Here are all the links I've promised + timestamps: Tutorials (2nd channel): kzread.info/dash/bejne/nZmTr9CrirTKd9I.html 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: kzread.info/dash/bejne/ZmSGupSBgq7Wp6Q.html Sariel's gear ratio table: sariel.pl/wp-content/uploads/2016/01/gear-ratios-table.jpg CVTs: kzread.info/dash/bejne/YqZsmaxpf5PUldo.html kzread.info/dash/bejne/kYmasMlupbunpaQ.html Planetary Gears: kzread.info/dash/bejne/dWirzZuIlpadeZM.html 2:1 Ratios: kzread.info/dash/bejne/n6mnj8OElcbgcto.html Rebrickable: reb.li/m/173492

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

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

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!

@devoarco

3 ай бұрын

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

3 ай бұрын

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.

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

@kricker8562

3 ай бұрын

What is an ALU?

@thehammmann

3 ай бұрын

en.m.wikipedia.org/wiki/Arithmetic_logic_unit

@nikkiofthevalley

3 ай бұрын

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

@zoranradakovic2199

3 ай бұрын

@@nikkiofthevalley thinky is my new favorite word

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

3 ай бұрын

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

@yanikb.1312

3 ай бұрын

Biblically accurate 1:6 ratio

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

3 ай бұрын

when the ratio isnt rational

Give this man an Oscar for howtobasic audio

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.

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

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

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

@in1

3 ай бұрын

Yeah, that was a really fun project :)

Imagine those gearboxes powering a single car

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

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.

Tremendous!!!! Absolutely...

Brilliant!

cool, lot of work!!

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

Where is my 1:pi ratio

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

3 ай бұрын

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

3 ай бұрын

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

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

3 ай бұрын

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

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

@in1

3 ай бұрын

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

3 ай бұрын

@@in1 Hm now i want to try it

@silentobserver3433

3 ай бұрын

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

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

@in1

3 ай бұрын

Yep :)

Wow so clever

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

Where is the 14 tooth gear?

@in1

3 ай бұрын

The flat gray one

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

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

@in1

3 ай бұрын

kzread.info/dash/bejne/q4112ZlyY5uch6w.html this might help

@VocalMabiMaple

3 ай бұрын

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

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

@deidrabair6286

3 ай бұрын

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

@richardjulien1329

3 ай бұрын

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

@in1

3 ай бұрын

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

3 ай бұрын

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

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

what about irrational gear ratios

@in1

3 ай бұрын

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

Can you do a 1001:1000 gear ratio

@in1

3 ай бұрын

Theoretically yes

@MichaelDarrow-tr1mn

3 ай бұрын

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

@in1

3 ай бұрын

@@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

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

how about 1:7.5

@in1

Ай бұрын

Same as gearing up 2 and then gearing down 15

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

3 ай бұрын

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.

me when pi:1 ratio

One of the first people

Interesting. But the annoying music adds nothing.

@in1

3 ай бұрын

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

3 ай бұрын

@@in1 that makes sense

1:0,418732813921?

@in1

3 ай бұрын

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