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Geometric Constructions for Determining the Screw Reciprocal to Five Lines

[+] Author Affiliations
Curtis L. Collins

University of California at Irvine, Irvine, CA

Paper No. DETC2004-57413, pp. 1063-1072; 10 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


Screws reciprocal to five lines appear in the inverse Jacobian and statics equations of many serial and parallel robots. By closely examining the geometry of systems of five lines, a set of geometric procedures for computing reciprocal screws is derived. The methodology is based on the fact that one screw in a cylindroid reciprocal to four lines is reciprocal to a fifth independent line. The constructions are easy to implement and provide geometric insight into reciprocal screws and singularities.

Copyright © 2004 by ASME
Topics: Screws



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