More ramblings from a crazy old man. I was thinking that for producing solely cylindrical objects such as vases and the like, one could have a rotating build platform. Then the print head would only need to move in one direction - either the x or y and then only after one complete rotation. It'd probably need to move in z as well on layer change because having a build platform that rotates as well as moves up and down might be a bit too tricky. The bed could be some sort of "lazy Susan" type arrangement and you'd probably want it to turn with constant linear velocity, rather than angular velocity (a bit like a DVD player head). I'd have thought it ought to be pretty simple to do and potentially very fast and stable, as there would be no changes of direction for any of the moving parts (except at layer change) but one would be spinning the printed object of course.
Then I got to thinking actually, if one varied the speed of rotation at the same time as moving the head back and forth in X, one could in fact do straight lines and so produce any shape, not just circular. So effectively, X is linear but Y is circular (but doesn't change direction, only speed).
Just thought I'd toss those thoughts into the pond and see what ripples come back.