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The geometry of configuration spaces for closed chains in two and three dimensions. (English) Zbl 1065.55010

The authors describe the topological structure of various linkages in \(E^n\). One object of study is an arbitrary subspace of configurations of points in \(E^n\) consisting of those configurations which correspond to the vertices of a (possibly singular) polygon with fixed side lengths. The homeomorphism type of this space (and others) depends on the lengths, but, as it is remarked, not their order. The possible homeomorphism types are made quite explicit. Other linkages studied, for example, allow one side to vary in length. Applications to robotics are discussed.

MSC:

55R80 Discriminantal varieties and configuration spaces in algebraic topology
14P05 Real algebraic sets
68T40 Artificial intelligence for robotics
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