@cromos - Indeed it is, Breguet’s masterpiece of so many years ago - 18th century I think?, but I have a question, or two:
- Do you want to just animate the tourbillon movement?
- Are you considering a double tourbillon?
- Is it the main drive spring you are referring to?
- Is it the escapement spring, you want to animate?
As far as the tourbillon itself is concerned, that is pretty easy to rig, if you have ever done an epicyclic gearbox, or rear axle differential, if not, it is not easy at all! 
For an escapement, or main spring, the best approach will be a curve object, probably Bezier, with a bevel object to get the 3D form, then use a series, of hook modifiers linked to bones in an armature to simulate the winding/ unwinding of the spring.
A chain of bones with drivers on each such that they rotate in unison is a good start. So bone 1 has bone two parented, for each rotation of bone 1, bone 2 has an equal amount as a driver - thus if bone 1 rotates 10 degrees, bone two also rotates 10 degrees relative to bone 1 meaning 20 degrees in total. It may be better to gradually reduce this as you go down the chain so the movements get smaller the nearer to the centre of the spring you are.
Or, it could be done with a IK chain, I would need to play a little.
Many years ago I built and rigged a complete long case clock mechanism - on here somewhere… so an anchor escapement rig is already there, I will see if I can find it… (here it is) I will need to find the blend file though.
Right now I am freezing my ass off in Stockholm, so don’t have access to my server and all my blend files of this nature, so it will be a week, or so before I can extract one of those. However, if you would like to have a go based upon what I have said I should be happy to help.
Cheers, Clock. 
