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Geometric Properties of Point-Line Trajectories

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

Tennessee Technological University, Cookeville, TN

Paper No. DETC2004-57296, pp. 781-788; 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 refers to the combination of a directed line with an endpoint along the line. To trace a point-line trajectory, one must control not only the trajectory of the endpoint but also the direction of the point-line. This paper examines point-line trajectories by regarding a point-line trajectory as the combination of the endpoint trajectory referred to as the directrix and the trajectory of a unit vector in the point-line direction referred to as the indicatrix. A point-line trajectory is therefore characterized by the characteristics of the directrix, indicatrix, and the relationship between them. The paper presents (1) the characteristic numbers to characterize a point-line trajectory, especially the relationship between the directrix and indicatrix; (2) concepts of velocity at the striction point, the shifting velocity along the striction curve, and the shifting speed along the point-line; (3) The visualization of a point-line motion up to the second order; (4) the coordination of the indicatrix and directrix. An example is given to demonstrate the orientation control of the point-line with respect to the point trajectory.

Copyright © 2004 by ASME



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