This is a little tool very useful for the lazy turner who doesn't want to remove its chuck and wants to rough turn a piece of wood between centers.
This is a homemade live center, with cylindrical shank, that can be inserted in the chuck.
It is made, like another drive center (the conical one) I have already showed :
Homemade Wood Lathe Drive Center
using a tap seat reamer (don't know the exact name for that).
It makes a perfect grip for the wood.