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arXiv · 1604.08742

Hidden cusps

Michel Coste·Philippe Wenger·Damien Chablat
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Abstract

This paper investigates a situation pointed out in a recent paper, in which a non-singular change of assembly mode of a planar 2-RPR-PR parallel manipulator was realized by encircling a point of multiplicity 4. It is shown that this situation is, in fact, a non-generic one and gives rise to cusps under a small perturbation. Furthermore , we show that, for a large class of singularities of multiplicity 4, there are only two types of stable singularities occurring in a small perturbation: these two types are given by the complex square mapping and the quarto mapping. Incidentally , this paper confirms the fact that, generically, a local non-singular change of solution must be accomplished by encircling a cusp point.

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Michel Coste, Philippe Wenger, Damien Chablat. 2016-04-29. Hidden cusps. https://arxiv.org/abs/1604.08742

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