The configuration space of planar spidery linkages
Jun O'Hara
Abstract
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 Re2(k-1)πni. 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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