How to Design the Perfect Shaped Wheel for Any Given Road

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Published 2022-04-16

Last video, we looked at finding the ideal road for a square wheel to roll smoothly on, but what about other wheel shapes like polygons and ellipses? And what about the inverse problem: finding the ideal wheel to roll on any given road, such as a triangle wave?

Previous episode: • The Perfect Road for a Square Wheel a...

=Chapters=
0:00 - Intro & Review
1:48 - Polygon Wheels
3:49 - Elliptical Wheel
5:30 - Focus-centered Ellipse
8:50 - Wheels From Roads
11:24 - How to Get a Closed Wheel
14:10 - The Many Wheels for a Sinewave
16:24 - The Wheel for a Triangle Wave Road
19:16 - The Wheel(s) for a Cycloid Road
20:24 - The Wheel for a Parabolic Road
20:58 - A Look Ahead and a Challenge

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Many of the ideas in this video came from, or were inspired by, "Roads and Wheels," an article by Leon Hall and Stan Wagon that appeared in Mathematics Magazine, Vol. 65, No. 5 (Dec 1992). If you want a deeper dive, I encourage you to read it yourself. As far as math papers go, it's fairly easy to read:
web.mst.edu/~lmhall/Personal/RoadsWheels/RoadsWhee…

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CREDITS

► The song at the beginning of this video is "Rubix Cube" and comes from Audionautix.com

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Thank you for your support!

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The animations in this video were mostly made with a homemade Python library called "Morpho".
I consider it a pretty amateurish tool, but if you want to play with it, you can find it here:
github.com/morpho-matters/morpholib