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Paul,What lathe do you have?You can certainly make a drawbar to hold the collet chuck from a set like you show. I have done some myself, either from rod that I have threaded, or using threaded rod in a pinch.Sets like you show would provide the sizes you need with some others for future uses.Looking at information on the different ER collet ranges, you may have identified ER16 as what you need.It is possible to make a collet chuck: There are others' projects which show what is involved. Unfortunately I can't easily find one to link to.... You do need to cut threads to make one.There is another consideration for collet chucks and that is whether you want to be able to feed long stock through the headstock, if your lather allows it. I don't know whether you can find one for your lathe and for ER16.ShopShoe
Bolt on ER chucks exist in various shapes and sizes...
Giving up access to the spindle hole of your lathe is not a decision to be made lightly. There are other ways to use collets for work holding on the lathe.
I found a suitable ER32 spindle-mounted chuck online at a really good price, I'll pick up some collets and a spanner etc at the show hopefully.