RESEARCH PAPERS: Design Automation Papers

A General and Efficient Method for Dynamic Analysis of Mechanical Systems Using Velocity Transformations

[+] Author and Article Information
S. S. Kim, M. J. Vanderploeg

Center for Computer Aided Design and Department of Mechanical Engineering, College of Engineering, The University of Iowa, Iowa City, IA 52242

J. Mech., Trans., and Automation 108(2), 176-182 (Jun 01, 1986) (7 pages) doi:10.1115/1.3260799 History: Received June 17, 1985; Online November 19, 2009


This paper presents a new formulation for the equations of motion of interconnected rigid bodies. This formulation initially uses Cartesian coordinates to define the position of the system, the kinematic joints between bodies, and forcing functions on and between bodies. This makes initial system definition straightforward. The equations of motion are then derived in terms of relative joint coordinates through the use of a velocity transformation matrix. The velocity transformation matrix relates relative coordinates to Cartesian coordinates. It is derived using kinematic relationships for each joint type and graph theory for identifying the system topology. By using relative coordinates, the equations of motion are efficiently integrated. Use of both Cartesian and relative coordinates produces an efficient set of equations without loss of generality. The algorithm just described is implemented in a general purpose computer program. Examples are used to demonstrate the generality and efficiency of the algorithms.

Copyright © 1986 by ASME
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