Square centres

— it suggests the square centre is to be used more for correcting an inaccurately placed centre hole on the work rather than driving the work

Years ago after this they made center laps . Used them many times when machining and grinding large Worthington Pump shafts . After HT the shafts they sometimes relieved and would not clean up to the existing centers . We just relocated the centers accordingly .
 
Center laps are useful tools for many things, including high accuracy and getting the center polished and cleaned up.
 
I might end up trying something just for the fun of it. If a 60 deg divot is cut very deep so that the edge is rather large in diameter then use a 3 or 6 flute 82 deg countersink as a centre. The countersink should get some bite into the edge of the divot in the work because of the difference in angles.
Instead of using a countersink I used a broken 3/8 inch shank 4 flute end mill. It was a 1/8 cutter which was broken off at the root leaving a nice 60 deg shoulder with four sharp flutes. This repurposed end mill was held in an ER collet and used to drive some work between centres without a dog.
A live center was used in the TS and some weight was added to the hand wheel to provide thrust on the centres.
It worked out quite well. By using a live center most of the traction from the headstock center was available to drive the cut.
There are obvious limits to the concept but it seems to be viable approach for some situations.
 
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I've done similar using a Philips head screwdriver bit as a small spur centre. Worked fine, but as you said, the applications are finite. In my case it was to turn a small bit of coco bolo and I didn't want to set it up on the big wood lathe.

-frank
 
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