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An Algebraic Elimination Based Algorithm for Solving the Geometric Design Problem of Spatial 3R Manipulators

[+] Author Affiliations
Eric Lee

Rutgers University, Piscataway, NJ

Constantinos Mavroidis

Northeastern University, Boston, MA

Paper No. DETC2004-57570, pp. 1457-1463; 7 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


In this paper, the geometric design problem of serial-link robot manipulators with three revolute (R) joints when three precision points are specified is solved using an algebraic elimination method for the first time. Three spatial positions and orientations are defined and the dimensions of the geometric parameters of the 3-R manipulator are computed so that the manipulator will be able to place its end-effector at these three pre-specified locations. In this problem, six of the design parameters are set as free choices and their values are selected arbitrarily. For the specific case studied in this paper, a twelve-degree single variable polynomial is calculated that has eight roots that are the design solutions and the other four roots are extraneous solutions.

Copyright © 2004 by ASME



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