At even 0.001Nm of torque on the output, you'll need 0.001Nm* 1000rpm/(1/24/60))=1440 Nm of torque (1060 ft-lb) on the input, excluding all losses.  How much space do you have?  100m?

I would suggest worm gears - but make sure you have a good frame if you're using these. They introduce a lot of extra forces in unexpected directions.

Also, because of the laws of The Way Things Are, you're going to need a lot of torque on the slow-turning gear. I'm sure that there is a name for this, but as an Erector-educated engineer, I do not know what it is.

Oh. I notice now that you are asking for non-gear solutions. In that case, pneumatics are cool (but, as stated above, I don't have as many degrees as most of the people on here).

Thank you very much for your contribution. I will be using a combination of all that I've been inspired to try here, and worms gears _will_ be included! Thanks, appreciate it much. Have a great weekend!

nice post

Well, this is an engineering project. To give meaningful answers we need as much requirements as possible. What's the torque/power required at the output? Are there efficiency constraints? What torque and power can the input provide? What size, weight and cost may the machine have?

RPM means very different speeds and power depending on the diameter of the shaft/wheel/gear. So if your drive wheel is big enough and your driven shaft is small enough you may not need a transmission at all. Just use a small moon...

You're absolutely right. I'm somewhat embarrassed that my mathematical skillset is simply not adequte to provide those answers. So that's what I'm working towards as is. Thanks for your contemplations.

Well, this is not about mathematical skills or precise numbers. But you need an idea what you are actually building. Most solutions won't scale up or down well. It is a difference whether this is an art project that pits two very different speeds against each other or if you leach a bit of energy for a small device from a huge but slow machine or if you try to convert most of the energy of a huge but slow flywheel to electricity. 

Look up compound planetary gears, such as the youtube channel "Gear Down For What?". The carrier-driven (or in this case carrier-out) version with no sun gears is simplest.

For 1200:1 ratio, one option is input half 12 tooth planets 109 tooth ring, output half 11 tooth planets 100 tooth ring. Total reduction is "one minus the ratio of the ratios", in this case 1 - (109/12) / (100/11) = 1/1200. Two of those in series will get your desired 1440000:1 reduction.

It may not be backdriveable with such high ratio though, especially with 3D printed gears. But there are tricks to find metal gears that will work.

What sort of torque does the slow wheel have?

>what sort of torque does the slow wheel have?

I've tried to look into calculating the torque, but I'm afraid I'm lacking in the Newtonian physics department and mathematics in general. Will need to absorb som knowledge and get back to you. Thanks for your input, much appreciated!

Can you at least describe the slow wheel? Is it something that already exists, or something you will be building? What causes it to turn?

These gear sets have a poor efficiency. Gear drives need reasonable efficiency to be back drive-able. So this will probably not work even with a gear box that had the right ratio.

Only because of poor quality 3D printed gears or poor quality design. With precision gears and a carrier rigid enough to prevent them tilting under load, the efficiency should be as high as any other gearset. And since the carrier-driven version only has two tooth interactions, then say you get 96% efficiency per interaction, total efficiency is 92%.

These are two separate things. Yes, 3D printed gears have poor performance compared to properly lubricated steel gears. But I am talking about the type of gear set here - they have poor efficiency no matter what type of manufacturing being used. For normal gear sets like a classical planetary gear set your calculation is correct. But for the compound gear set the planets have to work with the high output torque but instead of just going around once (like in a normal gear set) they have to go around very often (which is where the high reduction comes from). So they waste a factor more energy for one revolution. This is where the poor efficiency comes from. It took me quite a while to understand. I have been wondering why these gear sets are not more common. They would be really great for all these small, fast spinning electric motors. But my guess is that the efficiency kills that. 

carbon fiber composite flywheels are being looked at for energy storage, gives a good idea of what it means to build a gyro in that order of craziness: https://beaconpower.com/carbon-fiber-flywheels/)

I want to thank you all for your suggestions, they really got my imagination going. It's clear to me now that I'm going to need to extract some kind of violent reaction from the slow wheel and store power in the kind of buffer you speak of, @Krzysztof ,  to smooth out the opposite reaction that'll get me my 1000 rpms. Thinking of the big wheel having many teeth, on top of which sits a springloaded 'finger' which regularly snaps into the gab between two teeth, creating mechanical motion to drive the tiny generator you speak of, @Xasin. 

Thanks again. By all means let me know if you should think of any further input, it's been very valuable to me.

Just go Rube Goldberg and have it dump water onto a person's bed so that they will wake up and start pedaling the bike again. :)

There are some reasonable suggestions for what to do here, which I like - how about some unreasonable ones?

I was thinking a clock mechanism that translates the low input rotation speed into a moderate rotation speed, which can feed a small magnet generator. Feed that into a simple energy harvester, charge up a supercap or similar, and use that to spin up a small drone motor.

Kinetic Energy Recovery System

w Polsce używano nawet autobusów zasilanych kołem zamachowym, jedno ładowanie starczało na ponad godzine (jeden kurs). https://pl.wikipedia.org/wiki/%C5%BByrobus żyrobus

teraz sa takie maszyny na łozyskach magnetycznych do kupienia jako ups do komputerów lub nawet małych elektrowni (ale na 20 sekund) chyba w Danii

I think you misclicked. Translation:

> In Poland there were buses powered by flywheels, one charging lasted about an hour, enough for one course. Now there are such machines with magnetic bearings used as UPS for computers and small power plants (but only for 20sec) probably in Denmark.

I don't think you could charge a flywheel directly from slow wheel and whole post is about how to do it.

Why? No this is not misclicked ;-) Text in Polish is not important. 

- You could attach cam or rod and a big cylinder to compress some air or you could pump some liquid and release it in another turbine to spin your fast wheel.

- You could attach a cable and wind it over your wheel and store power in a big spring or lift something, then use that to feed your 1000rpm wheel

Basically if you don't want gearbox to extract rotating motion for impedance change, you have to have some buffer. And going from 0.0007rpm to 1000rpm is A LOT of torque manipulation (8 orders of magnitude), so gearbox is not really feasible here.