Cusp Points in the Parameter Space of Degenerate 3-RPR Planar Parallel Manipulators
This work addresses a specific problem in robotics (parallel manipulator design) for engineers, but appears incremental as it amends existing algorithms.
This paper tackles the problem of identifying cusp points in degenerate 3-RPR planar parallel manipulators to enable non-singular assembly-mode changes and increase workspace. It proposes an accurate algorithm combined with algebraic methods to partition the parameter space and classify manipulator families.
This paper investigates the conditions in the design parameter space for the existence and distribution of the cusp locus for planar parallel manipulators. Cusp points make possible non-singular assembly-mode changing motion, which increases the maximum singularity-free workspace. An accurate algorithm for the determination is proposed amending some imprecisions done by previous existing algorithms. This is combined with methods of Cylindric Algebraic Decomposition, Gröbner bases and Discriminant Varieties in order to partition the parameter space into cells with constant number of cusp points. These algorithms will allow us to classify a family of degenerate 3-RPR manipulators.