Dynamics of Constrained Multibody Systems

[+] Author and Article Information
J. W. Kamman

Department of Aerospace and Mechanical Engineering, University of Notre Dame, Notre Dame, Ind. 46556

R. L. Huston

Department of Mechanical and Industrial Engineering, Location 72, University of Cincinnati, Cincinnati, Ohio 45221

J. Appl. Mech 51(4), 899-903 (Dec 01, 1984) (5 pages) doi:10.1115/1.3167743 History: Received October 01, 1983; Revised February 01, 1984; Online July 21, 2009


A new automated procedure for obtaining and solving the governing equations of motion of constrained multibody systems is presented. The procedure is applicable when the constraints are either (a) geometrical (for example, “closed-loops”) or (b) kinematical (for example, specified motion). The procedure is based on a “zero eigenvalues theorem,” which provides an “orthogonal complement” array which in turn is used to contract the dynamical equations. This contraction, together with the constraint equations, forms a consistent set of governing equations. An advantage of this formulation is that constraining forces are automatically eliminated from the analysis. The method is applied with Kane’s equations—an especially convenient set of dynamical equations for multibody systems. Examples of a constrained hanging chain and a chain whose end has a prescribed motion are presented. Applications in robotics, cable dynamics, and biomechanics are suggested.

Copyright © 1984 by ASME
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