Triple Gear

April 26, 2013 6:00 AM

Mathematicians Henry Segerman and Saul Schleimer have produced a triple gear, three linked gears in space that can rotate together. A short writeup of the topology and geometry behind the triple gear on the arXiv.
posted by escabeche (36 comments total)

Oh, and here's a video of the triple gear I just found.
posted by escabeche at 6:02 AM on April 26, 2013 [3 favorites]

Sometimes I worry that the NSA and TFA have been diverting funds away from the Physics Police.
posted by Archibald Edmund Binns at 6:03 AM on April 26, 2013 [5 favorites]

This is an incredible breakthrough for the steampunk time machine industry.
posted by Strange Interlude at 6:04 AM on April 26, 2013 [24 favorites]

God, I love living in the future.
posted by Tomorrowful at 6:04 AM on April 26, 2013 [3 favorites]

I'm having fun envisioning practical uses - you'd need to mount each of the rings in a collar with a pinion to provide or remove power - it looks like the gear intermeshing has some flexibility, so it can be used to transfer power in a high-vibration and/or high flex application. Like monster trucks.

This is why mathematics matter: the monster truck dividend.
posted by Slap*Happy at 6:08 AM on April 26, 2013 [12 favorites]

So when will xscreensaver be updated to include this?
posted by RonButNotStupid at 6:10 AM on April 26, 2013 [10 favorites]

Just exactly what I need for this 7th dimensional machinery I'm building!
posted by Erasmouse at 6:17 AM on April 26, 2013

Alright, who converted to the engineers to the worship of Tzeench? FESS UP, HERETIC SCUM!
posted by Pope Guilty at 6:26 AM on April 26, 2013 [5 favorites]

Thanks. This looks really neat!

Moar ArXiv-based posts pl0x.
posted by kengraham at 6:27 AM on April 26, 2013

None of the videos are very clear, but there appears to be a lot of lateral movement of meshed surfaces as they "rotate" past each other. In other words, it's a very inefficient energy transfer.
Pretty, though.
posted by rocket88 at 6:31 AM on April 26, 2013 [1 favorite]

A relatively common sight in graphic designs is a planar arrangement of three gears in contact. However, since neighboring gears must rotate in opposite directions, none of the gears can move.

The snark is strong in this one.
posted by DU at 6:38 AM on April 26, 2013

Making the city work together
posted by Lanark at 6:42 AM on April 26, 2013 [4 favorites]

[looks]
Ow. My brain.

[watches video]
OW. Damn. My brain.
posted by ardgedee at 6:42 AM on April 26, 2013 [1 favorite]

Is there a .stl file I can use with my 3D printer so I can have my own set?
posted by Confess, Fletch at 6:42 AM on April 26, 2013 [3 favorites]

I got to play with it and some of Saul's other toys last week. He's a mensch.
posted by gleuschk at 6:52 AM on April 26, 2013 [1 favorite]

Sometimes I worryhope that the NSA and TFA have been diverting funds away from the Physics Police.
posted by Halloween Jack at 7:10 AM on April 26, 2013 [1 favorite]

I love that this is 3d printed.

There's no magical interlocking here, but this visualization of planetary gearing with your choice of frame of reference made a little lightbulb go off in my head when I first saw it.
posted by Nelson at 7:14 AM on April 26, 2013 [4 favorites]

Archibald Edmund Binns: "Sometimes I worry that the NSA and TFA have been diverting funds away from the Physics Police."

What?
posted by schmod at 7:19 AM on April 26, 2013

Is there a .stl file I can use with my 3D printer so I can have my own set?

Triple Gear Solid?
posted by brain_drain at 7:31 AM on April 26, 2013 [1 favorite]

A relatively common sight in graphic designs is a planar arrangement of three gears in contact. However, since neighboring gears must rotate in opposite directions, none of the gears can move.

Yes, that's one of my pet peeves. Also it galls me to see gears that have pitch ratios that don't mesh.

Designers: please consult a reference book before using gears.
posted by charlie don't surf at 7:35 AM on April 26, 2013

That is really neat, though I would get my finger caught in the centre in about three seconds flat. It's a little bit of an optical illusion to me too, as I keep thinking it's a single trefoil knot.

Our two pound coin has a odd numbered ring of gears on it, which I thought was appropriate in a British sort of way.
posted by lucidium at 7:42 AM on April 26, 2013 [1 favorite]

So, this looks cool as hell, and since my maths is horrible, it looks baffling, too.

But, is this an achievement, a breakthrough of some sort? An honest question, I have no context for gauging how hard this was to produce (mathematically speaking).
posted by oddman at 7:58 AM on April 26, 2013

Finally, just what I need for pedaling my Big Wheel between the extra dimensions.
posted by RobotVoodooPower at 8:16 AM on April 26, 2013 [2 favorites]

Finally, just what I need for pedaling my Big Wheel between the extra dimensions.

Bobby was way ahead of these guys.
posted by 3FLryan at 8:28 AM on April 26, 2013 [1 favorite]

Before there was 3D printing, there was always that old guy sitting on his porch up the road a piece who could carve this out of a single hunk of wood.
posted by George_Spiggott at 8:38 AM on April 26, 2013 [3 favorites]

They say that applying pressure to the outsides of the gears makes them seize up, and their drive mechanism is a single helical shaft that doesn't provide any power transfer. But maybe this could be the basis for the coolest-looking design ever for a vehicle that ascends and descends along a tall rotating tower.

Segerman's autoglyphs are fun too.
posted by mubba at 8:45 AM on April 26, 2013 [2 favorites]

But, is this an achievement, a breakthrough of some sort? An honest question, I have no context for gauging how hard this was to produce (mathematically speaking).

Naah, not really. From a mathematical perspective, this it's very neat but not really anything near a "breakthrough".

Still, it's pretty dope.
posted by gkhan at 9:11 AM on April 26, 2013

But will it blend?
posted by Riki tiki at 10:16 AM on April 26, 2013

Designers: please consult a reference book before using gears.

America's linkage design skills have declined precipitously in the past several decades. My grandfather, a graduate of a technical high school, would during his life have been able to not only design but build a functional geared device of moderate complexity like a small transmission using trigonometry, a text like the above, and a metal lathe. I hold two (non-mechanical) engineering degrees and would struggle to repair a simple problem with mantel clock.
posted by monocyte at 10:25 AM on April 26, 2013 [2 favorites]

I assume the video stopped a few seconds before Pinhead arrived.
posted by Etrigan at 11:59 AM on April 26, 2013 [1 favorite]

Mathematicians Henry Segerman and Saul Schleimer have produced a triple gear oscillation overthruster.
posted by jquinby at 12:36 PM on April 26, 2013 [2 favorites]

Wow, that's amazing! After looking at it for five minutes, I can close my eyes and still see it turning, but that isn't enough for me to really grasp it.

I've read that imagining arrangements of gears in space was essential for Maxwell in coming up with his famous equations, though I haven't seen his original writings to that effect.

Suppose you had two flat identical gears which meshed in such a way that their teeth did not bottom out in the gap between the teeth of the other gear when they were meshed together, then suppose you had a third gear you could bring up perpendicularly to the first two at their point of intersection, but which had slender, sharp and alternating teeth that would fit into the gap between tooth and body of the first two gears, first on one side then the other.

Wouldn't those three gears mesh each with the other two and turn together-- rather uninterestingly since they all meet at the same point and you could add more-- or am I missing something?
posted by jamjam at 12:56 PM on April 26, 2013

I think that would work, jamjam; you could also use three identical double-sided bevel gears to get the same effect.

What's interesting about this (I think?) is that it's a chain of three gears.
posted by hattifattener at 1:45 PM on April 26, 2013

I know, monocyte. I feel one of the legs up I always had on my classmates was endless permutations of LEGO Gears, such as these. I didn't have to learn precise gear ratios that I remember, but I did absorb things like energy transfer and understood things like axles and steering linkages.

I'm having a hard time seeing how this particular iteration could be of use but I'm wondering if it's really a potential breakthrough that leads to something more functional.
posted by dhartung at 3:04 PM on April 26, 2013

As I continue to look at escabeche's first link, I find myself wondering whether, if these gear rings were very flexible, you could cut each one of them, then glue each cut end back together, not to the end it was originally parted from, but to the cut end of another ring so that the three nested but separate rings would be transformed into a continuous trefoil knot, but with the meshing zones preserved, and then you would have a circulating, self-driving, meshed trefoil knot which would make an interesting counterpart (and counterpoint) to the geared, Möbius strip trefoil knot.
posted by jamjam at 8:56 PM on April 26, 2013 [1 favorite]

America's linkage design skills have declined precipitously in the past several decades.

This is primarily because industrial systems are no longer driven by a single rotary shaft, like a water mill or a steam engine. If you look at the next chapter in that book I linked to, you'll see elaborate belt and pulley systems that can work as transmissions to deliver any amount of power and rotational speed. This was fairly common in factories and even pretty common in smaller scale applications like agriculture.

I'm not sure that modern systems are an improvement, having factories with hundreds of small motors, each with its own inefficiency, as opposed to a single motor driving everything with only simple inefficiency at the power source, plus simple mechanical losses in the belts and pulleys. But belt drive systems were extremely dangerous and people got pulled into the belts and crushed all the time.
posted by charlie don't surf at 9:30 AM on April 27, 2013 [1 favorite]