Chucks for drilling holes can hold small turned projects as well
This shows our 13mm drillchuck fitted with a 2 Morse taper arbor and a (removable) threaded drawbar and nut. The idea is that the arbor will be tightly held in the taper socket and cannot spin or fall out. You can then use the drillchuck as a miniature wood chuck for small items such as draw pulls. It will only work if there is a through hole in you lathe headstock. The drawbar can also be used in the tailstock of some lathes but not if your lathe tailstock has two barrels which telescope together - so the effective length of the tailstock barrel changes as you wind it.
The drawbar will of course only fit our special Morse taper arbors which have a female thread at the end