The team discovers thousands of new transferable nodes

Nodes are used in a variety of ways, every single day. They ensure safety both indoors and in outdoor activities such as boating or sailing, are used as sutures, or as decorations, and can be found even on nanoscales in nature, for example in DNA molecules.

Elastic knots are those that bounce back to their original shape in the absence of friction. There are open elastic knots tied to a single length of wire with two ends, which loop back into a straight line, and closed elastic knots in which the two ends of the wire used to tie them together are joined. These tend to revert to a curved shape.

Focusing on closed nodes, researchers at the Engineering Computing Laboratory of the Federal Polytechnic School in Lausanne, led by Professor Marc Polley, along with colleagues in Canada and the United States, have discovered thousands of new switchable nodes including three new shapes represented by the humble figure. Eight knots can be assumed, which is double the number documented so far in the scientific literature.

The results are published in the journal ACM Transactions on Graphics.

To make these discoveries, the team first developed a computational pipeline that combined random spatial sampling with physical simulations to efficiently find the stable equilibrium states of elastic nodes. Leveraging the results of node theory, they ran their pipelines on thousands of different topological node types to create a comprehensive data set of multistable nodes.

“By applying a series of filters to this data, we discovered new, switchable nodes with interesting physical properties and beautiful geometries,” explained PhD assistant Michele Vedoulis, lead author of the paper “Computational Exploration of Multistable Elastic Nodes.”

“This rich array of wonderful shapes can be created simply by knotting a flexible wire, and we have noticed how such seemingly simple objects can sometimes show dozens or even hundreds of different stable shapes. The new geometric patterns we identified were sometimes surprising. For example, “We found that most, but not all, of the preferred shapes for flex nodes are flat and planar, while a few are 3D.”

The team conducted further analysis across node types that revealed new geometric and topological patterns with constructive principles not seen in previously tabulated node types, demonstrating how flexible, multistable nodes can be used to design new structures.

“As a result of our research, we can see the use of elastic nodes in the process of designing self-deploying structures, such as pop-up tents or lightweight emergency shelters. New metamaterials can be designed that combine multiple flexible knotted elements to build a network with complex mechanical behaviour,” explained Vedoulis.

The team also created engaging entertaining puzzles with the challenge of deforming an elastic knot and manually finding some interesting geometries which they calculated using their algorithms.

Satisfying though these new findings are, Fedoulis and his team believe the work opens the way to many other potential new research directions.

“We want to explore the design of self-deployable structures, and consider the coupling of flexible rods with textile materials. Also, although thousands of different nodes have been simulated, our exploration has only scratched the surface of the millions of known nodes. We also plan to study more complex combinations of complex systems, which may New mechanical properties arise from the way the individual components mesh with each other.”