Controlling the configuration space topology of mechanisms

TL;DR

This paper presents a novel method for designing the topology of a linkage's configuration space by identifying critical points and perturbing around them, demonstrated through a mechanism controlling soliton propagation.

Contribution

It introduces a new approach to control the configuration space topology of linkages, enabling targeted mechanical behavior design.

Findings

Successfully designed a mechanism to gate soliton propagation.

Method effectively identifies and perturbs critical configurations.

Demonstrates potential for advanced linkage design in physics applications.

Abstract

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 to perform certain tasks from the physics community. 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. We then demonstrate our procedure by designing a mechanism to gate the propagation of a soliton in a Kane-Lubensky chain of interconnected rotors.