Thermal Fluctuations of Singular Bar-Joint Mechanisms

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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.

Original languageEnglish (US)
Article number208005
JournalPhysical Review Letters
Issue number20
StatePublished - May 20 2022

ASJC Scopus subject areas

  • General Physics and Astronomy


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