This is a remix of Parkinbot's Cut your own gears with profile shift - OpenSCAD library, modified to work with any arbitrary shape of gear tooth on a cycling tool to cut gears out from a circle, just the way gears are crafted in industry.

Put the gears_mod.scad file in a directory searchable by OpenSCAD, and put the line
use
in your scripts to use the library.

Refer to Parkinbot's design for a full explanation and instructions.

The concept is best illustrated by Parkinbot's video:

What I did was add additional tooth rack styles, and included a rack_id parameter in all the gear modules.

The default value rack_id=0 gives the original involute gear tooth.

Here are the additional tooth styles:

rack_id=1 - beveled sawtooth
This is basically the standard involute gear tooth with beveled corners, with one side of the tooth being perpendicular to the driving force direction.

rack_id=2 - sinewave
I recommend the sinewave gear teeth for 3D printing. It has naturally round curves suitable for small teeth using a 0.4mm diameter nozzle, minimal friction due to rolling surfaces between the teeth, and more pushing surface than the cycloidal teeth.

rack_id=3 - tilted sinewave
I have used the tilted sinewave teeth in an application where the force is always in one direction against the teeth. Asymmetrical teeth have some sliding friction, but in practice I found these teeth to be quite smooth.

rack_id=4 - semicircle
These teeth are made of semicircles. They approximate a cycloid and have low rolling friction although they may want to slip apart under high loads. These teeth are easiest to 3D print also.

rack_id=5 - cycloidal (new update, March 2022)
Cycloidal teeth have the least amount of friction because the surfaces roll against each other instead of rub. They transfer a decent amount of force without slipping. Probably overall the best kind of teeth for 3D printing. (Many thanks to Jack for helping me get this correct.)