Is there a drive that does the opposite? A drive that converts intermittent rotary motion to continuous rotation? I never studied this sort of thing in school, unfortunately.
From the perspective of a mechanical watch, there is a component known as the mainspring. It is a spring that stores energy from either manual winding or automatic winding.
With manual winding, turning the watch's crown to wind the mainspring is an intermittent, rotary motion. Alternatively, with automatic winding, a rotary weight that moves intermittently (e.g., when the wearer's arm is moved) is used to wind the mainspring.
In either winding scenario, manual or automatic, the result is that intermittent, rotary motion causes energy to be stored in the mainspring, which is then subsequently available to provide for continuous rotation of the watch's mechanics.
I caught myself thinking along the lines of "of course it's not possible, that would be preposterous!", but as you say, a watch spring mechanism does exactly this.
The key concept here is "stores energy".
If you're ever bored, look at what four bar linkages can do. Stereotypical mech eng topic where its shocking just how many different things four chunks of metal and some bearings can achieve. A really poor analogy would be its kind of the turing machine of the mech eng world in that it can seemingly do almost anything with a minimal amount of parts.
There is an interesting scaling effect where the math for linkages scales pretty scarily as the number of bars increases.
(edited to add, and you can see an applied model in some stair stepper exercise machines where the arm actually moves thru an arc, which I guess is the intermittent rotary motion you're looking for?)
I would like to transfer the movement from the red wheel into the smooth continuous rotary movement of the green wheel.
These are fascinating to watch: http://en.wikipedia.org/wiki/Hit-and-miss_engine