ELI5; When you have an absurd gear reduction, why is it harder to turn the final gear?

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I honestly don’t get this. I see these absurd gear reduction videos, 25k:1, Googol:1, etc. The first gear is easy to turn but the last barely turns due to gear reduction. They always show themselves trying to turn the last gear by hand and it doesn’t turn easilly. Why is that the case? why can’t the last gear become the first if you turn it first?

In: Engineering

Gears exchange torque for speed.

3:1

1 speed and 3 torque –> 3 speed 1 torque

The rest can be extrapolated from this.

Gear reductions work this way: You have two gears, one of them is small and the other is big, but both share the same size of ‘knobs’ (idk the terminology). So you have the big gear with 24 knobs and a small one has 6, that is a ratio of 4:1, because it takes 4 full rotations of small gear to rotate the big one once (each knob has it’s match, but the small ones are lapping before they meet their match, so they have multiple, in this case 4 knobs matched to each of them).

To make a ridiculously high gear ratio, you hard attach big and small gears in pairs, so when you spin the small gear the big one (having the same rotational velocity) is moving small gear of the next set, and in turn moving next big gear with a ratio. You can imagine it as actually having a chain of ratios 1:1 (fixed together) > 1:4 (interacting) > 1:1 > 1:4…..

Now, this is working pretty easily one way, because when you move in the direction of 1024:1, you’re making one rotation on the first gear, then 1/4th of a rotation on the second, 1/16th on 3rd and so on. When you try to go 1:1024, you’re trying to move 1st gear one time, the second 4 times, 3rd 16 times and so on. (someone do the math)

As you can imagine spinning last gear, by reverse, even a fraction of a googol times would take a lot of energy, not to mention friction between gears and chassis, and rotating each gear in between the last and the first.

To turn the final gear you have to apply the same amount of total force necessary to turn it by spinning the first gear. So if it takes 25,000 rotations of the first gear to turn the final gear, it would take 25,000 times the amount of force to turn the final gear than it does to turn the first gear.

The system is not reversible like you implied, because bigger gears are turning the smaller gears (which is what makes them spin so fast). The smaller gear is on an axle with another big gear (which keeps them rotating the same speed) and that gear turns another small gear etc.

Basically, when you turn a gear, there are two factors torque and RPM (or speed).

Torque x RPM = Force of the gear.

If you want to increase the RPM, you have to lower the torque. This is why the last gear turns super quickly (but because of the low torque can be stopped or started really easily). The first gear has the inverse effect, where it spins really slowly, but is super hard to start or stop.

Because you need to spin the final gear with the same force to spin the first gear x amount of times, so if its 25k:1, you have to use the same force as spinning thr fast gear 25 thousand times for 1 rotation of the final gear

Gears are basically converting force to speed or vice versa.

If you rotate a gear with 20 teeth that’s connected to one with 10 teeth, the 10 toothed gear will rotate twice as fast. But you can’t get a free lunch with physics. In order to spin twice as fast, it has half as much force behind it.

The opposite is true too. If you spin the gear with 10 teeth, the gear with 20 will turn half as fast. But because it’s slower it has twice as much force behind it.

So in your example the ratios are extreme. The gears will have some friction and resistance between them. If you’re spinning the ‘smallest’ gear, you’re converting speed to force. So the last gear will spin very slowly, but has an immense amount of force behind it. Each gear in the train will spin slower, but with more force and each once can easily overpower the friction. But if you go backwards that isn’t the case. The force will decrease gear to gear until eventually it’s just not enough to overcome that friction. So the whole thing will lock up.

If you take one of those gazillion:1 gear trains and run the final gear at 1 rpm, you’re now trying to turn the first gear at a gazillion rpm. Even without friction, that’s trying to accelerate something incredibly quickly, which takes a lot of force (and with some of those gear trains you would actually be hitting relativistic speeds so classical physics don’t even work).