Planar Linkages and Algebraic Sets

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.