Thanks for all the replies so far.
I forgot to mention that this joint obviously also needs constant length properties. One end will be clamped in the 3 jaw, and the other clamps and turns the workpiece. The workpiece will be supported by a bearing at the clamp end and a live/dead center at the other.
It needs to be rigid and zero backlash because the 2" stock might be aluminum, and get cut with a 3/8" end mill.
The swivel impact joint seems like a good inexpensive idea, but I couldn't find out anything about a "ball and paddle" joint.
You can make a form of CV joint that may be adequate for this task.
One shaft has a ball on the end and there is a pin through the ball at right angles to the shaft. The other shaft has a hollow barrel with an inner diameter to accommodate the ball and two slots to take the pins.
OK, but does it have CV properties? This design has the splines in the socket pivoting relative to a fixed point on the ball, whereas in the animation by small planes, the pivot point is moving back and forth along the ball.
As for how big this joint has to be, I dunno, as long as it meets the stiffness requirements, and costs preferably less than than 20-30 USD.
Any more, and I'd rather spend my time tilting the 4th axis back and forth manually.
The bridgeport quill master is too expensive.
I have to think a little bit about just how important it is for the joint to be totally CV. I'll be cutting a bunch of helices and overlapping spirals, so it would be nice if they are straight and not wavy.