Every LEGO Gear Ratio is Possible

Hi everyone,
when designing a model, you often need a specific gear ratio. Most of the time, that's pretty easy: just throw together a few gears and that's it. But actually, there are prime-numbered gear ratios that you simply can't get with normal gear ratios. In this video, I'll try to explain how :)
Enjoy watching,
2in1
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Links:
Tutorials (2nd channel): • How to Build All Lego ...
Gear Ratios explained: • Everything about Gear ...
Sariel's gear ratio table: sariel.pl/wp-content/uploads/2...
CVTs: • 3 Continuously Variabl...
• 2 Continuously Variabl...
Planetary Gears: • 5 Planetary Gearsets i...
2:1 Ratios: • 10 Ways to Build a 2:1...
Rebrickable: reb.li/m/173492
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Timestamps:
0:00 Intro
0:06 Gear Ratios in general
0:56 Simple 2-Gear Ratios
1:30 Combining Ratios
4:01 Differentials
7:45 Other possible things
8:00 Thanks for watching?
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#lego #technic #gearbox #gearratio #mechanism

[@in1]

Here are all the links I've promised + timestamps: Tutorials (2nd channel): kzbin.info/www/bejne/oZbCfqGoj7aXfdE Timestamps: 1/1: 0:56 2/1: 1:04 3/1: 0:22 4/1: 2:16 5/1: 1:16 2:34 5:47 6/1: 2:43 7/1: 1:21 3:31 8/1: 1:10 9/1: 1:35 10/1: 2:49 5:06 11/1: 6:23 12/1: 2:56 13/1: 6:58 14/1: - (forgot that one, but it's just a 7/1 + 2/1) 15/1: 3:07 16/1: 3:12 17/1: 7:15 18/1: 3:18 19/1: 7:34 20/1: 3:24 Gear Ratios explained: kzbin.info/www/bejne/amG1iWV-h7CjraM Sariel's gear ratio table: sariel.pl/wp-content/uploads/2016/01/gear-ratios-table.jpg CVTs: kzbin.info/www/bejne/ZqObaH1mhJWhm9k kzbin.info/www/bejne/lYbJf5prqr10q6M Planetary Gears: kzbin.info/www/bejne/eWXanGyFm5hqf5I 2:1 Ratios: kzbin.info/www/bejne/o6bWXpSBmsiteNk Rebrickable: reb.li/m/173492

[@Morganinism2]

I had never thought of a differential as a mechanical average machine before

[@cloudedarctrooperdtq3532]

Dude, the way you solved each of the prime number ratios was so damn awesome

[@hithere-cz4oc]

If anyone wants a formal proof: We can construct gear ratios for composite numbers by linking together the ratios for their prime factorizations. Therefore, it suffices to show that if we can create every prime, we can create every integer. Let p be the smallest prime which cannot be created with gear ratios. We know that we can construct p-1, because it is less than p and all numbers in the prime factorization of p-1 will be as well. We also know that we can construct p+1, since we know p+1 is even, and therefore we know p+1/2 can be constructed as well. Therefore, we can average p+1 and p-1 with the differential to get p, thus a contradiction is shown and therefore there is no such smallest gear ratio that cannot be made!

[@devoarco5084]

the prof has a little flaw: 2 is a prime number and 3 = (2+1) is not even. you have to show this seperatly but it shouldn't be a problem. Otherwise nice job!

[@jjjannes]

You can generate every odd number by rotating the side n revs, and the case 1 rev, the result will be n+2 revs. Because we know that a 1:1 and a 2:1 gear ratio exists, all other prime gear ratios also exists, since they are contained in the odd numbers.

[@hellothere_1257]

1/6 ratio? For each rotation of the left axle, the differential rotates by 7/12. The differential doubles that to 7/6 for the output. Then you have to to subtract the 1 rotation in the opposite direction from the differential's internal rotation, leaving you at 7/6 - 6/6 = 1/6

[@in1]

Congratulations, both the solution and the explanation are absolutely correct :)

[@yanikb.1312]

Biblically accurate 1:6 ratio

[@jackolson9845]

Lmao you almost started making an ALU just to get those prime numbered ones.

[@kricker8562]

What is an ALU?

[@thehammmann]

en.m.wikipedia.org/wiki/Arithmetic_logic_unit

[@nikkiofthevalley]

​​@@kricker8562Arithmetic Logic Unit. It's the part of a CPU that does all the thinky.

[@zoranradakovic2199]

@@nikkiofthevalley thinky is my new favorite word

[@polygrum]

For irrational gear ratios, I think it would be more practical not to use binary, but the nice approximations like 22/7 for pi, 17/12 for sqrt2 etc.

[@wallonice]

when the ratio isnt rational

[@BulkedAmbulance]

Give this man an Oscar for howtobasic audio

[@btf_flotsam478]

Optimising the sets of gears (whether it be for the number of gears or the amount of force applied) seems like an interesting mathematics problem.

[@bowfuz]

you actually did itttt!!!!!! thanks for taking the idea! :3

[@in1]

Yeah, that was a really fun project :)

[@jackpomeroy5855]

Speaking of the differential, I one time created a differential using k'nex gears, and it worked pretty well as a friction clutch

[@maciusiomek635]

Great video! I will use it for a car project to slow down the engine + to turn the wheels with a normal motor

[@BulkedAmbulance]

Imagine those gearboxes powering a single car

[@hologaster]

I don't know why this comes up on my feeds, and I don't really have played Legos. But I still watched.

[@guntheruberbacher5264]

Hallo,ich habe da mal ne frage. wie ist es möglich eine knicklenkung zu machen,auch mit motor, ABER OHNE DREHKRANZ? Z.b. bei einem traktor, ... ich würde mich auf ein paar ideen oder videos freuen.

[@piiodermatt2954]

Tremendous!!!! Absolutely...

[@heho1]

cool, lot of work!!

[@Ivan-xe1xv]

Brilliant!

[@CubeR4t]

would it be possible to build a pi to 1 ratio (of course not exactly but like the first 5 -10 digits)?

[@in1]

That would be possible, at least in theory. You could maybe use the binary transmission I showed in the end for that, but of course in practise with friction etc. it's going to get pretty annoying

[@CubeR4t]

@@in1 Hm now i want to try it

[@silentobserver3433]

355/113 is accurate to 7 digits. Since 355 = 2^5 * 11 + 3 and 113 = 2^4 * 7 + 1, it seems pretty doable. There are also probably better ways to achieve this than that

[@user-jg2sb4zr3f]

I need help so I want to build a Lego engine but I don’t know how to make a motor spin fast enough to power it what would be best gear ratio

[@VocalMabiMaple]

How does the differential case not just break itself? Im struggling to understand the mechanics involved in it.

[@in1]

kzbin.info/www/bejne/r4qkqGpvaJ1pjas this might help

[@VocalMabiMaple]

@@in1 i will definitely watch that! Just not right now. I hope I will understand it better once I do xD

[@VocalMabiMaple]

Looking at that picture of gears just unlocked something in my brain. Idk if this is true or not, but here is what I observed. Given that the length of the teeth and the spacing between teeth are equal, you can make gears of different sizes by adjusting the size of the wheel to the count of the teeth. Instead of measuring by size, you can measure by tooth.

[@in1]

Since the circumference is proportional to the radius/diameter, a wheel that is twice as big will always have twice the teeth if the "tooth density" is the same. And if you want to drive one gear with another, they'll need to have the same "tooth density", so yeah, gear ratios are usually measured by count of teeth.

[@VocalMabiMaple]

@@in1 cool! It's always a great feeling discovering something new I didnt know. Thanks for confirming for me!

[@TannerJ07]

Where is my 1:pi ratio

[@sarkedev]

You mention that to reverse the gear ratio you just switch input and output; however, this does not work with worm gears. So, for example, how would you do a 1:8 or 1:7?

[@in1]

You're right. 1:7 is possible by reversing any of the other 7:1 ratios without a worm gear, and a 8:1 just by putting a 4:1 and 2:1 together

[@kaderen8461]

when you started combining the gear ratios i went "ooh"

[@user-zy2nu7gk6i]

Where is the 14 tooth gear?

[@in1]

The flat gray one

[@wasditus2408]

Try to approximate irrational ratios! Pi, e, the golden ratio, etc.

[@lordbraddy69]

Creating a blackhole using Lego Gears by spinning it at the speed of light!!

[@deidrabair6286]

Um I don't think that is possible but I would love to see that

[@richardjulien1329]

Someone already tried to do that but the friction makes the all thing break appart at the end

[@in1]

Yeah, when you want to turn something in 1000000x the speed, you need to be 1000000x as strong Also, E=mc² says we need to accelerate an infinite mass for that... that's going to be hard

[@curtisclewett5249]

not infinite mass infinite inertia mass does not increase with speed@@in1

[@richardjulien1329]

Lol i remember this transmission, you asked in a poll a few month ago which was the results XD

[@in1]

Yep :)

[@extremepayne]

what about irrational gear ratios

[@in1]

Good point, I guess the best way to do that is to approximate it in binary, but you will never get a 100% correct solution

[@fededig]

Wow so clever

[@drdca8263]

4:13 : well, if none of the gears have a number of teeth divisible by 11, then, of course you can’t get an 11:1 ? I’m not sure what the script is for Edit: 4:37 : ooh, cool

[@MichaelDarrow-tr1mn]

Can you do a 1001:1000 gear ratio

[@in1]

Theoretically yes

[@MichaelDarrow-tr1mn]

@@in1 it should be easyish since 1001=7*11*13

[@in1]

@@MichaelDarrow-tr1mnYeah, you'll need to do something like /11 *10 /7 *10 /13 *10 tho, so that it doesn't get too fast and gets stuck

[@ur.atom.made.rylie.6974]

I bought a 60 tooth gear and thought it was 56 tooth😂

[@Cool_kid_the_real]

how about 1:7.5

[@in1]

Same as gearing up 2 and then gearing down 15

[@Simple_But_Expensive]

Exact gear ratios are unnecessary in most machines because they are throttled. Step on the gas to go faster, let off to go slower. As long as the speed/torque don’t cause problems, you are within the window. If the speed is too great, or the torque bogs down your prime mover, change the ratio. Whether to increase or decrease the ratio depends on if you are using the gear as a speed increaser or decreaser.

[@in1]

Exact ratios are relevant when you want parts to move relative to each other in a specific speed ratio, like in a clock, or something like a production process where even a slight offset can break things.

[@marmaladetoast2431]

me when pi:1 ratio

[@joatomcrack4846]

One of the first people

[@_rlb]

Interesting. But the annoying music adds nothing.

[@in1]

If I remove the music, you get a similar experience to just muting the video, and there are many people who enjoy it so I went that way

[@_rlb]

@@in1 that makes sense

[@Idiot354]

1:0,418732813921?

[@in1]

The only thing impossible would be a truly irrational number, like e, but this should (theoretically) be possible with enough differentials