Geometry and Topology of Polygonal Linkages

There is a long and involved history of linkages starting at least in the nineteenth century with the advent of complicated and intricate mechanical engineering. Some of these practical problems led to interesting, nontrivial geometric problems, and in modern mathematics there has been significant progress on even very basic questions. Over the years, several different points of view have been taken by various groups of people. We will attempt to survey these different perspectives and results obtained in the exploration of linkages.