Publication
A fast branch-and-prune algorithm for the position analysis of spherical mechanisms
Conference Article
Conference
IFToMM World Congress on Mechanism and Machine Science (IFToMM)
Edition
15th
Pages
549-558
Doc link
https://doi.org/10.1007/978-3-030-20131-9_55
File
Abstract
Different branch-and-prune schemes can be found in the literature for numerically solving the position analysis of spherical mechanisms. For the prune operation, they all rely on the propagation of motion intervals. They differ in the way the problem is algebraically formulated. This paper exploits the fact that spherical kinematic loop equations can be formulated as sets of 3 multi-affine polynomials. Multi-affinity has an important impact on how the propagation of motion intervals can be performed because a multi-affine polynomial is uniquely determined by its values at the vertices of a closed hyperbox defined in its domain.
Categories
optimisation, robots.
Author keywords
multi-affine polynomials, parallel spherical robots, forward kinematics, position analysis, branch-and-prune algorithms
Scientific reference
A. Shabani, S. Sarabandi, J.M. Porta and F. Thomas. A fast branch-and-prune algorithm for the position analysis of spherical mechanisms, 15th IFToMM World Congress on Mechanism and Machine Science, 2019, Krakow, Poland, in Advances in Mechanism and Machine Science, Vol 73 of Mechanism and Machine Science, pp. 549-558, Springer.
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