Involute Gears 2: Undercut and Profile Shift

In this video I'm trying to tackle undercutting and profile shifting of involute gears.
Animation manim sources:
github.com/GarryBGoode/Involu...
Gear drawing toolbox for manim:
github.com/GarryBGoode/manim-...
CAD utils for manim for dimension drawing:
github.com/GarryBGoode/Manim_...

[@harriehausenman8623]

The voice is understandable, the audio perfect, great editing and the visuals are just astonishing and beautiful. 👍

[@harriehausenman8623]

That's a really great in-depth look at undercuts. Love the math! 🤗 Now I guess I have to watch the rest of the series 😉

[@freebeerecords]

Thanks, that really clears up the rolling vs sliding question. Very nice animations and analysis, many thanks!

[@MedEngd]

Absolutely fantastic explanation, thank you so much!

[@5eurosenelsuelo]

This series is amazing.

[@diegoitaliani181]

Clearest video i watched see.

[@mattiaslaserskold137]

I wish I had seen this and the previous video first. Seriously, thanks!

[@AmitKumar-xw5gp]

great animations and explanation.. great work..

[@andrewh2341]

Super awesome work man 🙂

[@debasishsahu3082]

Really very good explanation

[@attilahaas2396]

Egy isten vagy köszönjük 😍

[@justRD1]

Awesome video! Can’t wait for part 3!! Any chance of doing that final animation to compare high contact ratio vs low contact ratio to see how the total sliding is affected?

[@gergelybencsik8626]

I did not know sliding is related to contact ratio. Is it really? I need to look into that, I'll think about it. On the technical side, that last animation uses a lot of control points to superimpose a wave on the gear surface curve, meaning it renders quite slowly, so it's a bit hard to work with.

[@PeterBaumgart1a]

Nice! Regarding your last argument: It can be shown mathematically that there has to be sliding, or rotation will not be smooth.

[@smoke3090]

Where can I get the parametric equation that defines the trochoid curve for each specific gear? I need it to draw it in CAD system

[@iayoub777]

great vid man

[@gergelybencsik8626]

thanks :)

[@samarthshetty1327]

thank you so much

[@lepistes3227]

thanks

[@Mr.TransparentleFraud]

oh, man. your vids are bible-like. every day i seeem i learn something more

[@user-pm5lz5ik3f]

Awesome video series on gears! Keep up the good work. I have one question for now: Why do you use "=1.25m" in the equation at 6:14 instead of "=m"? It seems like others use "=m" from what I've found on blogs online. Thanks!

[@gergelybencsik8626]

I talk about it later at around 11 minutes - I'm still not entirely sure what's right. I use 1.25m in order to include the clearance, and simulate a perfect trapezoid-shaped cutting tool with 1.25m height. With those assumptions, the math works out that way with 1.25m. I know most sources use 1m for this, I think because real cutting tools are not perfect trapezoids, but rather have a straight edge up to 1m, and the rest of the 0.25m for the clearance is rounded off, and usually does not cause undercut. Or they just hand-wave and simplify away the clearance.

[@user-pm5lz5ik3f]

@@gergelybencsik8626 Ahh you anticipated my question >.< Thank you so much for taking the time to answer and create this terrific explainer on involute gears. Keep up the good work and I look forward to watching what you release in the future!

[@ILSCDF]

Have you found a closed form for the intersection of the involute and the trochoid with your ideal rack?

[@gergelybencsik8626]

Eh no, I just used scipy's root finder to get that, and it's a bit finicky, sometimes screws up and you need to adjust the initial guess, but it gets the job done. And since it worked, I moved on, never really tried to get the closed form - but maybe one day I'll punch it into Wolfram and see if it can solve it.

[@RZWRr9g]

Can you make a video about `how we measure the undercut?` Thanks for your work about gearing!

[@gergelybencsik8626]

Thanks for the comment. Sorry though, I won't make more gear videos, this is about as much as I know about them. So for example, I don't know how to measure the undercut after the gear is already made...

[@volbla]

For a few weeks i've been agonizing over where exactly the involute curve and the undercut curve meet. Is there a closed formula for it? I'm starting to fear there isn't.

[@gergelybencsik8626]

I haven't seen a any closed formula for it, sorry. I used scipy root finder to solve that problem numerically for these animations.

[@volbla]

@@gergelybencsik8626 Yeah, that might be the only option. The real reason i want it is to make a continuous parametric in desmos which can be filled with a solid color :3

[@yousefalshehri9411]

I have a question, does the profile shift apply only to the pinion? or to both gear and pinion?

[@gergelybencsik8626]

I don't really understand the question. Do you mean 'pinion' as the smaller gear out of a pair? Profile shift can be applied to any gear. It's just that larger ones don't necessarily need it.

[@poornachandra80]

@@gergelybencsik8626 Pinion - in general is a smaller gear of the two.

[@oosmanbeekawoo]

Is there any use for gears nowadays? Gears to me seem like Renaissance-era old stuff

[@gergelybencsik8626]

They're literally everywhere. Cars. Power drills. Clocks. Printers. Any gadget or machine that moves, I'd say has about 40% chance it has gears in it somewhere. They're not new and exciting, I'll give you that, but far from obsolete.

[@randomaccessbrains]

Luckily my textbook also uses 1.25m for hd, so it was easier to follow along

[@poornachandra80]

YOU ARE AWESOME!!!

[@Mobosh]

whats the point of undercut gears though?

[@gergelybencsik8626]

You don't want undercut gears, you want small gears with low tooth count to maximize reduction ratio. Undercutting is the trade-off you need to manage for that.

[@Mobosh]

@@gergelybencsik8626 certainly but if we strive for greater reduction to the point where the teeth cant bear the load anyways, whats the point? surely theres a breakpoint where the optimal tooth thickness lies.

[@gergelybencsik8626]

@@Mobosh yes, I guess there is an optimal thickness, but I never looked into engineering gears for strength. Profile shift can mitigate the thickness issue fairly well, but increases the alpha angle and puts more load on the bearings of the gears. Gear design is not actually my field, so I have no real world experience here... But I saw some colleagues working on them, and it ends up being a delicate balance. You need to design for high strength, small size, large tolerance or low precision, wear, lubrication, even sound. You'll end up with a somewhat optimal design for those... but it all depends on the use case.