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Singularity Analysis of the 4-RUU Parallel Manipulator Based on Grassmann-Cayley Algebra and Grassmann Geometry

[+] Author Affiliations
Semaan Amine, Stéphane Caro, Philippe Wenger

Institut de Recherche en Communications et Cybernétique de Nantes, Nantes, France

Mehdi Tale Masouleh, Clément Gosselin

Université Laval, Québec, QC, Canada

Paper No. DETC2011-48226, pp. 1017-1026; 10 pages
doi:10.1115/DETC2011-48226
From:
  • ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
  • Volume 6: 35th Mechanisms and Robotics Conference, Parts A and B
  • Washington, DC, USA, August 28–31, 2011
  • Conference Sponsors: Design Engineering Division and Computers and Information in Engineering Division
  • ISBN: 978-0-7918-5483-9
  • Copyright © 2011 by ASME

abstract

This paper deals with the singularity analysis of parallel manipulators with identical limb structures performing Schönflies motions, namely, three independent translations and one rotation about an axis of fixed direction. The study is developed through the singularity analysis of the 4-R UU parallel manipulator. The 6 × 6 Jacobian matrix of such manipulators contains two lines at infinity, namely, two constraint moments, among its six Plücker lines. The Grassmann-Cayley Algebra is used to obtain geometric singularity conditions. However, due to the presence of lines at infinity, the rank deficiency of the Jacobian matrix for the singularity conditions is not easy to grasp. Therefore, a wrench graph representation for some singularity conditions emphasizes the linear dependence of the Plücker lines of the Jacobian matrix and highlights the correspondence between Grassmann-Cayley algebra and Grassmann geometry.

Copyright © 2011 by ASME

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