'Bigon Rings': Princeton Researchers Unveils Mathematics That Changes Form Based on Specific Conditions

Ever heard of bigon rings? It is a new technology inspired by intriguing patterns of lace that professional artist and designer Lauren Dreier spotted while browsing the 19th-century book by the German architect Gottfried Semper.

The post-doctoral student at Princeton University's School of Architecture often incorporates technology with her designs and thought about recreating the patterns into 3D using a plastic material she had been experimenting with. She could form a bumpy geometry from the semi-rigid strips, which is not what she expected.

She consulted Sigrid Adriaenssens, an associate professor in Princeton's Department of Civil and Environmental Engineering, who said she was intrigued as well with the shape. Dreier called the reconfigured structure bigon rings, wherein they could produce different geometries that arise from the looping behaviors, SciTech Daily reported.

They described the mathematics behind the structure in their paper, titled "Numerical modeling of static equilibria and bifurcations in bigons and bigon rings," published in the Journal of the Mechanics and Physics of Solids, and said that it could be applied to any general elastic rod network that could lead to the creation of new products and technologies that can change form to improve its performance under variable conditions.

How Bigon Rings are Formed?

Dreier also worked closely with other collaborators to investigate the physics behind bison rings. The team arranged their creating into loose, looping forms, unlike the lace that uses soft threads that are twisted.

The team started by making bigons, which are closed structures formed by fixing the ends of two straight strips at a certain angle and end up creating almond-eye formations. They found that these bigons were also exhibiting bistability or have two different stable shapes that the structures could toggle when they apply little pressure.

According to Princeton University's news release, researchers then started arranging these bigons into a chain and loops by connecting their ends. By doing so, they were able to form different geometries that they call bigon rings, which were multistable and exhibited similar behavior as a bandsaw blade that loops back on themselves.

Researchers noted that bigon rings could be tuned by adjusting the intersection angle and the aspect ratio of the strips and changing the number of bigons that make up the bigon rings.

As they make the physical structures, they also made a numerical model using Kirchoff rod equations to describe the thinness, elasticity, and behavior of bigon rings when force and displacements were added into the picture. The computational model successfully identified the different configurations that the structure might be able to take theoretically.

Eventually, they were able to form a new numerical model that describes multistable behavior, which can be applied to other studies that focus on the mechanics of general interlaced elastic networks.

ALSO READ: Fractal Pattern in Romanesco Cauliflower Mystery Finally Discovered by Replicating It is a Common Lab Plant

Potential Real-World Applications of Bigon Rings

The team plans to conduct further studies on the bigon rings. But for now, they hope their findings could lead to new designs for various technologies that might be packed to take as little room as possible but will assume a much larger form once unpacked, like the materials sent to space, according to the news release.

Moreover, other potential real-world applications include novel soft robotic arms, toys, wearable devices, and special textiles that can change form depending on the conditions to support someone's arm.

Undoubtedly, this research demonstrates the largely untapped value of interdisciplinary collaboration between artists and engineers, driven by intuition and feelings that can lead to interesting discoveries.