Self-propulsion of V-shape micro-robot

TL;DR

This paper analytically investigates the self-propulsion mechanisms of a symmetric V-shape micro-robot with periodically changing arms, revealing optimal configurations and efficiency comparisons with linear micro-robots.

Contribution

It provides explicit analytical expressions for the velocity and efficiency of a V-shaped micro-robot, highlighting optimal orientations and performance advantages over linear designs.

Findings

V-robot aligned perpendicularly is fastest and most efficient.

V-robot outperforms linear micro-robots in speed and efficiency.

Maximal velocity is smaller than that of microorganisms.

Abstract

In this paper we study the self-propulsion of a symmetric V-shape micro-robot (or V-robot) which consists of three spheres connected by two arms with an angle between them; the arms' lengths and the angle are changing periodically. Using an asymptotic procedure containing two-timing method and a distinguished limit, we obtain analytic expressions for the self-propulsion velocity and Lighthill's efficiency. The calculations show that a version of V-robot, aligned perpendicularly to the direction of self-swimming, is both the fastest one and the most efficient one. We have also shown that such $V$-robot is faster and more efficient than a linear three-sphere micro-robot. At the same time the maximal self-propulsion velocity of V-robots is significantly smaller than that of comparable microorganisms.