Can anyone tell me the model of my craftsman atlas lathe 12x36

I don't think that your lathe is a 12x36' It looks like an early 109 with some missing parts. The 109 is a 6x12 lathe. Why do you think that your lathe is a 12x36?
 
Is the plate with the model number on the back of the ways or the right end? Had to ask.

There are part numbers cast into the various parts. See what those are, find a parts diagram and see what size lathe the parts match up to.

Measure from the center of the chuck to the top of the ways. If it's 6" you have a 12" lathe, if it's 3" you have a 6" lathe.
 
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