How can I create WORKING gears in Illustrator?

Question 1

I cannot seem to get this right.. I want to create 2 gears that work together.

enter image description here

I can create gears, but I cannot seem to figure out the math needed to make them uniform, or where they work together.

There is a mathematical way to do this. I do not know the formula..

What I’m trying to accomplish.

not my artwork

What I tried:

Create a circle 800px x 800px
Create a circle 600px x 600px
Create a star with inner radius 200 (400 diameter), 500 (1000 diameter) outer, with 12 points.
Compound the smaller circle and star. Intersect the remainder.

Do the same thing, except half each value and the points.

I would think this would make a 2:1 gear ratio where both gears match exactly, but they don’t…

enter image description here

Question 2

The same way one would create a real working gear. Here are tools which will create gears:

http://geargenerator.com — this tool will allow one to save an SVG which can be edited in any vector drawing program
http://sourceforge.net/projects/gggears/?source=directory — opensource tool
http://www.idleamusements.com/?page_id=367 — an on-line tool, it will create a .dxf which can then be opened in Illustrator
http://www.cabinetpartspro.com/GearMaker/GearMaker_Setup.exe — Windows tool

See the site http://woodgears.ca/ for more information on gears — they have a Gear template generator as well: http://woodgears.ca/gear_cutting/template.html

Alternately, you can draw them by hand — you just need to use basic geometry to ensure that the diameter of each gear is an integral ratio.