Thermal Fluctuations of Singular Bar-Joint Mechanisms

TL;DR

This paper develops a formalism to analyze how singularities in the shape space of bar-joint mechanisms influence their thermal fluctuations, with implications for nanomechanical design.

Contribution

It introduces a method to study the thermal behavior of mechanisms with shape-space singularities, highlighting their impact on equilibrium configurations.

Findings

Mechanisms tend to be found near shape-space singularities at low temperatures.

Singularities significantly influence the free-energy landscape of mechanisms.

Design considerations can leverage singularities for improved nanomechanical performance.

Abstract

A bar-joint mechanism is a deformable assembly of freely rotating joints connected by stiff bars. Here we develop a formalism to study the equilibration of common bar-joint mechanisms with a thermal bath. When the constraints in a mechanism cease to be linearly independent, singularities can appear in its shape space, which is the part of its configuration space after discarding rigid motions. We show that the free-energy landscape of a mechanism at low temperatures is dominated by the neighborhoods of points that correspond to these singularities. We consider two example mechanisms with shape-space singularities and find that they are more likely to be found in configurations near the singularities than others. These findings are expected to help improve the design of nanomechanisms for various applications.