Our design dept is getting 'creative' again, and has asked me if it's possible to machine a thread.

The catch is, the thread is a taper thread which then runs smoothly into a parallel thread. In other words, we have a bar with a taper at the end. Then we want to put a thread on all of it, smoothly running up the taper and along the bar, all at the same pitch, same form, etc.
No, I don't really know why they want to do that.

Now of course there are lots of ways to do it, but none of them are particularly easy....
Any thoughts? At my disposal I've lots of 4 axis mills, a 5 axis integrex mill-turn and a few two-axis lathes.