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Planar Linkages and Algebraic Sets

Henry C. King
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Abstract

A linkage is a finite graph with lengths assigned to each edge. A planar realization is a map to the plane which preserves edge lengths. It can be thought of as a mechanical device formed from stiff rods and rotating joints. We look at the configuration space of all planar realizations of a linkage (following work of Kapovich-Millson). We also look at configuration spaces of cabled linkages, where some edges are flexible cables. These configuration spaces are classified up to analytic isomorphism.

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Henry C. King. 1998-07-04. Planar Linkages and Algebraic Sets. https://arxiv.org/abs/math/9807023

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