On planar self-folding magnetic chains: Comparison of Newton–Euler dynamics and internal energy optimisation

Abstract

Within the wide field of self-assembly, the self-folding chain has the unique capability to pass through narrow openings, too small for the assembled structure, yet consists in one connected body. This paper presents a novel analytical framework and corresponding experimental setup to quantify the results of a self-folding process using magnetic forces at the centimetre-scale, with the aim to put experimental results and prediction methods in the context of surgical anchoring and therapy. Two possibilities to predict the folding of a chain of magnetic components in 2D are compared and investigated in an experimental setup. Folding prediction by system Coulomb energy, neglecting folding dynamics, is compared with a simulation of the system dynamics using a novel approach for 2D folding chains, derived from the Newton–Euler equations. The presented algorithm is designed for the parallel computation architecture of modern computer systems to be easily applicable and to achieve an improved simulation speed. The experimental setup for the self-folding chain used to validate the simulation results consists of a chain of magnetic components where movement is limited to one plane and the chain is agitated by the magnetic forces between the chain components. The folding process of the experimental setup is validated for its stability and predictability under different deployment modes. Finally, the results are discussed in light of the folding prediction of longer chains. The implications of the presented findings for a 3D folding chain are discussed together with the challenges to apply the novel dynamics simulation algorithm to the 3D case. The work clearly demonstrates the potential for this novel approach for complex self-folding applications such as magnetic compression anastomosis and anchoring in minimally invasive surgery.