Wonky spheres can be sculpted to roll eternally downhill along any possible path, as long as the path repeats. These 鈥渢rajectoids鈥� could be used to design robots that follow particular routes, or to model how the spin of quantum computer bits, called qubits, will change over time.
Most objects, such as spheres or tyres, will roll down a smooth hill in a straight line. There are some objects that trace curved paths 鈥� such as oloids, three-dimensional objects formed from two intersecting circles covered in material 鈥� but these still follow relatively simple, repeating circular paths.
The trajectories of oloids have been studied mathematically, and they are used in some industrial settings. An , for example, can be used to oxygenate ponds or stir water in sewage treatment plants.
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Now, at the Institute for Basic Science in Ulsan, South Korea, and his colleagues have come up with an algorithm to make an object that will roll down almost any possible smooth path forever, as long as the path repeats twice. The researchers also constructed a mathematical proof to show that as long as a path repeats in this way, then they could always make a shape that rolled down it.
鈥淔or any path, you can always find such a sphere, of some radius, that when it completes two periods of the path, it will restore its 3D orientation perfectly,鈥� says Sobolev. 鈥淭his allows you to make a particle that will roll forever downhill, always tracing the path again and again.鈥�
The shape has to be a certain size for this to work, depending on the length and the shape of the path.
The algorithm works like someone pressing a mouldable clay ball into the ground to make it match each segment of the path. As the ball rolls down the hill, it will take on an imprint of its contact with the ground at each point, and from then on be able to roll down this path eternally. 鈥淲e鈥檙e talking here about infinite rolling,鈥� says team member , also at the Institute for Basic Science.
Sobolev and his colleagues then 3D printed trajectoid shells to go around a hard metal interior, and showed that almost any shape they made could roll downhill, although slight differences between the predicted and printed shape meant that they didn鈥檛 all roll perfectly. The is publicly available.
The trajectoid algorithm could prove useful for simulating quantum properties like the spin of qubits, which can be modelled as spheres that rotate along a specific pathway over time, says Sobolev. By better understanding how qubit spin evolves over time, quantum computers could be made more accurate.
Trajectoids could also be used for designing robots, says at the Budapest University of Technology and Economics in Hungary. 鈥淚t鈥檚 always a challenge to guide very small robots along a given trajectory, and this work suggests that by modulating the shape, one can maybe be successful in guiding a very small robot along the desired trajectory.鈥�
Nature
