I'm not unreasonable - enough begging and I'll relent almost every time.
Right, the wotsit is to aid the drilling of chisel tang holes in handles of varying diameter using the drill press. Viz: A collar of appropriate size is pushed on the ferrule end of the handle, and then handle is pushed up tube where the collar is a nice fit in the end - thus the handle is centred.
The concave cup device is popped in the support the rounded end of the handle, the plug added to the bottom to hold it all in and there it is, all ready to drill. Except it needs a bit of shimming to cope with shorter handle lengths - Chas thinks a threaded bottom plug is probably the way to go.
It's an ingenious solution to the problem, I must say, and let's face it, not one I'd have come up with 'cos I wouldn't be capable of the necessary accuracy in turning it! But as Chas says, really the best solution is a "proper" chuck instead of the lash-up jobs I've been using for years. We'll see...