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I have heard that it is good practice to always chose the number of teeth of two gears to be relatively prime. This is because there can be impurities in the metal, and if you have a small part of a tooth that is harder than the rest it will erode the opposing gear (there is always some friction going on). By choosing the number of teeth to be relatively prime, the wear and tear is distributed uniformly on the gears, and thus they last longer.

This is a similar problem to riding a fixed gear bike. When using skidding as a braking technique, specific areas of the tyre will wear faster unless you select a gear (front chainring and rear sprocket) combo with a large amount of skid patches. This is due to the rider always engaging in a skid with their crankset in a specific position - either left or right foot at 90 degrees, and the other at 270 degrees.

Here's a fun calculator for it: https://www.surplace.fr/ffgc/

Notice that a very common gear combo, 44/16 only gives 4 skid patches, so if you're after longer lasting tyres avoid this setup.

Anyone that is fascinated by gears owes themselves a visit to This Old Tony's video on YouTube titled "Gears! - But Were Afraid To Ask"


He goes into the nerdy depths of gear make-up, metallurgy, meshing, machining and mistakes as he manufactured metal gears on a mini-lathe.

I second TOT, his videos are just fun to watch. Plus, you learn something.

Going through his page, I immediately thought of his video on gears. Suprise! when it was mentioned at the end.

That's also what I was taught as a best practice, but it's not always possible. Otherwise, best practice is to index the gears (ie mark a specific tooth on each). That way, when you disassemble the gearbox (it's bound to happen sometime for maintenance), you can make sure it's reassembled so that the same teeth will continue to mesh, preserving the wear pattern. Otherwise, wear is substantially increased.

  That's also what I was taught as a best practice, but it's not always possible.
Well of course it's possible -there are infinitely many sets of coprime numbers! Silly engineers

Good luck for when you need exactly 2:1 ratio, like eg in clocks.

Just add more gears in between.

So it's a bit like violence.

Gears: If it's not solving all your problems, you simply aren't using enough of it.

I look forward to trying out your infinite gearbox implementation.

By relatively prime, do you mean the largest denominator == 1? Or in other words, 15 and 22 should be relatively prime?

This is what is commonly meant by ‘relatively prime’, yes. Also referred to as being coprime.

Defn: a & b are coprime/ relatively prime iff GCD(a,b) = 1

Yes, relatively prime means coprime means gcd=1

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