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New Simplified Three-Spheres Intersection Algorithm for the Forward Pose Kinematics of Cable-Suspended Robots

[+] Author Affiliations
Robert L. Williams, II, Noah Needler

Ohio University, Athens, OH

Paper No. DETC2014-35185, pp. V05AT08A097; 9 pages
  • ASME 2014 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
  • Volume 5A: 38th Mechanisms and Robotics Conference
  • Buffalo, New York, USA, August 17–20, 2014
  • Conference Sponsors: Design Engineering Division, Computers and Information in Engineering Division
  • ISBN: 978-0-7918-4636-0
  • Copyright © 2014 by ASME


A novel simplified analytical three-spheres intersection algorithm is presented for use with forward pose kinematics solutions of a four-cable-suspended robot (the method is applicable to various other cable-suspended robots with equal pole heights and three cables intersecting in one point). It is required that the vertical center heights of all three spheres are equal (otherwise one can use the existing more-complicated algorithm). We derive this new algorithm and show that the multiple solutions, algorithmic singularity, and imaginary solutions do not cause any trouble in practical implementation. The algorithmic singularity of the original three-spheres intersection algorithm regarding equal Z heights is eliminated with the new algorithm. The new algorithm requires significantly less computation compared with the original algorithm. Examples are presented to demonstrate the new three-spheres intersection algorithm for a 4-cable robot.

Copyright © 2014 by ASME



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