A ball turner is kind of a unique accessory for your lathe. Most every machinist at one time or another will have a need to turn spherical shapes. The easiest way is with a ball turner. You can buy one, but they are simple enough to make yourself, and there are all kinds of instructions out there on building them. Usually the cutting tool travels in a circular arc in a horizontal plane or else in vertical plane along the centerline of the workpiece. I have built a couple of them, one quite large with a capacity of about 6" diameter and the other smaller, with maybe 2" diameter. I'll just show the small one today. I need to mention this is a demonstration picture. Normally when I'm turning ball ends I hold the work in one of those 5C collet chucks. That way I do not risk having the chuck jaws strike the ball turner, and cause all sorts of commotion.
On this one I used some features of a plan that I found, but modified it so that it would work on the quick change tool post. I have found it handy for making the balls for fly ball governors, ball ends for guard rail posts for railing around models, etc. One use was to form the ball ends on a helping hands work holding fixture for silver soldering.
For this demonstration picture I just clamped three pieces of brass and positioned them together. From here it would be a simple task to daub the joints with flux and silver solder it together. To assemble that same configuration without the fixture would be a difficult task.
By the way if you do not want to build your own helping hand fixture Harbor Freight has an in store coupon sale going on right now, till Feb. 11, for $1.97. (normally $3.99) It is smaller and does not have as many joints to move and position things as my home made one, but at that price I could not pass it up, even though I already had one. They also include a magnifying lens. Take that off attach a nice handle and do a little detective work on the side.
In closing I suppose a ball turner could be compared to a bull on the farm. It is not the amount of work it does to earn his keep, it's the occasional service it performs.