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

--------------------------------------------------------------
Links:

--------------------------------------------------------------
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?

--------------------------------------------------------------
#lego #technic #gearbox #gearratio #mechanism

[in]

Here are all the links I've promised + timestamps:
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

[cloudedarctrooper]

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

[hithere-czoc]

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!

[Morganinism]

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

[MdnghtEther]

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

[hellothere_]

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

[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.

[JUMPCRGHN]

Give this man an Oscar for howtobasic audio

[maciusiomek]

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

[mayviepixelcanon]

you actually did thanks for taking the idea! :3

[btf_flotsam]

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.

[jackpomeroy]

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

[JUMPCRGHN]

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.

[drdca]

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

[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.

[guntheruberbacher]

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.

[yenshuochengynps]

i like the python part where you tried to find 11:1 it was awesome and also very funny that you typed so much script and yet there was no result🤣

[kaderen]

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

[Im-ev]

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