These little collets superficially resemble ER ones but look of proportionally shorter taper; and their chuck nut engages a simple rebate rather than uses a ring and groove. This chuck is missing.
They range from 1/8″ to 5/16″ by 1/32″ increments, work diameter. The set includes an unfinished collet too: un-drilled and un-slotted. The peg on the (owner-made?) wooden storage block likely held the chuck.
I have only just noticed that oddly, the 5/16″ capacity specimen collet I measured for the drawing below, does not have a full-diameter through-hole, just a tiny pilot hole. All of its brothers are full-bore through.
The photograph includes perhaps a drawbar for their, or a, small chuck in a lathe like the ‘Peatol’ they came with – but I no longer have that lathe and the collets bear no names or numbers. The sleeve on the end of the drawbar is a cylindrical nut with a slot for a screwdriver. Though not certain the nose thread seems 3/8″ X 24tpi UNF by thread-gauge. It also fitted a couple of spare Jacobs Chucks, smoothly.
(I don’t know why these items, and a backplate, did not go to the lathe’s new owner, other than doubt over correlation.)
What might they be, please?
Home-made, even?
I am unable to photograph anything so tiny as an individual collet, so measured one as best I could and produced a quick, slightly inaccurate drawing. The plotted slots are too wide, for a start, but it shows the general shape.
Overall length 14.5mm, maximum diameter 13.4mm (unclamped). The ‘Alibre’ model shows nominal 6mm capacity.

