Allow me ask possibly one dumb question. If it proves to be dumb. The world is one dumb question less, which is good.
When design or selecting gears, we want the numbers of teeth of two mutually contact gears be mutually prime. This is to avoid the following situation. If the numbers are not good enough, there is a good chance that two specific teeth will repeatedly meet each other, causing uneven wear and tear. By using prime numbers, the meeting of two teeth is more random. It seems that no book ever mentions this, could even be one of the "secrets" of gear designers, but I know this is a good practice many engineers are well aware of.
So, naturally, the next question is, does this apply to chain & gears combinations, like the one used in a typical bicycle. Obviously the two gears are not in direct contact. At a specific moment, only a certain number of teeth and the slots in the chain are stressful, other are slack. We want the combining of this stress from three parts (two from gears and one from the chain) be as random as possible, in order to avoid uneven wear and tear.
Should this be a consideration for chain/gear design? Does my argument make sense. It seems that nobody talked about this before.
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