Non-Transitive Gears

This CAD model was designed by Oskar van Deventer, copyright (c), 5 October 2018.

Non-Transitive Gears is a puzzling mechanism based on an idea by Alexander Poddiakov. In his article "Intransitive Machines", Poddiakov writes about non-transitivity, wher A is larger than B, B is larger than C, and C is larger than A. There exist many examples, including non-transitive dice, and non-transitive election results. Poddiakov also showed an example of a set of three gears that are non-transitive. When two of these are put against each other, then A spins faster than B, B spins faster than C, and C spins faster than A. See also Poddiakov's post at trv-science.ru with lots of interesting responses.

A physical implementation would not allow Poddiakov's gears to be put all three together, as then the mechanism would jam. A solution was the addition of three ratchets. Whichever of the three knobs you turn, one of its neighbours will turn 2x faster and the other 2x slower.

Here are some links about this design.
https://www.youtube.com/watch?v=nAllI4TDm6Y
https://i.materialise.com/en/shop/item/non-transitive-gears
https://www.shapeways.com/product/WTE57BWNK/non-transitive-gears
https://i.materialise.com/forum/t/non-transitive-gears-by-oskar/1167
https://www.shapeways.com/forum/t/non-transitive-gears-by-oskar.98801/
https://twistypuzzles.com/forum/viewtopic.php?t=34316

Feel free to 3D-print an extra sample to give to a friend, as long as you mention the designer and don't charge money.

If you are planning to sell some samples, then please contact me for a license agreement. The royalty fee is 10% of your selling price.

Please do not upload the design to a commercial service, or redistribute the design in any way other than linking to the YouTube video: https://www.youtube.com/watch?v=nAllI4TDm6Y

Enjoy!

Oskar
3 March 2025

Contact: 
https://oskarvandeventer.nl/index_contact.php?subject=Print%20It%20Yourself


