In this paper, a general methodology is introduced in order to formulate the FKP of symmetrical parallel mechanisms in a 7-dimensional projective space by the means of the so-called Study’s parameters. The main objective is to consider rigid-body displacement, and consequently the FKP, based on algebraic geometry, rather than rely on classical recipes, such as Euler angles, to assist in problem-solving. The state of the art presented in this paper is general and can be extended to other types of symmetrical mechanisms. In this paper, we limit the concept of kinematic mapping to topologically symmetrical mechanisms, i.e., mechanisms with limbs having identical kinematic arrangement. Exploring the FKP in a higher dimensional space is more challenging since it requires the use of a larger number of coordinates. There are, however, advantages in adopting a large set of coordinates, since this approach leads to expressions with lower degree that do not involve trigonometric functions.
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ASME 2010 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
August 15–18, 2010
Montreal, Quebec, Canada
Conference Sponsors:
- Design Engineering Division and Computers in Engineering Division
ISBN:
978-0-7918-4410-6
PROCEEDINGS PAPER
A General Methodology for the Forward Kinematic Problem of Symmetrical Parallel Mechanisms and Application to 5-PRUR Parallel Mechanisms (3T2R)
Mehdi Tale Masouleh,
Mehdi Tale Masouleh
Universite´ Laval, Que´bec, QC, Canada
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Manfred Husty,
Manfred Husty
University of Innsbruck, Innsbruck, Austria
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Cle´ment Gosselin
Cle´ment Gosselin
Universite´ Laval, Que´bec, QC, Canada
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Mehdi Tale Masouleh
Universite´ Laval, Que´bec, QC, Canada
Manfred Husty
University of Innsbruck, Innsbruck, Austria
Cle´ment Gosselin
Universite´ Laval, Que´bec, QC, Canada
Paper No:
DETC2010-28222, pp. 1279-1288; 10 pages
Published Online:
March 8, 2011
Citation
Tale Masouleh, M, Husty, M, & Gosselin, C. "A General Methodology for the Forward Kinematic Problem of Symmetrical Parallel Mechanisms and Application to 5-PRUR Parallel Mechanisms (3T2R)." Proceedings of the 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. pp. 1279-1288. ASME. https://doi.org/10.1115/DETC2010-28222
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