Instantaneous Invariants and Curvature Analysis of a Planar Four-Link Mechanism

[+] Author and Article Information
An Tzu Yang

Department of Mechanical and Aeronautical Engineering, University of California, Davis, Davis, CA 95616-5294

G. R. Pennock

School of Mechanical Engineering, Purdue University, West, Lafayette, IN 47907-1288

Lih-Min Hsia

Department of Mechanical Engineering, California State University, Los Angeles, CA 90032-8153

J. Mech. Des 116(4), 1173-1176 (Dec 01, 1994) (4 pages) doi:10.1115/1.2919504 History: Received December 01, 1993; Revised August 01, 1994; Online June 02, 2008


This paper shows that the canonical system and the instantaneous invariants for a moving plane, which is connected to the fixed plane by a revolute-revolute crank, are functions of the derivatives of the crank angle. Then closed-form expressions are derived for the curvature ratios of the path generated by an arbitrary point fixed in the moving plane, in terms of the coordinates of the point and the instantaneous invariants of the plane. For illustrative purposes, numerical results are presented for the instantaneous invariants (up to the fourth-order) of the coupler of a specified crank-rocker mechanism, as a function of the input angle. In addition, the paper shows the variation in the first and second curvature ratios of an arbitrary coupler curve during the complete operating cycle of the mechanism. The authors hope that, based on the results presented here, a variety of useful tools for the kinematic design of planar mechanisms, with a rotary input, will be developed for plane rigid body guidance as well as curve generation.

Copyright © 1994 by The American Society of Mechanical Engineers
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