# Determining the ratios needed in gear reduction

I am trying to work out the math behind building a gear box for turning a gear a specific RPM from a small motor.

Given that a typical DC hobby motor turning at 200 RPM, and a target in the final gear of 0.25 RPM I used this formula to find the ratio:

R = Gear2RPM / Gear1RPM

R = 200 / 0.25

So the ratio would be 800:1. Now as far as I understand things, for gears to turn the teeth need to follow the same ratio of teeth to circumference, so no matter what size teeth or diameter of the gears, it will always need to be 800 times larger.

A 1cm drive gear would turn a 800cm gear at 200rpm to meet my goal. An 8 meter gear is not really going to work I'd image in practice though.

The solution here is to use gear reduction to bring the size of the final gear down to a manageable level, is that correct?

I know that the reduction gearing needs to multiply together to reach the target ratio, so for a 400:1 reduction a 16:1 gear turning a 25:1 gear would be 400:1.

It seems to me that given the size of the gear on the motor, and the size I would like the final gear to be (well close at least) I should be able to use the products of ratio to find the correct number and ratio of the reduction gears.

Am I off the mark here? If not, is there a formula that I could use to solve problems like this? If I am wrong, is there an easier way?

If it helps, I'm trying build a very small camera platform with sidereal tracking. 0.25 RPM is sidereal rate: 360/(23.93447*60)

• This sounds accurate. – RandomUser May 14 '14 at 15:27
• A worm gear is probably the best way to get such a drastic reduction... – abiessu May 14 '14 at 15:32
• @abiessu Can you go into more detail? – asawyer May 14 '14 at 15:45

For example, consider a worm gear which engages one tooth of another gear per rotation. Then the receiving gear needs $800$ teeth to achieve the $800:1$ ratio. In a pair of circular gears, each of the gears has a minimum number of teeth to be effective, say $6$, and this is a multiplier against each part of the gear ratio; a $16:1$ ratio becomes $96:6$ and so on, and an $800:1$ ratio becomes $4800:6$, which is virtually untenable.
One potential drawback of a worm gear/drive system is that it changes the direction of rotation by $90^\circ$, instead of the familiar $180^\circ$ with a pair of circular gears.