EPFLの研究チームが数千の新しい変形可能な結び目を発見(EPFL team discover thousands of new transformable knots)


2023-09-05 スイス連邦工科大学ローザンヌ校(EPFL)



多安定な弾性結び目の計算による探索 Computational Exploration of Multistable Elastic Knots

Michele Vidulis,Yingying Ren,Julian Panetta,Eitan Grinspun,Mark Pauly
ACM Transactions on Graphics  Published:26 July 2023


We present an algorithmic approach to discover, study, and design multistable elastic knots. Elastic knots are physical realizations of closed curves embedded in 3-space. When endowed with the material thickness and bending resistance of a physical wire, these knots settle into equilibrium states that balance the forces induced by elastic deformation and self-contacts of the wire. In general, elastic knots can have many distinct equilibrium states, i.e. they are multistable mechanical systems. We propose a computational pipeline that combines randomized spatial sampling and physics simulation to efficiently find stable equilibrium states of elastic knots. Leveraging results from knot theory, we run our pipeline on thousands of different topological knot types to create an extensive data set of multistable knots. By applying a series of filters to this data, we discover new transformable knots with interesting geometric and physical properties. A further analysis across knot types reveals geometric and topological patterns, yielding constructive principles that generalize beyond the currently tabulated knot types. We show how multistable elastic knots can be used to design novel deployable structures and engaging recreational puzzles. Several physical prototypes at different scales highlight these applications and validate our simulation.