How are high gear ratios achieved in a small space?

I have a very basic understanding of how gears work, and while trying to learn more, I've run into a small point of confusion.

If a 2:1 gear ratio is achieved by having twice as many teeth on one gear than the other, then how are 250:1 ratios achieved? Certainly there aren't gears with 2500 teeth on one gear, and 10 on the other...

For example, here's a very tiny motor with a 250:1 gear ratio: DC Motor with Gearhead

One simple way is to do the gearing in a number of stages in a gear train. Such a system uses gears which have two different gear sizes on the same wheel. In the example shown in the image below (from the How Stuff Works article on gear trains) each gear has a ratio of 2:1 such that the final ratio of the magenta gear to the blue gear is 8:1.

• Thank you, but I'm a little confused by something. I've been taught that gear ratios are determined by the first and last gear in a set, no matter how many gears there are. So, what do you mean by "staging" and how does "staging" gears increase the ratio to more than the first and last provide? Sep 29, 2015 at 23:55
• @Soviero My original answer didn't explain very clearly, I apologize. Take a look at my edited answer, and I think you will understand. Sep 30, 2015 at 12:07
• Oh, I've seen those types of gears before, but I never knew what they were for... Thank you for explaining! Sep 30, 2015 at 13:12
• You can also fit the gear train on two axles such that all gears spin freely on each axle (except for the driving gear, which is afixed to one of the two axles). See this picture of a 6 speed Tamiya gearbox as an example: i.ytimg.com/vi/mXXZMxo5_6k/maxresdefault.jpg
– Paul
Feb 17, 2016 at 16:55

Using a worm drive you can have one tooth per rotation on one shaft and have that drive a gear with 250 teeth, for a 250:1 ratio in one stage.

• It's worth noting that a worm drive changes the axis of rotation by 90 degrees. Sep 30, 2015 at 12:40

Planetary Gear Sets can provide a high reduction in a small space. Also, they can be connected in a similar fashion to gear train to further increase the reduction. Also, one benefit is the output shaft is co-axial with the input shaft.

What determines the gear ratio is the ratio of input and output angular velocities. This is traditionally done by interlocking different sized circles together, but for high gear ratios other designs are often used because they can reduce the output angular velocity sufficiently without needing several stages of gears interacting. One of the most ingenious examples is the harmonic gear. There are plenty of videos of how they work on Youtube.