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I was pondering teh theoretical limits of gear ratios and the concept of "infinite" ratios came to mind. Obviously, in the physical world, we're limited by things like material strength, size constraints, and manufacturing precision. But ignoring those practical considerations, is there a purely theoretical upper limit to how high a gear ratio could be achieved in a single stage, or even across multiple stages?
My initial thought is no, there isn't. You could theoretically keep increasing the number of teeth on the driven gear while shrinking the driver gear arbitrarily. The force multiplication would get exponentially larger, but as long as your dealing with mathematical ideals (perfectly rigid gears, no friction, etc.) it truly seems like you could approach infinity.
However, I wonder if any fundamental physics come into play at extreme scales? Perhaps quantum effects or even gravitational influences would start to become relevant when dealing with gears on a microscopic or astronomic scale. Has anyone else thought about this,or come across interesting articles or thought experiments exploring the theoretical limits of gear ratios? I'm interested in hearing different perspectives.