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Conceptual Design of Lower-Mobility Parallel Manipulators Based on Wrench Graphs

[+] Author Affiliations
Gamal El-Ghazaly

Université Montpellier 2, Montpellier, France

Stéphane Caro

CNRS-IRCCyN, Nantes, France

Paper No. DETC2014-35494, pp. V05AT08A074; 13 pages
doi:10.1115/DETC2014-35494
From:
  • 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

abstract

This paper presents a design methodology for lower-mobility parallel manipulators based on classification of wrench systems into four main classes. Wrench systems are represented in a three-dimensional projective space ℙ3 using wrench graphs where it is easy to incorporate geometric constraints to have simple singularity conditions using Grassmann-Cayley algebra (GCA). The main idea of the approach is to design a PM with an overall (constraint and actuation) wrench system that complies with a given wrench graph for which singularity conditions have been predetermined. The main advantage of this methodology is that the singularity conditions are already known a priori and consequently, it gives an opportunity to avoid such conditions at the design stage and make them unreachable. In the worst case scenario, where none of singularity conditions cannot be avoided, one can have a PM with known singular configurations which are always difficult to determine for already designed manipulators. As illustrative examples, two different five degrees-of-freedom (dof) mechanisms have been designed based on some of the defined wrench graphs giving 3T2R motion pattern. The first mechanism has some avoided singularities and the second one is free of singularity.

Copyright © 2014 by ASME

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