Nautilus gears based on logarithmic spirals. The gear profiles were generated using this Maple script for which full credit goes to the original author:
http://www.maplesoft.com/applications/view.aspx?SID=95483&view=html&L=G
Rendered animation of the gears: http://www.youtube.com/watch?v=dtkEyZwuwH4
Don't own a 3D printer? Now available for purchase at Shapeways (http://shpws.me/Kdit) The design will always stay free and open. https://www.youtube.com/watch?v=vTMVMf_3fCw
I'm not going to upload the SolidWorks file because it is frankly a mess of different experimentation, but I uploaded the DXF which should be easy enough to modify with most CAD software.
Update: No more breaking pins!
I've replaced the pins with a simple press fit design. Print two of the Connector Bar v2 or the Curved Connector Bar v2 (same idea, just curved for aesthetics) and snap them together! On a well calibrated printer they should snap together easily and hold tightly with friction.
If they aren't sticking together just add a drop of glue! Warning, these bars are one time use, they will be very hard to pull apart without breaking the pin.
I will keep the original bars on for reference.