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Making a GOOGOL:1 Reduction with Lego Gears

Brick Experiment Channel · Youtube · 151 HN points · 0 HN comments
HN Theater has aggregated all Hacker News stories and comments that mention Brick Experiment Channel's video "Making a GOOGOL:1 Reduction with Lego Gears".
Youtube Summary
Building a long gear train using 186 Lego gears. Many different types of Lego gears are used. Enjoy!

Inspired by Daniel de Bruin's "universe's biggest gear reduction":
https://www.youtube.com/watch?v=nFslB0AcVmM

The finished gear ratio:
10341796308487334800992832804222885104773611498499997696000000000000000000000000000000000000000000000:1
or 1.0342e100:1
or 1.034 GOOGOL:1

Rotation time for the last gear:
52433879932503535381614991275498187972589101825233846406570841889117043121149897330595482546 years
or 5.2434e91 years

Formula for the gear ratio:
24/8 * 40/8 * 40/8 * 40/8 * 60/1 * 12/1 * 168/1 * (140 / 8 + 1) * 141 * 20/12 * (40/8)^20 * 20/12 * (24/1)^20 * 56/16 * (36/1)^10 * (40/1)^18 * 15/9 * 56/1

List of gears used:
27x Gear 8 Tooth [3647]
1x Gear Expert Builder 9 Tooth [g9]
6x Gear 12 Tooth Bevel [6589]
2x Gear 12 Tooth Double Bevel [32270]
1x Gear Expert Builder 15 Tooth [g15]
1x Gear 16 Tooth [94925]
2x Gear 20 Tooth Bevel [32198]
23x Gear 24 Tooth [3648]
10x Gear 36 Tooth Double Bevel [32498]
49x Gear 40 Tooth [3649]
2x Turntable Large Type 2 [48452cx1]
1x Turntable Large Type 3 [18939 / 18938]
8x Gear Rack 11 x 11 Curved [24121]
1x Gear, Hailfire Droid Wheel [x784]
1x Gear Worm Screw, Short [27938]
51x Gear Worm Screw, Long [4716]

For those wondering, the visual effect I used in the end montage is called Find Edges, comes with Adobe Premiere 14.

Music (used with permission):
Alpha Centauri B by Anders Enger Jensen
https://www.youtube.com/user/HariboOSX
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Hacker News Stories and Comments

All the comments and stories posted to Hacker News that reference this video.
Jul 15, 2020 · 133 points, 49 comments · submitted by DamnInteresting
simoneau
See also "Machine with Concrete", by Arthur Ganson https://www.arthurganson.com/concrete-1
dmos62
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.
zimpenfish
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."

rafaelturk
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

ioulian
Sorry to be a buzz kill, but AFAIK you can't "reverse" a worm gear.
zaarn
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.
hrydgard
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.
the_cramer
I wonder how much energy it would take to spin it at all
throwaway_pdp09
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.
zaarn
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.

throwaway_pdp09
Of course it would, which is why I talked about a hypothetical material.

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

ses1984
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-...

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

danfromberlin
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/

tzs
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.

Akronymus
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.

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

Someone
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)
rland
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)
simias
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

jonahrd
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

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

amelius
Are these original Lego parts?
bonzini
Yes, unless noted otherwise he only uses original parts.

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

whywhywhywhy
Anyone know what set the weird giant wheel at 1:35 is from?
bonzini
https://rebrickable.com/parts/44556/wheel-22-x-172-with-fins...
hoppla
Wonder how much energy is required to turn Zeus around a turn.
theqult
what if you try to spin it the other way around ?
doublesCs
Now do Googolplex:1
syats
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
ainiriand
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.
hoseja
Unless space-time is quantized.
nkrisc
So we could measure its movement in arc-Plancks?
saalweachter
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".

trentdk
My mind just exploded. Would you have to breach a threshold to jump to the next state?
sjwright
It’s true for converting liquid into gas.
Akronymus
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.

lmilcin
Yeah, and also this is material for kids and something we already teach them at schools and not "intellectually stimulating" stuff for HN.
frabert
On a practical level: no, it's not moving at all since all the movement is being absorbed by the slack between the gears.
StavrosK
There's a video of one of these constructions where the last gear is bolted to a wall or something.
pwagland
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 ;-)

sgerenser
Might be think of “machine with concrete” https://m.youtube.com/watch?v=5q-BH-tvxEg
StavrosK
Yep, that's exactly it, thanks!
lumberingjack
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
May 21, 2020 · 1 points, 0 comments · submitted by doener
May 18, 2020 · 5 points, 0 comments · submitted by DamnInteresting
May 17, 2020 · 9 points, 1 comments · submitted by bem94
yasinaydin
I think Lego should use this video as their ad instead.
May 16, 2020 · 3 points, 1 comments · submitted by snalty
snalty
Sorry, I know this is very off topic but I found the video fascinating and thought other people would enjoy it too. Feel free to remove if this is too far from the point of HN.
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