Compound gear train is a gear mechanism with a number of gears fixed together to reduce or increase the speed. And its biggest advantage is the ability to speed reduction without making gears with large diameters. Therefore, we can achieve a high-speed reduction, in a compact size.

Compound gear train is used when the required gear reduction ratio is more than 5 to 1 and less than 100 to 1.

Find the Square root of the desired reduction ratio

First, we need to find the square root of desired reduction ratio. And the reduction ratio is the ratio between the input speed and the required final speed.

Pressure angle and select the minimum number of teeth on pinion

System of Gear Teeth	Minimum No. of Teeth
14 ½ Composite	12
14 ½ Full-depth involute	32
20 Composite	14
20 Full depth involute	18

Interference can occur when the number of teeth is less than the minimal number allowed. Therefore, one gear’s involute component may come into contact with the other gear’s non-involute component.

The number of teeth necessary for the mating gears

The number of teeth necessary for the mating gears = Number of teeth × SQRT of desired train ratio

Even the required number of teeth can be calculated using the above equation, it usually keeps giving decimal values. Yes, you can round it, but when you do so, the SQRT of reduction ratio changes. So, that means your output rpm will be more likely to be different from the expected one.

To fix this error, you can do the calculation for different numbers of gear teeth (it should be more than the minimum number of teeth) and round the number of teeth necessary for the mating gears. And then calculate the SQRT of reduction ratio for each rounded value. And then you can select the closest and most possible reduction ratio.