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.
- Design Engineering Division and Computers in Engineering Division
A General Methodology for the Forward Kinematic Problem of Symmetrical Parallel Mechanisms and Application to 5-PRUR Parallel Mechanisms (3T2R)
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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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