There have been times that I wanted to put a ball end on a short workpiece but the turner ran into the chuck. Here is how I solved the problem.
I made a sleeve with an R-8 taper to fit the collets that I have for my mill. Once I had finished the taper I placed a 1/2" collet in the sleeve and a piece of 1/2" material in the collet. I used a rotating center to apply clamping pressure so I could turn the outside to ensure that it was concentric. I can now turn a ball on a workpiece that is little more than twice the diameter of the ball in length.
The material used was a piece of heavy wall pipe, Schedule 80 in the US, approx. 6 inches long. The wall thickness is .133" which was enough for the taper but I had to press a reducer bushing in the other end so I could bore it for the .950" end of the collets. I then made a cap to close the end and provide support for the 7/16" bolt used as the drawbar.
Here is what it looks like.



Joe