Trajectoid

Animation of a rolling sphericon which makes a sinusoidal path.

A trajectoid is a geometric shape designed to trace a predetermined periodic trajectory when rolling under gravity.

Physicists and mathematicians from the Institute for Basic Science in South Korea and the University of Geneva, in collaboration with colleagues from other institutions, developed an algorithm that links the deformation of objects to their trajectory on an inclined plane. This theoretical framework was then realized through 3D printing technology, printing two halves and a spherical hollow center which would contain a metal sphere for mass.

Unlike conventional rolling bodies such as spheres or cylinders, which follow linear or sinusoidal paths, trajectoids are mathematically engineered to follow complex, custom trajectories. The concept extends earlier studies of rolling motion in objects like sphericons and oloids, introducing greater diversity in possible rolling paths.

References

• Trajectoids: Creating a shape that rolls along a desired path September 12, 2023
• Wonky shapes can be made to roll along a specific path of your choice Video by New Scientist