Can anybody point out gear design fundamentals?

Hey guys,

I was wondering if anyone could point me towards some reading about designing gears, especially matching sets.

Gears feel intuitive and I see that there is plenty of room for applying mathematics to gear design though unfortunately for me, I know very little math and very little about gears. I understand what gears look like and how they function but do not understand the fundamentals of designing gears, especially ones that match each other.

I feel like it would be easier to ask for references and literature than sit here and try to re-invent the wheel (ha).

Thanks for the help!

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1 Answer

It is very hard to give a short answer to this question since there is so much to tell about gears. I'll try to explain the question you've specifically asked for, which was on 'how to match gears' + I'll provide some useful sources on the rest of gear fundamentals. So here goes:

Basically when you're trying to find matching gears, what you're looking for is a thing called the 'module'. I'll explain the term 'module' using an example: we take a pinion with 28 teeth (Z) and a diameter (d) of 28mm; Note this is the diameter on the pitch circle. The circumference (O) of the pinion is then given by multiplying π by d = π * 28 = 88mm. The pitch (t) is then found by deviding O by z = 88 / 28 = π (or 3,

The metric (imperial is a different case) module is defined as m = t / π. So in this case m = π / π = 1mm. You can now calculate the diameter of the spur wheel (again, this is the pitch circle): d = z * m.

When you want a 1:2 gear ratio, your spur wheel will need 28*2 = 56 teeth. You want the modules to match to make the pinion and spur wheel work with eachother, so you take m = 1 and z = 56. This would give a diameter of d = 56 * 1 = 56 mm.

I've now given you a example on how to match gears, but my explanation doesn't provide any information on WHY you would choose these specific values. This, among others, has to do with the intended reduction ratio and the power that needs to be transferred.

At this site ( you'll find more on the fundamentals of gears (the English text is displayed on the right side of the site). The wiki page ( on gears gives a very good explanation of all the terms involved with gear calculations as well.

Hopefully I've been of any assistance. If you would run into any problems with the calculations I've provided or if you have any other questions, please do ask!

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