Basically you don't want any common denominators in teeth count, otherwise the same sets of teeth will engage at some frequency. If there is a small imperfection on a tooth it'll wear out quicker. E.g. a set with 5:14 teeth will theoretically wear better than a set with 5:15 teeth.
The simplest explanations I have found for involute gears is from one of those old 50's training films[0]. Not sure if this is the same one, but the first few minutes give a very intuitive explanation of where the involute shape comes from.
Reading this kind of stuff always makes me admire Victorian engineers even more, who had to do all the math by hand, to say nothing of the machine designs to cut and create these types of gears and mechanical systems. I suppose they learned a lot from prior tech, like clockmaking, but even there it would seem that fundamental problems would have needed solutions from scratch (eg shear failure probably isnt much of a…
The thing is, a lot of that math by hand is probably not long division, it's Greek style compass and straightedge stuff. There's an absolute ton of things you can do just tracing things out with a stick, and at adequate precision at that.
As an aside, for those not familiar with the author's other posts, do take a look. They are lovingly illustrated and explained, and cover a wide variety of topics.
A fun simple gear related concept is "hunting tooth". https://en.wikipedia.org/wiki/Gear_train#Hunting_and_non-hun... Basically you don't want any common denominators in teeth count, otherwise the same sets of teeth will engage at some frequency. If there is a small imperfection on a tooth it'll wear out quicker. E.g. a set with 5:14 teeth will theoretically wear better than a set with 5:15 teeth.
It's cool to learn the term for this, I have used the same principle before with bicycle gearing, so the chain would wear more evenly. Not sure if it makes much difference but it was worth doing anyway.
The simplest explanations I have found for involute gears is from one of those old 50's training films[0]. Not sure if this is the same one, but the first few minutes give a very intuitive explanation of where the involute shape comes from. [0] https://www.youtube.com/watch?v=Wlp8RxFt0ec
This old training video is great too, it also mentions the idea touched upon in the article that gear teeth are levers:
The simplest explanations I have found for involute gears is from one of those old 50's training films[0]. Not sure if this is the same one, but the first few minutes give a very intuitive explanation of where the involute shape comes from. [0] https://www.youtube.com/watch?v=Wlp8RxFt0ec
The idea of shining polarized light through gears made of Lucite to view the stress lines at the point of tooth contact is genius!