Jun O'Hara
Published 2005-05-23, updated 2006-06-25Version 2
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.
Comments: 33 pages, 41 figures
Covers of surfaces
Complex hyperbolic cone structures on the configuration spaces
Quotients of $S^2\times{S^2}$
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