# Optimal Design for Purcell Three-link Swimmer

arXiv: https://arxiv.org/abs/1412.8133 · HTML: https://mlsanity.com/paper/1412.8133/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Dec 2014.

## Built on by (most cited first, 1 of 1)

- [Enhancing Efficiency and Propulsion in Bio-mimetic Robotic Fish through End-to-End Deep Reinforcement Learning](https://mlsanity.com/paper/2506.04627/) (2025)

## Abstract (arXiv)

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%.