flexible links. The equations are derived using Hamilton’s principle, and are nonlinear integro-differential equations. The formulation is based on expressing the kinetic and potential energies of the manipulator system in terms of generalized coordinates. In the case of flexible links, the mass distribution and flexibility are taken into account. The approach is a natural extension of the well-known Lagrangian method for rigid manipulators. Properties of the dynamic matrices, which lead to a less computation, are shown. Boundary-value problems of continuous systems are briefly described. A two-link manipulator with one rigid link and one flexible link is analyzed to illustrate the procedure.

Copyright © 1988 by ASME
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