Nautilus gears based on logarithmic spirals.
Gear profiles generated based on research by Ágnes Dabi, Zsigmond Istvan Varju, Dr. Laczik Balint et. al. at the Budapesti Muszaki es Gazdasagtudomanyi Egyetem.
Agnes, Dabi (2005). Változó áttételű fogaskerék tervezés (Doctoral dissertation).
Budapesti Műszaki és Gazdaságtudományi Egyetem
The gear profiles were generated using this Maple script for which full credit goes to the original authors:
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)
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.
Print two gears and two connector bars.
Place the gears onto a connector bar, make sure the gears align as in the pictures, snap in the second bar and enjoy.