[Scrounging Thread] Gear Mathematics

Good evening (to those of the GMT+1 persuasion)! I’m recently into gears and realized I haven’t the foggiest about some very basic concepts.
What I’m thinking about is the intricate relationship between gear diameter, number of teeth, and - in consequence) rotations spaeeds.
After this long and winding introduction: I’m afraid I need formulae.

Any of you gals and gents stumbled upon such formulae that I may “inadvertently” make my own for a time?

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So, there are many good examples.
Start here: Gears and Crankshaft Movement MASTER CLASS
Also, one of my first faces, cosmetically but not functionally updated:
Bodestone - Simple Simon Gubbins V4 - watch face for Apple Watch, WearOS, Galaxy Watch, Pixel Watch, Huawei Watch, and more - Facer

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In general the gears teeth have to be made of fitting size.
The speed ratio is inverted teeth count ratio…
What else do you need to know?

My favorite tool for creating wheels with teeth that actually mesh and roll on contact surface is GearGenerator

Check these threads too:

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You can find sites about gear ratios and even calculators out there.
I think it is a must, that the gears mesh nicely. I do not think much of watch faces with a whole bunch of gears in the background that do not interact with each other.

About gears and ratios:
The obvious is if both gears are the same, then they will run at the same speed, but in opposite direction. And also quite common sense is that if one has 20 teeth, the other 10 teeth, then the smaller one will run twice as fast as the larger one. I would start with these basics.

20 tooth gear,
sample rotation speed: (-6-#Dsm#*120)
(Note, Dsm is broken, better to use #DWFSS#/6)

10 tooth gear
sample speed. (10+#Dsm#*240)

For sizing and positioning, sometimes a bit of a trial and error:
Below an inspectable sample. Once you get the hang of it, then yes, check out the master class.

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Very nice example with included images my friend, bravo :clap: A big like for me is the Wake Up Hands, which I normally like to use myself nowadays :+1:

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Yesssss! Exactly what I was looking for. Thanks yet again! Deliberately titled “Scrounging Thread” because all I found in a much too quick search was very deep scientific physics departmental *.edu papers that are far beyond my abilities.

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Bookmarked as new all in one resource for me too.
This is why we want new people. To ask and bring together this stuff.
@petruuccios and @tom.vannes Stars as always with the eye on the ball and the memory to match.

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Hope you share your finished design with us all :grin:
I think most of us have had a “Cogs&Gears” phase at some point in our creative journeys lol

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No, no and so much detail no (yes amazing and fantastic but… overload) . My brain breaks just looking at how I might do that much. My Gubbins was functionally accurate and it pushed me.

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“plain and simple” lol. there’s mayhem going on :smiley: Loving it!

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It is a masterpiece

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One more example (I had thousands to look through :joy:) -

If anyone wants any bits, just let me know and I’ll get the laptop out to share next time :slightly_smiling_face:

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I’m gonna need some time with that one and 2 springs.

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On the cog front, those 3d images are great but with one flaw. The lighting does not work dynamically on the face:
ezgif-410610ec1db86f
If you use a flat cog and a duplicate, lighter underlay, offset then you get dynamic highlight:
ezgif-442dea7fd93ee8

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Yes I know … 3D effects sometimes do not do it…

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Time and place. Leaning that as I go. The offset highlight is a recent for me on hands and thought it would be good here.

3d all the way for static though.

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Yes, definitely. For some gears (especially the Geneva ones) I went a lot less 3D or no 3D, just shadow.

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So, for beginners

Also I think either this thread has been hidden or everyone is fine and not letting me know I am the onely one for 2 days?

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Strange thing, though:

Mayve they got haxx0red?

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Okay, well, I did 3 gears, one with 60, others with 30 and 20 teeth and half/third radius.

Seems to work. It’s not perfect, because I suck at Photoshop, and the two gears aren’t really symmetrical - or it may be a positioning thing, probably both. But I will figure this out soon. It’s also not easy to get the teeth in the same size, regardless of number. Gotta fiddle with a lot of parameters in the “Polygon” feature of PS. Ah well.

So rotational speed is directly dependent on number of teeth. That’s at least something, I guess.

Thanks for the wealth of information I got here - will work myself through it soon. Wanna get this right :slight_smile:

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