Here's how you do it. The center's path isn't circular, so simple gearing won't work, but an Oldham coupler does nicely.

http://www.thingiverse.com/thi...

Obviously, the thing is just a toy not a real drill bit -- I can't fab metal.

You should redesign it so it has sharp edges so it can actually cut things:

http://web.mat.bham.ac.uk/C.J....

Turns out thins would work perfectly in a three gear planetary system where the center gear is held in position

Sorry to be a buzz kill, but the part shown in the picture will simply make a circle. Look up the motion on Wikipedia:
http://en.wikipedia.org/wiki/R...

The center point of the bit would have to move in an "circular pattern" apart from the rotation of the drill. Cool concept though! :)