Controlling the configuration space topology of mechanical structures

Linkages are mechanical devices constructed from rigid bars and freely rotating joints studied both for their utility in engineering and as mathematical idealizations in a number of physical systems. Recently, there has been a resurgence of interest in designing linkages in the physics community due to the concurrent developments of mechanical metamaterials, topological mechanics, and the discovery of anomalous rigidity in fiber networks and vertex models. These developments raise a natural question: to what extent can the motion of a linkage or mechanical structure be designed? Here, we describe a method to design the topology of the configuration space of a linkage by first identifying the manifold of critical points, then perturbing around such critical configurations. Unlike other methods, our methods are tractable and provide a simple visual toolkit for mechanism design. We demonstrate our procedure by designing a mechanism to gate the propagation of a soliton in a Kane-Lubensky chain of interconnected rotors.