Researching into Non-Singular Transitions in the Joint Space

It is known that cuspidality phenomenon appears in some parallel manipulators, called cuspidal manipulators, being able to perform non-singular transitions between different assembly modes. In this paper, the authors will present a methodology for obtaining the locus of cusp points in the joint space, which will be applied to generic 3-RPR planar parallel manipulators. This will permit analyzing non-singular transitions in a slice of the joint space and in the 3-dimensional joint space. It will be shown that as well as encircling a cusp point, analyzing the coalescence of solutions in the singular curves will be necessary so as to perform non-singular transitions.

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