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Shaped to roll along a programmed periodic path

An algorithm has been developed for constructing a 3D shape that follows an infinitely repeating path as it rolls under gravity. The approach could have applications in quantum computing and medical imaging.
  1. Elisabetta Matsumoto

    1. Elisabetta Matsumoto is in the School of Physics, Georgia Institute of Technology, Atlanta, Georgia 30332, USA.

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  2. Henry Segerman

    1. Henry Segerman is in the Department of Mathematics, Oklahoma State University, Stillwater, Oklahoma 74078, USA.

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A single wheel follows a straight line as it rolls downhill, but can change direction by rotating about its contact point with the ground. Two wheels connected by an axle have much less freedom — with no common point about which to rotate, they are forced to move along parallel straight lines forever. Trains use an ingenious method to solve this problem: their wheels are conical, so the wheel on the outside edge of a turn can keep up with the other wheel by riding the train track at the wide end of the cone. The outside wheel spins at the same rate as the inside wheel, but travels farther (see go.nature.com/3jjykjc). In this way, the track’s shape controls the train’s path.

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Nature 620, 282-283 (2023)

doi: https://doi.org/10.1038/d41586-023-02335-9

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Competing Interests

The authors declare no competing interests.

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