Updated Ver.1.4 (Fixed Rendering!)
Generates a compatible pair of involute gears. It's nice!
This is a clean write from the math formulas. Consult the usual literature on involute gears for more info.
Ver1.1 adds a function to calculate center distance to use in the rest of your model.
Also added GearAGhost and GearBGhost parameters so you can design quickly by avoiding calculation time in the design process. These allow you to show a simplified cylinder representation of your gears on an individual basis.
Ver1.2 (Broken Rendering!) Improved calculation on the corner cases. The corners of the teeth will form better without resorting to excessive angular resolution to the parameterized functions.
Ver1.3 (Broken Rendering!) Improved GearAGhost and GearBGhost to show both the pitch diameter (red) and outer diameter (grey).
Ver1.4 Fixed Broken Rendering that existed in V1.2 and V1.3 !!! Sorry about that!
With OpenSCAD, include this library in the same folder as your design. You provide the parameters and it generates a pair of Involute gears to be used in your OpenSCAD Design. See the provided example files.
( http://www.openscad.org/ ) OpenSCAD is free and amazing. Use it!
You need the free program called OpenSCAD. OpenSCAD can generate stl files from your design to use with other tools.
Using Parameterized circular involute functions.
t is the input to the parameterization
R is the radius of a point in the involute
Rb is the base radius of the circular involute
Theta is an angle on the coordinate system of a point on the involute
t=(R^2-Rb^2)^0.5 / Rb (radians)
Theta=arctan( (sin(t)-tcos(t)) / (cos(t)+tsin(t)) )
This is the sum of the base circle vector and the tangent vector
f(t)=[x(t),y(t)]= Rb ([ cos(t), sin(t) ] + t [sin(t),-cos(t)])