Making a Googol:1 Reduction with Lego Gears [video] | Hacker News Reader

Making a Googol:1 Reduction with Lego Gears [video]

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The video is very good. i) It teaches basic gear-ratio concepts ii) it showcases an amazing repertoire of reduction modules, iii) it poses interesting questions regarding power transmission like: how much power is being dissipated throughout the system? or.. where is all the power of the motor going if you leave it running for 1 hour? iv) it motivates borderline philosophical question like: is the figurine at the end actually moving at all due to the gears? v) it has really good video editing / camera work

On a practical level: no, it's not moving at all since all the movement is being absorbed by the slack between the gears.

There's a video of one of these constructions where the last gear is bolted to a wall or something.

Might be think of “machine with concrete” https://m.youtube.com/watch?v=5q-BH-tvxEg

Yep, that's exactly it, thanks!

I feel like doing the project in Lagos is going to confuse people but when you put the final gear bedded into concrete that sort of gets the point across

And as per that top voted comment:

The question of whether the last gear will break the concrete is moot. The gears themselves will erode away to nothing before they get a chance to apply much torque to the final gear.

I think that the same argument can be made to this Lego demo as well ;-)

If we consider the gears a perfect mechanism with no loss due to friction or wear then yes, it moves. Probably in a sub-atomic scale, but yes.

Unless space-time is quantized.

My mind just exploded. Would you have to breach a threshold to jump to the next state?

From my understanding, you start with a 0% chance to be in one state and 100%[1] to be in the other. Then the probability starts shifting more and more, till it is the other way around.

At least that is what I think it is, due to me having a very limited amount of knowledge in quantum physics. If a expert could confirm/deny my reasoning, it'd be appreciated.

[1] That is probably an exagerration as it would likely span more than just 2 possible states at any one time, but I chose two as a way to make it more understandable.

It’s true for converting liquid into gas.

So we could measure its movement in arc-Plancks?

Assuming the query [10^100 planck lengths to lightyears] is a correct interpretation of the question, a tooth on the first gear would need to move ~10^49 light years (well, in a circle) before a tooth on the last gear moved 1 Planck length.

I am less familiar with arc-Plancks, but I assume that is sufficient to say "the last gear doesn't move".

Yeah, and also this is material for kids and something we already teach them at schools and not "intellectually stimulating" stuff for HN.

See also "Machine with Concrete", by Arthur Ganson https://www.arthurganson.com/concrete-1

I remember this art installation that was spinning gears setup in a high gear ratio and the last gear was cemented. When looking at it you couldn't help but picture the gears and the motor starting to grind against the resistance of the cemented gear, but the reality was that that wouldn't happen for many many years.

https://www.youtube.com/watch?v=5q-BH-tvxEg

"With the motor turning around 200 revolutions per minute, it will take well over two trillion years before the final gear makes but one turn."

Now put the motor on the back end and watch the first gear spinning at the speed of light!

- from youtube Timon Di Mare's comment

I wonder how much energy it would take to spin it at all

Sorry to be a buzz kill, but AFAIK you can't "reverse" a worm gear.

You can, worm gears that can't be reversed are called self-locking, but depending on setup, it's possibly to drive them in reverse with some effort.

Can't do it with Lego worm gears though. Maybe if you add some machine oil, but otherwise the plastic-vs-plastic friction is just too much.

Were one to do this assuming hypothetical material that wouldn't break up under the stress, nor expand due to stress alone - hypothetical like I said - reversing it would cause relativistic expansion + general weirdness at the fast end. Wouldn't that expansion cause the gears to hbe forced apart and rupture, or something? I have a feeling it would somehow not but I can't imagine what would happen. They must expand, yet still remain engaged, which seems contradictory.

The material will break eventually. Other gears provide some structural support against expansion, but that is not what is going to break a gear. IMO the thing that would break it would simply be the mass of the gear; the fast acceleration would tear the gear out of it's axis or break it's teeth.

If it doesn't, at some point the material will give, likely away from the driving gear, and the entire thing will fling itself apart.

Of course it would, which is why I talked about a hypothetical material.

If it did not, though, what would relativity make it do?

I'm not a physicist but it's hard to have a thought experiment where you introduce ideas like ignoring materials strength, because that could be a factor in what relativity would make it do.

Anyway as you approach the speed of light the energy required to accelerate approaches infinity, so you would just not get it there because of the energy requirement.

I think a simpler version of this experiment is a really long rigid rod. What happens if you pick one end of the rod to be the axis and then you try to rotate the rod about the axis? https://physics.stackexchange.com/questions/455189/rotating-...

Also: You'd not be able to apply anywhere close to the amount of torque that'd be needed.

Typically when you try to rotate something in a way that makes it move faster than the speed of light it'll just rip itself apart.

Actually I think this typically happens when you reach speeds somewhere on the order of the speed of sound of the material.

It's safe to say that any human capable of rotating that lego man, even just a single degree within his or her lifetime would cause the outer rim of the input gear to move at orders of magnitude beyond relativistic baseball[0].

[0] https://what-if.xkcd.com/1/

I have no idea how the physics of this works.

At first it seems pretty simple--but at that overall reduction a small motion at the motor end translates to a motion at the far end that is ridiculously smaller than the Planck length. The motor end is a simple classical physics system, but that thing is a quantum system on the far end.

I have no idea how to figure out what would actually happen if you let that run for long enough that the far end should have moved significantly according to classical physics.

It will move but in such a small range, that the wobble of the atoms is MUCH larger over a "short" amount of time, than the effective movement of the axle. So, at some point, the wobble would just shift slightly.

And tolerances exagerrate that by a LOT.

Ha! I wonder (having no mechanical engineering background) ... is it possible to to drive e.g. a tank up a hill using a lego motor with a large enough gear ratio?

No, because the plastic gears connected to the drive wheel would snap under the immense torque.

Right, sure. In my mind, I was more interested in the relationship between gear-ratios, torque and the displacement of weight.

What if the motor gears were infinitely strong? That is: is the power output of a small electric motor theoretically sufficient to drive a tank up a hill with an arbitrarily large gear ratio?

Certainly. It would just happen arbitrarily slowly. (And, at that scale, other factors would come into play; the soil would deform under the wheels of the tank before it moved any distance, probably)

You can trade torque for speed basically. So yes. "Give me a lever long enough and a fulcrum on which to place it, and I shall move the world". That being said it would be so slow that you'd probably break something before you've moved a millimeter.

The same Youtube channel demonstrates how to use gear reduction to increase torque and bend a steel bar with legos: https://www.youtube.com/watch?v=jRn5waE0qfk

Yes. it would be equivalent to Archimedes’ claim “Give me a place to stand on, and I will move the Earth” (https://en.wikipedia.org/wiki/Archimedes#The_Lever)

This channel is a treasure trove for answer to similar questions:

[1] Can lego break a steel axle?

[2] How much load can the smallest lego gear handle?

[3] Testing lego gear and pulley systems

[1] https://www.youtube.com/watch?v=jRn5waE0qfk

[2] https://www.youtube.com/watch?v=YjhOGoZ-bNI

[3] https://www.youtube.com/watch?v=bWgTRHH656Y

I want to turn the last Gear backwards to see how fast the first Gear is rotating.

You probably won't be able to turn it at all with bare hands due to the sheer friction of the first few gear axles at the other end being amplified so much.

The friction of one wormgear is already enought to prevent rotation in the other direction. But with this many, impossible.

I also doubt if any of the gears except for the first ones rotate at all before the first gears are worn through, let alone before the battery to run out.

Are these original Lego parts?

Yes, unless noted otherwise he only uses original parts.

For example, in one video he uses Lego-compatible steel axles.

Anyone know what set the weird giant wheel at 1:35 is from?

https://rebrickable.com/parts/44556/wheel-22-x-172-with-fins...

Wonder how much energy is required to turn Zeus around a turn.

what if you try to spin it the other way around ?

Now do Googolplex:1

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