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TitleOn the determination of cusp points of 3-RPR parallel manipulators
Author(s) Chtcherba Arthur D., Russo Mark F., Guillaume Moroz, P. Wenger
TypeArticle in Journal
AbstractThis paper investigates the cuspidal configurations of 3-RPR parallel manipulators that may appear on their singular surfaces in the joint space. Cusp points play an important role in the kinematic behavior of parallel manipulators since they make possible a non-singular change of assembly mode. In previous works, the cusp points were calculated in sections of the joint space by solving a 24th-degree polynomial without any proof that this polynomial was the only one that gives all solutions. The purpose of this study is to propose a rigorous methodology to determine the cusp points of 3-RPR manipulators and to certify that all cusp points are found. This methodology uses the notion of discriminant varieties and resorts to Gröbner bases for the solutions of systems of equations.
KeywordsKinematics, Singularities, Cusp, Parallel manipulator, Symbolic computation
URL http://www.sciencedirect.com/science/article/pii/S0094114X10001187
JournalMechanism and Machine Theory
Pages1555 - 1567
Translation No
Refereed No