Crawling scallop: Frictionbased locomotion with one degree of freedom
Abstract
Fluidbased locomotion at low Reynolds number is subject to the constraints of the scallop theorem, which dictate that body kinematics identical under a timereversal symmetry (in particular, those with a single degree of freedom) cannot display locomotion on average. The implications of the theorem naturally compel one to ask whether similar symmetry constraints exist for locomotion in different environments. In this work we consider locomotion along a surface where forces are described by isotropic Coulomb friction. To address whether motions with a single degree of freedom can lead to transport, we analyze a model system consisting of two bodies whose separation distance undergoes periodic time variations. The behavior of the twobody system is entirely determined by the kinematic specification of their separation, the friction forces, and the mass of each body. We show that the constraints of the scallop theorem can be escaped in frictional media if two asymmetry conditions are met at the same time: the frictional forces of each body against the surface must be distinct and the timevariation of the bodybody separation must vary asymmetrically in time (so quickslow or slowquick in the extensioncontraction phases). Our results are demonstrated numerically and interpreted using asymptotic expansions.
 Publication:

Journal of Theoretical Biology
 Pub Date:
 May 2013
 DOI:
 10.1016/j.jtbi.2013.01.021
 arXiv:
 arXiv:1303.2669
 Bibcode:
 2013JThBi.324...42W
 Keywords:

 Locomotion;
 Scallop theorem;
 Friction;
 Crawling;
 Frictionbased locomotion;
 Physics  Biological Physics
 EPrint:
 Journal of Theoretical Biology, Volume 324, 7 May 2013, pp. 4251