1. The configuration space of planar spidery linkages
- Author
-
Jun O'Hara
- Subjects
Geometric Topology (math.GT) ,Surface (topology) ,Homeomorphism ,Mechanism (engineering) ,Combinatorics ,Mathematics - Geometric Topology ,Planar ,Configuration space ,57M50, 58E05, 57M20 ,Genus (mathematics) ,Planar linkage ,FOS: Mathematics ,Morse function ,Diffeomorphism ,Geometry and Topology ,Morse theory ,Mathematics - 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 $Re^{\frac{2(k-1)\pi}ni}$. 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., Comment: 33 pages, 41 figures
- Full Text
- View/download PDF