I would like to experiment with making my own gears using essentially a flycutter with straight sides to form the curved shape.

For those who think I'm nuts, see

My interest is in CNCing the process, and to that end, developing a spreadsheet listing all the variables for all the possibilities.

From that spreadsheet, I can (manually) plunk the values into a CNC program and start making gears.

So, I've been reading (and reading and reading) all about gears.

I think I understand most all of the numbers, formulas, constants and variables involved, save one: Pressure Angle.

I have not seen, in all my reading, an explanation of Pressure Angle that makes any sense to me.

I've seen all kinds of mechanical drawings showing an angle, calling it "Pressure Angle", and labelling the angle (usually 14.5 degrees), with absolutely no indication what that angle represents or how it's derived.

Often, there is an IDENTICAL drawing beside it with the angle now indicated to be 20 degrees, the "other common pressure angle".

Now, my reading of gears tells me that the cycloidal shape of gear teeth means that a (section of a) circle contacts another (section of a) circle.

And my simple remembrance of geometry tells me that a circle contacts another circle at a POINT, whereas an angle is defined by two intersecting LINES.

A pair of points don't define any sort of angle.

So what's a "Pressure Angle" ?

Any clarification greatly appreciated.

Alan