This ball turning tool was made to a design published in Model Engineer's Workshop Issue 26 December 1994. The purpose was to make the ball handles for my Tool and Cutter Grinder.
The design is one which turns about a vertical axis and works well. However if I did this again I should probably make on of the type that pivots around a horizontal axis and fits into the tool post. Below is shown the 3 stages in making a ball handle. First cut two grooves of distance from the ends equal to the diameter of the ball to be made. Then turn the body of the handle down to give two parallel portions to hold in the chuck. The larger diameter is large enough for the chuck jaws to clear the large ball end and the smaller diameter is large enough to allow the jaws to clear the smaller ball end. This enables the blank to be held in the chuck for turning the balls on the ends of the blank.

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Up And Over Turning
I do like the "up and over" version of ball turning tools where
the tool rotation axis is horizontal and at right angles to the lathe axis.
When thinking about this concept, it occurred to me that these types of
ball turners, are very similar to boring heads and I already had one of
those. I therefore mounted it in my shop spindle and bolted it to the cross
slide of the lathe as in the photo. The overhang looks impossible but it
is unimportant as the forces are pushing the tool horizontally not vertically
and the setup shown here works superbly.
For those interested in this style of ball turning, I wrote an article on
this in Model Engineer's Workshop - issue 133. I do find the system more
adaptable however, if the clamping arrangement is fastened to a vertical
slide. The dimensions of the tool bit are shown below

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BALL TURNING
A lathe home made attachment