RESEARCH PAPERS: Mechanism Papers

Motion Synthesis Using Kinematic Mappings

[+] Author and Article Information
B. Ravani

Department of Mechanical Engineering, University of Wisconsin, Madison, Wisc. 53706

B. Roth

Department of Mechanical Engineering, Stanford University, Stanford, Calif. 94305

J. Mech., Trans., and Automation 105(3), 460-467 (Sep 01, 1983) (8 pages) doi:10.1115/1.3267382 History: Received May 13, 1982; Online November 19, 2009


This paper studies planar motion approximation problems in the context of a kinematic mapping. Since a planar displacement is determined by three parameters, it can be mapped into a point of a three-dimensional space. A (single-degree-of-freedom) planar motion can, therefore, be represented by a space curve in the space of the mapping and the problem of motion approximation becomes a curve fitting problem in this space. A mapping introduced by Blaschke is used and a general theory for planar motion approximation is developed. The theory is then applied to dimensional synthesis of four-link mechanisms. Furthermore, since the structural error (i.e., the quality of motion approximation) is dependent on the closeness of the fit in the space of the mapping, a general algebraic theory for determining closest fits to points in this space is developed. The theory is illustrated by a numerical example.

Copyright © 1983 by ASME
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