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Workspace Analysis and Visualization of Mechanical Manipulators With Non-Unilateral Constraints

[+] Author Affiliations
Jingzhou Yang, Karim Abdel-Malek

University of Iowa, Iowa City, IA

Paper No. DETC2005-84180, pp. 717-726; 10 pages
  • ASME 2005 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
  • Volume 7: 29th Mechanisms and Robotics Conference, Parts A and B
  • Long Beach, California, USA, September 24–28, 2005
  • Conference Sponsors: Design Engineering Division and Computers and Information in Engineering Division
  • ISBN: 0-7918-4744-6 | eISBN: 0-7918-3766-1
  • Copyright © 2005 by ASME


An analytical method is presented to obtain all surfaces enveloping the workspace of a general n degree-of-freedom mechanism with non-unilateral constraints. The method is applicable to kinematic chains that can be modeled using the Denavit-Hartenberg representation method for serial manipulators. The method introduced in this paper is based upon analytical criteria for determining singular behavior of the mechanism. A perturbation approach is implemented to determine the interior and exterior of the workspace. The complete mathematical formulation is presented and illustrated using 3 and 4 DOF spatial manipulators. The paper present a rigorous analysis of the sub-Jacobians to determine a classification of singularities: Type I sets are position Jacobian singularities; Type II sets are instantaneous singularities that are due to a generalized joint that is reaching its apex; Type III sets are domain boundary singularities, which are associated with the initial and final values of the time interval; Type IV sets are coupled singularities, which are associated with a relative singular Jacobian, where the null space is reduced in one submatrix due to either of two occurrences: a Type II or Type III singularities. The paper presents a general formulation for determining the workspace.

Copyright © 2005 by ASME



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