# Thread: Ratio Calculation For 3 pulleys

1. ## Ratio Calculation For 3 pulleys

I know how to calculate 2 pulleys ratio but when 3 pulleys I have a little problem.

For example driver pulley is 10" diameter driven 30" pulley the ratio would be

3/1 or 3:1

How are about driver pulley is 10" turn the 20" driven pulley and the 20" pulley turn the 30" pulley.

How do you calculate this problem?

Thanks

2. the basic rule is to work them in pairs and then muliply the results:
10/20 = 1/2, 20/30 = 2/3
1/2*2/3 = 1/3

however, because the 2 middle pulleys are of identical size then and only then you calculate as follows:

driver pulley/driven pulley = 10/30 = 1/3

1/3 * motor RPM = output RPM

Motor RPM/output RPM = Reduction ratio which in your case would be 3:1

Best regards

Bruno

3. thank you

4. Just a comment: in a two stage reduction as was proposed, the center pulley must be a compound pulley or gear with two single components fixed side by side on a common shaft or hub. If these two components are exactly the same size, then they are considered to only be an idler and have no effect on the ratio, as Bruno alluded to, although perhaps implying that there was a 'special rule', but that is the basis for it.

If you have a 3 (or more) gear train with a 10 driving a 20 driving a 30, the center component(s) are still idlers and have no effect on the ratio, they are merely motion transmitters.