RESEARCH PAPERS: Mechanisms Papers

Application of the Vector-Network Method to Constrained Mechanical Systems

[+] Author and Article Information
Tai-Wai Li

Ontario Robotics Centre, Peterborough, Ontario, Canada K9J 5K2

Gordon C. Andrews

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

J. Mech., Trans., and Automation 108(4), 471-480 (Dec 01, 1986) (10 pages) doi:10.1115/1.3258757 History: Received July 10, 1986; Online November 19, 2009


The vector-network technique is a methodical approach to formulating equations of motion for unconstrained dynamic systems, utilizing concepts from graph theory and vectorial mechanics; it is ideally suited to computer applications. In this paper, the vector-network theory is significantly improved and extended to include constrained mechanical systems with both open and closed kinematic chains. A new formulation procedure is developed in which new kinematic constraint elements are incorporated. The formulation is based on a modified tree/cotree classification, which deviates significantly from previous work, and reduces the number of equations of motions to be solved. The dynamic equations of motion are derived, with generalized accelerations and a subset of the reaction forces as solution variables, and a general kinematic analysis procedure is also developed, similar to that of the dynamic formulation. Although this paper restricts most discussions to two-dimensional (planar) systems, the new method is equally applicable to 3-dimensional systems.

Copyright © 1986 by ASME
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