OpenSCAD and Gears
OpenSCAD is free software that you can use to create solid 3D CAD models. You use use code to build and then preview. There's ways to animate it too. Lots of neat features, and will export to a variety of CAD formats, including .STL files.
Sure, the UI/UX is circa 1996.. But it's free to download, and even the source code is open.
Then I noticed the gears the first two OpenSCAD programs produced... They do not have a lot of the characteristics of, what I assume to be, more operationally efficient machined gears.
After a bit more searching on Thingiverse.com, I found an OpenSCAD program that's public domain for designing involute parametrized gears.
After adjusting the variables (at the bottom of the code), instead of just getting one gear, you can get involute spur gears, helical gears, partial gears and even racks – that all fit together. Check out the Animate command found in the OpenSCAD View menu.
Alternative OpenSCAD web apps
CoffeeSCAD.net - Using CoffeeScript syntax, web app
ImplicitCAD.org - Built with and can use Haskell, has some neat features