Craftsman lathe

@Newbomb Turk i didn’t want to pollute up the other post but I thought I would show you this lathe I have. Here’s a few pictures from my cluttered house garage

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John,
I made some space in my inbox.

That is probably an early 12 x 24 lathe. Looks like it has babbit bearing, while later ones used Timken tapered roller bearings on the spindle. Nothing wrong with babbit as long as you keep the rpms in the appropriate range. You have to change the gears on the quadrant on the end in order to cut different threads or change feed rate. Did you get the change gears with it? I used to have some documentation on those and will see what I can dig up. The manuals are all out there either free or relatively cheap. I can't see what the issue is with your four-jaw. Can you be a little more specific? The chuck should bolt to the back plate with four bolts. Normally the backplate is turned so the chuck register diameter on the back is just under a slip fit. Falls on but no wiggle room, about 0.001" under, and it isn't as crucial on a four-jaw as it is on a three jaw. Back plate should be threaded for the four bolts to clamp it on.

ch1II has the more desirable late model Craftsman, one of the last versions they came out with. Has 1/2" thick rectangle bed ways instead of 3/8" on the older ones. In a lathe, mass is everything. It also has a quick change gearbox to select different feed rates for the carriage.

There is a lot of interesting historical information on this website.
Craftsman, Dunlap, Companion, metalcraft lathes, AA Lathes
Wander through there for a while. I'm thinking yours is probably one of the ones on this page. Early Craftsman Metalcraft & Metalmaster 9" and 12" Lathes
There may be a tag on the machine with the catalog number, which can be useful if you need to order replacement parts.