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.

中文翻译：

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关于平面自折叠磁链：牛顿-欧拉动力学与内能优化的比较

摘要 在广泛的自组装领域中，自折叠链条具有独特的能力，可以通过狭窄的开口，对于组装结构来说太小了，但却是一个连接体。本文提出了一种新的分析框架和相应的实验装置，以量化使用厘米级磁力的自折叠过程的结果，目的是将实验结果和预测方法置于手术锚定和治疗的背景下。在实验装置中比较和研究了在 2D 中预测磁性组件链折叠的两种可能性。忽略折叠动力学的系统库仑能量折叠预测与使用从牛顿-欧拉方程导出的 2D 折叠链的新方法的系统动力学模拟进行了比较。所提出的算法是为现代计算机系统的并行计算架构而设计的，易于应用并提高仿真速度。用于验证模拟结果的自折叠链的实验设置由一系列磁性组件组成，其中运动仅限于一个平面，并且链条由链组件之间的磁力搅动。验证了实验装置的折叠过程在不同部署模式下的稳定性和可预测性。最后，根据更长链的折叠预测来讨论结果。讨论了所提出的发现对 3D 折叠链的影响以及将新颖的动力学模拟算法应用于 3D 案例的挑战。