Notes on geometry of locomotion of 3-dimensional version of the Purcell's swimmer

TL;DR

This paper extends the Purcell's swimmer model to three dimensions, deriving a kinematic system description using Cox theory and resistive force theory for low Reynolds number locomotion.

Contribution

It introduces a 3D version of the Purcell's swimmer and formulates its equations of motion using advanced theoretical tools.

Findings

Derived a purely kinematic form of the 3D swimmer's equations

Applied Cox theory and resistive force theory to low Reynolds number locomotion

Extended the understanding of microscale swimming mechanisms

Abstract

We present a generalized, 3 dimensional version of the Purcell's swimmer which is a planar mechanism locomoting at low Reynlods number regime. We use Cox theory and resistive force theory to come up with the forces acting on the system. We finally come up with a purely kinematic form of the system's equations.