Triple gear

by henryseg, published

Triple gear by henryseg Apr 24, 2013

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33566Views 4599Downloads Found in Math Art
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In this unusual mechanism three gears mesh together in pairs, and yet they can turn!

If you take three ordinary gears and put them together so that each gear meshes with the other two, then none of the gears can turn because neighbouring gears must turn in opposite directions. Triple gear avoids this problem by having the three "gears" arranged like linked rings - the gears then rotate along skew axes, and the opposite direction rule no longer applies (although see also Oskar van Deventer's Magic Gears for another possible solution).

This is joint work with Saul Schleimer. We were inspired by another of Oskar's designs, his Knotted Gear, which consists of two linked rings that gear with each other, and of course we wondered if it would be possible to do three linked rings!

Paper describing the mathematics behind the Triple gear, and how we designed it.

Triple gear (solid) is a non-hollow version, which should make it easier to produce on a home printer.

Baseplate and axle for Triple gear is designed to work with this, and gives a way to drive the gears using a motor. For axles without the baseplate or motor fitting, see 15cm axle for Triple gear and 30cm axle for Triple gear.

Triple gear is also available at Shapeways.

Things that could be improved upon:

  • Make the motion smoother
  • Less wiggle room for the gears - at the moment they can move quite far out of the 3-fold symmetric position
  • Can the gears be made to rotate at different speeds?

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Triple gear by henryseg is licensed under the Creative Commons - Attribution license.

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Whew! After a solid 2hrs of removing supports and 4hrs printing finally got one printed out that looks alright at 60% scale. I wanted it keychain sized for fidgeting with and budget reasons. Surprisingly considering how coarse the thread is, even though I removed ALL supports, it won't rotate, the tolerance between the gears is just too small to allow enough free rotation at 60% scale. I'd need hands made out wrenches to get it to rotate correctly, even with the gears in the correct conformations. Still, really cool!

Replicator 2, 0.1mm layer height, PLA, with autogenerated supports and raft

I've had success with SLS prints of this at around 60% scale, but I haven't heard of anyone trying it using an FDM machine. It might loosen up with use?

After judicious use of very, very slender knives to pry and shave the gaps slightly larger and smoother, I can now wiggle the loops. I expect full rotation will be possible with more work. Unless it is dissolvable supports, I would not recommend 60% scale PLA print on a printer similar to mine. The gears were barely not fused together. I would bet that full scale would be fine though.

I expect it to be quite popular once fully operational with the kids, they love fiddling with tactile things, and if I can slip in some math and geometry while they're interested, it's totally worth it.

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I can't see the video, can you pass the url, please?

If you are using firefox, install this. It will fix it: https://addons.mozilla.org/en-us/firefox/addon/skip-cert-error/

Thank you!! I didn't know why the videos doesn't work suddenly.

What browser? Firefox?

I cannot wait to print this on the ProJet 3500 HD I have access to. This is TOO COOL. Thank you for sharing! I'll post photos once I have the print done.

Looks like it will need full support... giving it a try...

Needed alot of cleaning but it prints ok in PLA on my Rep2.

What are the tolerances on this part? I'm wondering how small I can print it before it fuses.

I think the gaps are pretty small, around 0.5 mm at the closest. I've only had it printed on an SLS machine, and there it sometimes needs a little prying apart.

Wow this is super cool. I dont suppose you would be able to upload a version with the gears filled in instead of hollow? its just that as is, it would be very difficult for a home printer to handle. I presume that the one you have was made on a powder former type machine and hence doesn't need to build support.

Ah, good point. I'll see what I can do.

Ok, solid version of the triple gear is here: http://www.thingiverse.com/thing:79310http://www.thingiverse.com/thi...

Triple gear (solid)

thank you i'll give it a test tomorrow.