That type of expanding anchor/holding joint was the type I fabricated for my
9x20 lathe shortly after I started using it.
Someone mentioned what that type of joint is, but I used it because I
remembered it from a bicycle I had.. it was used where the handlebar stem
was held in the fork tube.

After drilling the stock that's been turned to a slip-fit diameter for the
spindle I.D. (and leaving a stop shoulder), I made the diagonal cut with a
hacksaw, then filed the center hole oval at the contact point on both
sections to allow the two sections to shift on the angled surfaces when the
nut was snugged, effectively locking it in the spindle.

There may be a method of fabricating a hollow version (for longer workpiece
pass-thru), but I haven't encountered a need for one.
A hollow handle extension with an internal thread could be added to the left
spindle end, in place of the nut that's used to set/adjust the spindle
bearing preload (with a soft-point setscrew or other means of preventing
overtightening of the preload).

--
WB
..........


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Lots of the imported bench lathes don't have spindle speeds low enough to
make power threading short pieces practical.

You said it!

It never occurred to me that anyone would leave the power connected
when having the crank in place!

The plans for the crank I saw involve the sort of joint used in bikes
(I don't know the name, it is a bar which is cut diagonally and
connected by a bolt. when tightened it expands inside the spindle).