Details:
Title  On the determination of cusp points of 3RPR parallel manipulators  Author(s)  Chtcherba Arthur D., Russo Mark F., Guillaume Moroz, P. Wenger  Type  Article in Journal  Abstract  This paper investigates the cuspidal configurations of 3RPR 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 nonsingular change of assembly mode. In previous works, the cusp points were calculated in sections of the joint space by solving a 24thdegree 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 3RPR 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.  Keywords  Kinematics, Singularities, Cusp, Parallel manipulator, Symbolic computation  ISSN  0094114X 
URL 
http://www.sciencedirect.com/science/article/pii/S0094114X10001187 
Language  English  Journal  Mechanism and Machine Theory  Volume  45  Number  11  Pages  1555  1567  Year  2010  Edition  0  Translation 
No  Refereed 
No 
