### Triple gear

A smaller version of Triple Gear is available here. A baseplate and axle for using a motor to move the triple gear is available here. Also see 15 cm axle for Triple gear and 30 cm axle for Triple gear.

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!

Here is a paper on the mathematics behind the Triple gear, and how we designed it.

A note on materials: I have so far printed it in White Strong & Flexible, and Strong & Flexible Polished. It may arrive with the rings slightly fused together, but gently moving them back and forth will loosen them up, and the mechanism gets smoother with use. The polished and dyed versions seem to work fine as well, and may require less working in. I haven't tested any of the "frosted detail" materials, but I imagine that they should work fine. It isn't printable in the other "detail" materials because of cleaning problems.

Here is a video showing how to loosen the gears (for the small version of the Triple gear, but the large is similar) if they arrive somewhat fused together.

##### Tags:
Mathematical Art, Desk Toys, impossible
cm: 6.99 w x 7.412 d x 4.54 h
in: 2.752 w x 2.918 d x 1.787 h

@hi_byg We also put the design up on thingiverse, at http://www.thingiverse.com/henryseg/designs. The link is also in the paper!
First of all, well done. I would have tried to patent the design before publishing the article on Arxiv (someone may be interested in developing actual products! who knows…), but it's not for free so I understand. Since you don't plan any commercial development soon (given the lack of patent), I'm actually surprised you don't provide the model (o maybe you do? in this case, my bad). Let's be honest: not many people have 3D printers (outside our circles), you could still sell many units to other enthusiasts/geeks :) A 3D model would be useful also to allow other people to try to implement designs around this idea!
@pjansen Great! Let me know when you get it working :)
Just got mine in the mail a day ago. This is incredible! Nice work! And yes, there is a slight fusion from printing, but with a bit of wiggling back and forth and some patience, it freed right up. After maybe 30 min. of effort, it's running smoothly with the optional axle and baseplate. Now to get a motor on this...
@henryseg Understood. Thanks for the quick response!
@trevor_r the WSF rain only lasts a little while - that's the remaining unsintered powder that wasn't cleaned off, it isn't significantly damaging the solid object. I know this because I've run the motorised version for days on end and nothing changes. Shapeways don't do interlinked objects in metal. I think it would be near impossible to keep the parts separate at the bronze infusion stage. Possibly it could work with true sintered steel, but that's not a material that Shapeways offers yet.
I received mine and like it very much. One thing: Exercising the gears causes very fine WSF powder to rain off of it. Feasible to offer a metal version?
@jhlowry@Mac.com Sorry you had a bad experience with this. I haven't had the print come out like that so far. It may be a little late, but you might try sending a photo of the problem to service@Shapeways.com and they may do a reprint for it. If that doesn't work, send me a photo of the issue and I'll refund you.
It is a nifty concept but mine was "cure welded" so that I had to use knives and excessive force (flexing the gears with all my strength for an hour or more) to separate the gears. The first gear facing released with a loud snap and loss of part of the gear face. The others released with quieter snaps and the loss of some sand-sized particles. It now works partially - after several hours of moving the gears by hand and smoothing the faces. However, I now have a flat spot that prevents me from using the short shaft and base to create a display. I don't know if coating the freshly printed object with something like talc or corn-starch would prevent this, but suggest some kind of post printing treatment to keep what appears to be "cure welding" from occurring.
@henryseg maybe not impossible, but beyond the reach of most (carved puzzle balls seem similar, but require a lot of dedication to make). Amazing work!
Love it. Great work. Kind of reminds me of cruller donuts. Now I'm hungry.
Wow! Very impresive! :-)
I really like things that would be virtually impossible to make any other way than by 3d printing!
I love this.
Thanks Duann!
Sweet, just posted the video on the blog http://www.shapeways.com/blog/archives/1809-3D-Printed-Triple-Gear-by-Henry-Segerman-Will-Melt-Your-Brain-VIDEO.html

• ##### White Strong & Flexible

White nylon plastic with a matte finish and slight grainy feel.

\$40.00