The configuration space of planar spidery linkages

Details The configuration space of planar spidery linkages The configuration space of planar spidery linkages

2005-05-23

arxiv.org/abs/math/0505462v2

Mathematics

Geometric Topology

33 pages, 41 figures

Scientific paper

The configuration space of the mechanism of a planar robot is studied. We consider a robot which has $n$ arms such that each arm is of length 1+1 and has a rotational joint in the middle, and that the endpoint of the $k$-th arm is fixed to $Re^{\frac{2(k-1)\pi}ni}$. Generically, the configuration space is diffeomorphic to an orientable closed surface. Its genus is given by a topological way and a Morse theoretical way. The homeomorphism types of it when it is singular is also given.

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