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Constraint and Singularity Analysis of Lower-Mobility Parallel Manipulators With Parallelogram Joints

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

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

Paper No. DETC2010-28483, pp. 1317-1326; 10 pages
  • ASME 2010 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
  • Volume 2: 34th Annual Mechanisms and Robotics Conference, Parts A and B
  • Montreal, Quebec, Canada, August 15–18, 2010
  • Conference Sponsors: Design Engineering Division and Computers in Engineering Division
  • ISBN: 978-0-7918-4410-6 | eISBN: 978-0-7918-3881-5
  • Copyright © 2010 by ASME


This paper presents a general approach to analyze the singularities of lower-mobility parallel manipulators with parallelogram joints. Using screw theory, the concept of twist graph is introduced and the twist graphs of two types of parallelogram joints are established in order to simplify the constraint analysis of the manipulators under study. Using Grassmann-Cayley Algebra, the geometric conditions associated with the dependency of six Plücker vectors of finite and infinite lines in the 3 -dimensional projective space are reformulated in the superbracket in order to derive the geometric conditions for parallel singularities. The methodology is applied to three lower-mobility parallel manipulators with parallelogram joints: the Delta-linear robot, the Orthoglide robot and the H4 robot. The geometric interpretations of the singularities of these robots are given.

Copyright © 2010 by ASME
Topics: Manipulators



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