I have inherited a wood lathe (Spiegel "Precision Bilt" Model 87B630). The tail stock uses an 0.81" (assuming this is 13/16") diameter keyed shaft, and the live center screws into it with a 1/2-20 thread. I am trying to source a drill chuck to mount on the tail stock, but I don't know how to describe what I'm looking for. The shaft is definitely not tapered and is prevented from rotating by a set screw and keyway. I believe the lathe dates from the 60's. Was this a standard design that is no longer used, and if so, what it is called?
After a bit of research, I found that many impact drills also use a 1/2-20 thread to attach the chuck. I guess that due to the nature of what you're doing with an impact drill the chuck has a limited lifetime, so they're made to be easily replaced. Once I had that figured out, it was a simple matter to find one. (I happened to find mine on ebay). Here it is installed on my vintage lathe:
I am trying to source a drill chuck to mount on the tail stock, but I don't know how to describe what I'm looking for.
I don't know how to describe it either, but it'd be simple to adapt a standard chuck to fit your lathe. Drill chucks are typically connected to a lathe or drill press using an arbor with a Morse taper on one end and a Jacobs taper on the other, with the latter fitting a recess in the chuck. Here's one example:
You could buy an arbor with the right Jacobs taper for whatever chuck you want to use (one will likely come with the chuck), and then cut the Morse taper off and drill and tap for the threads on your headstock. As a practical matter, it might be best to have a machine shop do the work for you: once the arbor is cut you'll want to mill the cut face flat and square to the arbor's axis, and it's critical to center the tapped hole precisely.