On the determination of cusp points of 3-RPR parallel manipulators
| Autor: | Fabrice Rouiller, Philippe Wenger, Damien Chablat, Guillaume Moroz |
|---|---|
| Rok vydání: | 2010 |
| Předmět: |
Cusp (singularity)
0209 industrial biotechnology Pure mathematics Polynomial Mechanical Engineering 010102 general mathematics Bioengineering 02 engineering and technology Revolute joint Singular point of a curve System of linear equations Topology 01 natural sciences Computer Science Applications Computer Science::Robotics Gröbner basis 020901 industrial engineering & automation Prismatic joint Discriminant Mechanics of Materials 0101 mathematics Mathematics |
| Zdroj: | Mechanism and Machine Theory. 45:1555-1567 |
| ISSN: | 0094-114X |
| DOI: | 10.1016/j.mechmachtheory.2010.06.016 |
| Popis: | This 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 Grobner bases for the solutions of systems of equations. |
| Databáze: | OpenAIRE |
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