Exploring Trajectoids: A New Shape That Can Propel Itself Without Assistance

Saturday - September 16 2023, 15:01 UTC - 1 year ago

Scientists have designed an algorithm to create a custom 3D shape, called a trajectoid, that can be rolled along a predefined path. The trajectoids are designed using a basketball-shaped base material covered in flexible, trimmable material. By strategically removing portions of the cover material that make contact with the table, a unique shape can be created which will follow the same path when rolling along independently.

Normally, when we think of a rolling object, we tend to imagine a torus (like a bicycle wheel) or a sphere (like a tennis ball) that will always follow a straight path when rolling. However, the world of mathematics and science is always open to exploring new ideas and concepts. This is why researchers have been studying shapes, like oloids, sphericons and more, which do not roll in straight lines. All these funky shapes are really interesting to researchers as they can show us new ways to move objects around smoothly and efficiently. For example, imagine reducing the energy required to make a toy robot move, or mixing ingredients more thoroughly with a unique-looking spoon. While these peculiar shapes have been studied before, scientists have now taken it a step further.

Consider a game where you draw a path on a tilted table—similar to tilting a pinball table to make the ball go in a particular direction. Now, try to come up with a 3D object that, when placed at the top of the table, will roll down and exactly follow that path, instead of just going straight down. There are a few other rules of this game: the table needs to be inclined slightly (and not too much), there should be no slipping during rolling, and the initial orientation of the object can be chosen at launch. Plus, the path you draw must never go uphill and must be periodic. It must also consist of identical repeating segments—somewhat like in music rhythm patterns.

An international team of researchers affiliated with UNIST has pondered whether it’s possible to find a winning strategy for this game. They wanted to know if, for any given repetitive path, it would be possible to design a shape that can be rolled to follow this path on its own. The goal was to develop a general recipe that would work not just for simple curves, but also for complicated and intertwined paths. The strangely shaped objects created for this purpose were named “trajectoids.” .

At first glance, it appears impossible for a 3D object to automatically follow a predetermined rolling path while navigating all the angles and curves. However, the scientists started by simplifying the problem. They envisioned starting with a perfectly smooth basketball covered in flexible, trimmable material, akin to clay. By strategically removing portions of the basketball’s cover material that made contact with the table while ensuring the basketball itself always touched the path, it is possible to gradually sculpt the object into a custom shape. This resulting shape would then magically follow the same path when rolling independently. Applying this concept, the scientists successfully devised a new method for creating trajectoids.

These trajectoids aren’t just theoretical; the researchers 3D printed them and conducted successful experiments. They even ventured into making trajectoids that occasionally move uphill or follow self-intersecting paths. You can even try the new algorithm yourself for any path you desire, as the researchers have released an online tool for generating 3D-printing-ready files for trajectoids.

Credit: Nature (2023). DOI: 10.1038/s41586-023-06306-y .

For a trajecoid to be created, it must first be created from a bed like clay.