A Variational Principle for the Elastodynamic Motion of Planar Linkages

[+] Author and Article Information
B. S. Thompson

Dundee University, Dundee, Scotland

A. D. S. Barr

Mechanical Engineering, Dundee University, Dundee, Scotland

J. Eng. Ind 98(4), 1306-1312 (Nov 01, 1976) (7 pages) doi:10.1115/1.3439105 History: Received June 21, 1976; Online July 15, 2010


A variational principle is presented that may be used for setting up the equations describing the elastodynamic motion of planar linkages in which all the members are considered to be flexible. These systems are modeled as a set of continua in which elastic deformations are superimposed on gross rigid-body motions. Displacement continuity at pin joints, or any other special constraints that are peculiar to the linkage being analyzed, are incorporated by the use of Lagrange multipliers. By permitting independent variations of the stress, strain, displacement, and velocity parameters for each link approximate equations of motion, boundary and compatibility conditions for the complete mechanism may be systematically constructed. As an illustrative example, the derivation of the problem definition for a flexible slider-crank mechanism is given.

Copyright © 1976 by ASME
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