Configuration space engineering: Controlling configuration space topology with geometry

Many complicated systems from proteins to mechanical metamaterials are analyzed by describing them as linkages, or systems of joined bars and pivots. However, the configuration spaces for these mechanisms can be difficult to understand, and critical points, places where constraint counting fails to predict behavior, are surprisingly prolific. In this talk, we present a method for understanding these mechanisms by introducing a tensor field formalism that governs the location of singular points. We will then demonstrate how to use this tensor field formalization to analyze entire classes of mechanisms sharing the same connectivity but different geometries. This gives a geometrical approach to thinking about mechanism design.