Paradoxical Gear Sets

That's beautiful stuff. Gears are fascinating in their own right, these gears doubly so. As a kid I would disassemble (for the most part, sometimes I managed to put things back together again) all kinds of stuff and my favorites were alarm clocks and regular clocks. I must have destroyed what today would be worth a small fortune of clocks. Gears always fascinated me, they look so simple and yet they're quite complex.

The beginnings of the industrial revolution were grounded to some extent in the clock making industry, to aid the sea going nations. Cutting the gears for those clocks required a degree of precision that had not been seen for a long time and from that clock making industry we got to portable clocks (watches), mechanical computers and so on.

They just love it in French engineering schools. They bring it on the day of the test, if you make an odd number of sign error you completely miss the trick, if you check your results for general coherency you'll never believe they are rotating in the same direction and you'll loose quite some time checking your stuff.

See also: http://www.shapeways.com/model/458290/magic-gears.html. 3 identical gears that, depending on the way they are assembled on their axes, behave like normal gears or paradoxically.

Oh, I see. Normal gears can be flat, but paradoxical gears have to be 3D, they're like a pair of corkscrews driving each other. Right? Is there friction at the points of contact?

Are they still gears if they are powered independently and the only connection between them is that they may come in contact without blocking each other's rotation?