Can we produce gears of different sizes that still mesh correctly with each other?
I think so. This routine figures the tooth placement from the pitch radius which, if I understand it correctly, is the place where the teeth of meshing gears interact.
What you do is decide on a pitch radius, say 130 mm and 13 teeth. Then you if you wanted a 13:6 gear ratio you'd go for 60 mm and 6 teeth.
I did that and then placed the two gear centers 60 mm + 130 mm away from each other. As you can see they mesh very nicely.
Okay, Simon! Make us some gears! :-D
Here's a gear pair with a 24:11 ratio. It took me about a minute to design it on Art of Illusion.
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