Hidden cusps
Robotics
2016-05-02 v1
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.
Cite
@article{arxiv.1604.08742,
title = {Hidden cusps},
author = {Michel Coste and Philippe Wenger and Damien Chablat},
journal= {arXiv preprint arXiv:1604.08742},
year = {2016}
}