Optimal Design for Purcell Three-link Swimmer

TL;DR

This paper determines the optimal link length ratio for the Purcell 3-link swimmer to maximize displacement, using theoretical analysis and simulations, resulting in a 60% improvement over the classical design.

Contribution

It provides the first asymptotic estimate of optimal link ratio for the Purcell swimmer based on deformation dynamics and validates it with numerical simulations.

Findings

Optimal link ratio derived analytically

Theoretical displacement estimate matches simulations

Displacement gain of approximately 60% over classical design

Abstract

In this paper we address the question of the optimal design for the Purcell 3-link swim-mer. More precisely we investigate the best link length ratio which maximizes its displace-ment. The dynamics of the swimmer is expressed as an ODE, using the Resistive Force Theory [13]. Among a set of optimal strategies of deformation (strokes), we provide an asymptotic estimate of the displacement for small deformations, from which we derive the optimal link ratio. Numerical simulations are in good agreement with this theoretical esti-mate, and also cover larger amplitudes of deformation. Compared with the classical design of the Purcell swimmer, we observe a gain in displacement of roughly 60%.