RESEARCH PAPERS: Design Automation Papers

Computation of Spatial Displacements From Geometric Features

[+] Author and Article Information
B. Ravani

Computer Integrated Design and Manufacturing Laboratory, Department of Mechanical, Aeronautical, and Materials Engineering, University of California-Davis, Davis, CA 95616

Q. J. Ge

Department of Mechanical Engineering, University of New Orleans, New Orleans, LA 70148

J. Mech. Des 115(1), 95-102 (Mar 01, 1993) (8 pages) doi:10.1115/1.2919331 History: Received February 01, 1991; Online June 02, 2008


This paper develops the theoretical foundation for computations of spatial displacements from the simple geometric features of points, lines, planes, and their combinations. Using an oriented projective three space with a Clifford Algebra, all these three features are handled in a similar fashion. Furthermore, issues related to uniqueness of computations and minimum number of required features are discussed. It is shown that contrary to the common intuition, specification of a minimum of four points (planes) or three lines are necessary for computation of a unique displacement. Only when the sense of the orientations of these features are specified then the minimum number of required features reduces to three for points and planes and two for lines. The results, in addition to their theoretical interest in computational geometry of motion, have application in robot calibration.

Copyright © 1993 by The American Society of Mechanical Engineers
Topics: Computation
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