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A Matrix Based Mobility Criterion for Parallel Platforms

[+] Author Affiliations
José M. Rico

Universidad de Guanajuato, Guanajuato, Mexico

Luis D. Aguilera, Jaime Gallardo, Ramón Rodriguez, Horacio Orozco, Juan Manuel Barrera

Instituto Tecnológico de Celaya, Celaya, Guanajuato, Mexico

Paper No. DETC2005-84937, pp. 325-342; 18 pages
doi:10.1115/DETC2005-84937
From:
  • 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

abstract

This contribution presents a mobility criterion applicable to parallel platforms based on an analysis of the Jacobian matrices associated with the platform legs. It is important to note that this criterion is based on an analysis of the subalgebras of the Lie algebra, se(3), also known as screw algebra, of the Euclidean group, SE(3). The mathematical foundations of the method have been already presented in [1]. In this contribution it is shown that, employing a basic knowledge of linear algebra, it is possible to compute the correct mobility of a wider class of parallel manipulators, including the mobility of kinematically deficient parallel platforms and platforms with inactive pairs. Moreover, the criterion computes the passive degrees of freedom in parallel platforms. Finally, it should be emphasized that, unlike other attempts to develop a mobility criterion, the criterion developed in this contribution does not require any consideration of reciprocal screws.

Copyright © 2005 by ASME

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