The Infinity-Machine

[Raziel-117]

I hope I'm in the right sub-forum ^^

I have build an Infinity-Machine.

Here is some basic knowledge:

An infinity machine illustrates a progressive immobility.
In this case through multiple gear reductions of the gears involved, which run slower and slower with each stage.

For a motor with 350 revolutions per minute on the first axis, a reduction ratio per axis of 1 to 5 (8 to 40 teeth) and 10 axes to be included, the result is a factor of 5*10 = 9,765,625

The following numerical example follows from this:

After almost 9.8 million revolutions of the first gear, the last gear has completed one revolution.

Gear 1:
• 350 revolutions per minute
• 21,000 revolutions per hour (350x60)
• 504,000 revolutions per day (21,000x24)
• 183,960,000 revolutions per year (504,000x365)

This means that the last gear wheel would have completed one complete revolution after about 20 days.
This means that the last gear has moved one tooth after half a day.
For illustration I have fixed it with an axis ^^

Incidentally, with each additional axis, the whole thing increases by a factor of 5.

Here some examples:

15 Gears: 166 Years
16 Gears: 830 Years
...
20 Gears: 518.414 Years

Incidentally, the first development of the machine comes from Leonardo da Vinci.

I also have a video from the maschine!

Should anyone of you want to recreate it, I have also created a small Instruction.
 

[JintaiZ]

Cool build :)

[Johnny1360]

Probably has a considerable amount of torque on that last gear, lol

 

[TeamThrifty]

I remember doing this kind of thing when i was a kid, my maths weren't good enough to get the answer (!) but i used use all my 40's and make the lowest gearing i could and watch it for hours waiting for it to move!! 1980 was a sloooow year....

[deraven]

Very nice.  I like the interesting point being made with the pointlessness of it all.  

[astyanax]

Nice! Here's what happens if you take this to its logical conclusion:

 

[2GodBDGlory]

A few months ago, I was considering what would happen if you continued a sequence like that to infinity! I figured that, normally, friction would stop the motor immediately, but since torque increases constantly as well, it might be possible for it to run.

Is that the basic idea behind this machine?

[pleegwat]

You'd have an infinite number of gears contributing friction, but the total friction is actually finite. This is because as it gears down, the amount of friction in each subsequent gear pair is reduced geometrically, and geometric series (with r < 1) converge.

[Toastie]

45 minutes ago, pleegwat said:

You'd have an infinite number of gears contributing friction, but the total friction is actually finite.

So n -> infinity, but sum over F(n) does not?

We should also count in the first and second law of thermodynamics, I suggest. Otherwise, a great number of folks in the graves will stand up tonight and get us nightmares.

Best
Thorsten

[Captainowie]

14 hours ago, 2GodBDGlory said:

A few months ago, I was considering what would happen if you continued a sequence like that to infinity! I figured that, normally, friction would stop the motor immediately, but since torque increases constantly as well, it might be possible for it to run.

Surely an infinite chain of gears would behave very much as the very finite version at the top of this thread. The friction may well increase without limit, but that's no different than sticking an anchored axle through an off-centre hole.

[2GodBDGlory]

22 hours ago, pleegwat said:

You'd have an infinite number of gears contributing friction, but the total friction is actually finite. This is because as it gears down, the amount of friction in each subsequent gear pair is reduced geometrically, and geometric series (with r < 1) converge.

Okay, that makes sense. I sort of suspected that, but I didn't (and don't) have enough math education yet to understand why.