Theory of a triangular micro-robot

TL;DR

This paper develops an analytical model for the self-propulsion of a triangular micro-robot with periodically changing rod lengths, revealing its rotational and translational behaviors.

Contribution

It provides the first analytical expressions for the velocity and rotation of a triangle-robot with independently actuated sides using asymptotic methods.

Findings

The triangle-robot rotates with constant angular velocity around its centroid.

The centroid moves in a circular path during rotation.

Zero angular velocity case results in straight-line motion.

Abstract

In this paper we study the self-propulsion of a triangular micro-robot (or triangle-robot) which consists of three spheres connected by three rods; the rods' lengths are changing independently and periodically. Using the asymptotic procedure containing the two-timing method and distinguished limit arguments, we obtain analytic expressions for self-propulsion velocity the angular velocity. Our calculations show that a triangle-robot rotates with constant angular velocity around its centroid, while the centroid moves in a circle. The important special case of zero angular velocity represents rectilinear translational self-propulsion with constant velocity.