Updated Ver.1.6 (New! Added BacklashA and BacklashB parameters)
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!
Ver1.5 Fixed a bug in calculating the root clearance of the teeth.
Ver1.6 Added Parameters to add backlash to the gears. BacklashA and BacklashB narrows the teeth by the parameter's amount of millimeters along the pitch circle. BacklashA subtracts from each tooth of GearA and BacklashB subtracts from each tooth of GearB. This is better than the old Rescale parameter. Zero means no backlash. Oh yeah, Made it LGPL since this is a library to be included with other things. This is more permissive. Enjoy the satisfaction of gears.
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.
OpenSCAD-(Fix puking previews by Edit/Preferences/Advanced/ForceGoldFether).
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)])