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Spatial Distance of Point-Lines

[+] Author Affiliations
Yi Zhang, Kwun-Lon Ting

Tennessee Technological University, Cookeville, TN

Paper No. DETC2004-57450, pp. 1203-1210; 8 pages
  • ASME 2004 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
  • Volume 2: 28th Biennial Mechanisms and Robotics Conference, Parts A and B
  • Salt Lake City, Utah, USA, September 28–October 2, 2004
  • Conference Sponsors: Design Engineering Division and Computers and Information in Engineering Division
  • ISBN: 0-7918-4695-4 | eISBN: 0-7918-3742-4
  • Copyright © 2004 by ASME


A point-line is the combination of a directed line with a reference point on it. In this article, the spatial distance between two point-lines in space is defined based on a point-line displacement model. The displacement of a point-line from one position to the other is uniquely described as the composition of a pure translation along the point-line and a screw displacement about the common normal of the two positions. It is shown that such a displacement model leads to a simpler configuration of the underlying screw triangle and defines the shortest distance between two point-lines. The dual quaternion algebra is used to describe the idea with mathematic expressions.

Copyright © 2004 by ASME
Topics: Screws , Displacement



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