Involute Gears Explained

Involute gears are awesome.
Video made for Summmer of Math exposition 2 - #some2

I used Manim for this video, and developed an addon for drawing gears:

Manim sources for the video:

[andrewh]

I’m definitely sending my mechanical engineering students to this video when we get to the gears section of machine design. The animations really help illustrate the concept way better than I can draw on the whiteboard

[justRD]

Amazing!!! The way you visualized a profile shift at 2:45 on the two involutes based on center distance is phenomenal!! You should make a video expanding on the profile shift coefficient and it’s effects on sliding factor and undercut!

[sky]

This is one of the best graphical explanations of gears I've seen. I'd love to see more like it!

[matteo_vezzoli]

Awesome video! Very clear and simple explanations, everything made so much sense

[millwrightrick]

I had to learn all this when I was in trade school learning to be a millwright. Just a note that older gears had a 14.5 degree pressure angle and don't mesh with modern gears.

[neilthomas]

This is the best illustration I've seen on involute gears. Loved the 'all gears cut with a rack' demonstration.

[miniwizard]

Stunnningly demonstrated, explained and created. Something I had never thought about before, but makes perfect and sense when watching this video and the geometrical reasoning and constuction is truly beautiful.

[Doping]

I'm a chemist with no particular interest in mechanical engineering but you still hooked me. Impressive explanation video!

[inciaradible]

Fantastic video; never something I thought about before, but this is really beautiful to see.

[volbla]

For the last year or so i've been sporadically studying how gears are shaped, mostly just for fun. This was an eminent summary!

[mrwind]

I am a mechanical engineer and you have explained gears better in less than 7 min than my university did in 4 years. Thank you!

[bencesarosi]

Wow! This is among the best videos I've watched on the topic. Excellent work, thank you for the upload!

[vincentrobinette]

Excellent explanation! I will have to watch this video again, to remember the terms. It does make perfect sense, and good to know, that it's theoretically possible to make straight cut gears run smooth, quiet, and efficiently. In auto racing, we call these "spur gears".

[bertrc]

Glad to see the introduction of the rack principle which does away with complex maths for gear production. Not all gears are made with a rack cutter. In fact most are not.

[ddburdette]

I once worked as a shipping clerk at a machine shop that made precision gears that were used to check production gears. Although it was not strictly necessary for my job, I became fascinated with the geometry of gear teeth, otherwise known as involutometry. That was 40+ years ago, but I still find it interesting!

[tom-hykn]

The best explanation I have seen by far.

[AKfire]

Brilliant video ...Awesome animation...Totally incredible.. Loved it..

[MohammadHosseinMousavi-us]

The video about involute gear was great, please make more like it👌

[joels]

This is by far the best explanation of involute gears I've ever seen. Well done.

[paullinsay]

One thing that you didn’t point out, though it’s clear from your animation, is that the force applied to the gear at the point of contact is always perpendicular to the radius of the gear. This means that as the gears rotate they are always producing the maximum torque on each other and it is constant as they spin.