Optimal design of Purcell's three-link swimmer.

In this paper we address the question of the optimal design for the Purcell three-link swimmer. More precisely, we investigate the best link length ratio which maximizes its displacement. The dynamics of the swimmer is expressed as an ordinary differential equation, using the resistive force theory. 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 estimate 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%.