On the Geometry of Spatial Polygons and Screw Polygons

[+] Author and Article Information
C. Mavroidis

Department of Mechanical and Aerospace Engineering, Rutgers University, The State University of New Jersey, PO Box 909, Piscataway, NJ, 08855

B. Roth

Department of Mechanical Engineering, Stanford University, Stanford, California 94305

J. Mech. Des 119(2), 246-252 (Jun 01, 1997) (7 pages) doi:10.1115/1.2826243 History: Received July 01, 1996; Revised December 01, 1996; Online December 11, 2007


In this paper we study spatial polygons which are closed figures composed of ordered sets of lines and their common normals. It is shown how to solve for up to six of the parameters which define a polygon’s geometry, after all the other parameters are specified. It is also shown that when screws are used instead of lines, the resulting figures, called screw polygons, can be analyzed in order to determine up to twelve parameters, provided all the other parameters which define the screws and the screw polygon are known. Finally, it is pointed out that these results have many potential uses in kinematics.

Copyright © 1997 by The American Society of Mechanical Engineers
Topics: Screws , Geometry , Kinematics
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