Configuration space engineering: gating mechanisms by controlling configuration space topology

A linkage is a mechanical device built from rigid bars and freely rotating joints. Kempe's universality theorem tells us that we can design a linkage with a joint that traces out any algebraic curve we want, but the complexity of the linkage explodes rapidly for even modest complexity curves. In this talk, we approach designing linkages from another angle by designing the topology of the linkage's configuration space. Using a one degree of freedom linkage with a large number of branch points (singularities) in its configuration space as a starting point, we outline how modifications to the linkage change the topology of the configuration space. This gives us the ability to engineer the configuration space of a linkage by picking and choosing which singularities we keep, which ones we remove, and the specific way that we remove them. To demonstrate this process, we connect a linkage with a specifically designed configuration space to a 1D chain of connected rotors and use this additional linkage as a gate to block or allow the propagation of a soliton in the chain. We explore how modifying a small section of the combined linkage can be used to program the motion of the entire structure.