EG, make'm all like this and save the unnecessary material for something important.

Them guys got hit with the ugly stick

but thanks, illustrates what I was trying to say. In all this explanation I kinda forgot what that was but let's try to wrap it up a little ...

I think the question was, how can you figure out the tooth thickness ? The answer is, there's formulas

*but* what I was trying to express was, conventional terms will trip you up if you don't understand that they are just shorthand. Teeth don't have to be a 'standard' size, shape, or thickness. Even 'standard' teeth, you can scooch them out or you can scrunch them in. They will still work, altho not as well as having them be in the 'normal' middle of the range.

You calculate the tooth thickness by using the pitch diameter with formulas that are in several books - but it has to be the

**real** pitch diameter, the ones that the gears see, not "100 tooth 10 DP has a PD of 10" .... That isn't reality.

All that to get here, sorry, may as well use it for something useful ...

All of sane parallel-axis gearing is based on that idea of two friction disks, which

**are** the pitch diameters of which we speak all the time. (Module teeth are upside-down and backwards, as befits anything invented by the french. We're going to totally ignore that except to say, if you want to retain your sanity, figure everything out in DP then convert).

Imagine you are back in the tenth century or something, you have a grist mill with one three-foot stone friction driving a six foot stone. Basic 2:1 reduction but it doesn't work too good, put any pressure on and it slips. So you get a brainstorm, think "let's stick some prongs into the little one so the big one can't slip !" and if you have prongs in one, then you need holes in the other to accept the prongs. That's a biological concept which they understood even back then.

So you take the small stone, measure the circumference, divide it into even segments, and put 19 pegs in it. (The witch down the street said 19 was a good number, okay ? sheesh). 3'

**pitch diameter** times pi equals 9.425' circumference. Space your pegs at .496' or 5.95" -- 6" is going to be close enough for the tenth century, and since there's no bureau of standards yet and they say the average dick is 6" it's easy to get the village together, measure them all and average it out - - and you now have a 6" circular pitch pinion.

Circular pitch is really popular with gears made out of pegs - "lantern gears" because it's super easy to figure out.

If you made the sticks stick out about a foot (that'd be two dicks long, which is conveniently equal to one horse dick, in the old measurement system) you'd already be using modern practice

. We can call that the

**ad**dendum because it's

**add**ed to the pitch diameter, and the holes in the mating part get to be the

**de**dendum because they are

**de**ducted from the pitch diameter. {Sorry for the childish extra emphasis but it's a really easy way to remember which part of the tooth is which).

Once again I'l beat you in the head with this but remember the numbers are added to the

**real friction disk** not something the witch said because she didn't understand gearing yet and hadn't written up any tables. It's all from that damn friction disk.

The holes should be deeper than the stickouts, because you don't want the prongs to bottom out and get smushed and dirt needs a place to go and so on, so the dedendum is bigger than the addendum. Now you've got the modern terms pitch diameter, addendum and dedendum all figured out. We're well on our way to nukular submarine turbo-reduction boxes

Dead horse but the concept of the friction disks and the point at which they touch is

**basic** to all gear terms and geometry calculations. From this law hangs all the books and tables.

If you understand that then everything down the road makes sense but if you don't, you'll be forever beating yourself in the head with a frying pan because the only thing that will ever work right with book numbers is totally 'standard' sizes and dimensions. Since many or maybe most gears are not 'standard' then you're going to be plenty miserable if you skip that first piece of info.

The next step is improving them pegs by making them shapely and curvaceous but if the audience has evaporated, I can take a nap instead. Us old folks need our naps.