Symbolic Closed-Form Modeling and Linearization of Multibody Systems Subject to Control

[+] Author and Article Information
Junghsen Lieh, Imtiaz-ul Haque

Department of Mechanical Engineering, Clemson University, Clemson, SC 29634

J. Mech. Des 113(2), 124-132 (Jun 01, 1991) (9 pages) doi:10.1115/1.2912760 History: Received April 01, 1990; Online June 02, 2008


Symbolic closed-form equation formulation and linearization for constrained multibody systems subject to control are presented. The formulation is based on the principle of virtual work. The algorithm is recursive, automatically eliminates the constraint forces and redundant coordinates, and generates the nonlinear or linear dynamic equations in closed-form. It is derived with respect to principal body coordinates and a moving reference frame that allows one to generate the dynamic equations for multibody systems moving along curved track or road. The output equations may be either in syntactically correct FORTRAN form or in the form as derived by hand. A procedure that simplifies the trigonometric expressions, linearizes the geometric nonlinearities, and converts the linearized equations in state-space form is included. Several examples have been used to validate the procedure. Included is a simulation using a seven-DOF automobile ride model with active suspensions.

Copyright © 1991 by The American Society of Mechanical Engineers
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