On the Geometry of Spatial Polygons and Screw Polygons-Reference-Cited by-同舟云学术

On the Geometry of Spatial Polygons and Screw Polygons

Published:1997-06-01 Issue:2 Volume:119 Page:246-252
ISSN:1050-0472
Container-title:Journal of Mechanical Design
language:en
Short-container-title:

Author:

Mavroidis C.¹,Roth B.²

Affiliation:

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

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

Abstract

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.

Publisher

ASME International

Subject

Computer Graphics and Computer-Aided Design,Computer Science Applications,Mechanical Engineering,Mechanics of Materials

Link

http://asmedigitalcollection.asme.org/mechanicaldesign/article-pdf/119/2/246/5920564/246_1.pdf

Reference20 articles.

1. Blaschke, W., 1960, Kinematik und Quaternionen, VEB Deutscher Verlag der Wissenshaften, Berlin.

2. Bottema, O., and Roth, B., 1979, Theoretical Kinematics, North Holland Publishing Company.

3. Chace M. A. , 1965, “Solutions to the Vector Tetrahedron Equation,” ASME Journal of Engineering for Industry, Vol. 87, Series B, pp. 228–234.

4. Denavit J. , and HartenbergR., 1955, “A Kinematic Notation for Lower Pair Mechanisms Based on Matrices,” ASME Journal of Applied Mechanics, Vol. 22, pp. 215–221.

5. Duffy, J., 1980, Analysis of Mechanisms and Robot Manipulators, John Wiley & Sons, New York.

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