Mechanics of magnetic robots akin to soft beams supported at unanchored contacts

This article presents a novel algorithm to predict the shape and the support configurations of a magnetic robot acting like a supple beam, which deforms due to an imposed magnetic field. The soft magnet loosely rests on a flat horizontal surface, which provides the pivoting supports to the robot to attain its deformed shape. The key difficulty in analysis of the mechanics is the lack of any prior knowledge about the location of the contacts where the distorted beam finds support from the ground. This article outlines an algorithm in which different possibilities referred to as modes are checked systematically to locate the placement and the nature of such supports. Consequently, the 2D shape of the soft beam can be determined without any heuristic assumption about where the magnetic robot is touching the solid surface. This study focuses on single contact sections although the algorithm idea is valid for multiple contacts as well. The mathematical theory and the numerical scheme are validated by comparing the simulated results with existing experimentally obtained configurations. Also, the parametric space of system-defining nondimensional parameters is explored to determine when a transition happens from one mode to another and which magnetization methods are desirable for higher stability. Through theoretical simulation, the results show that a thin rectangular cross section provides higher deformation when compared to the other two tested shapes (circular and equilateral triangle cross section).