If it's a US machine, chances are very good we can tell you want it is by looking at it.
Davis (VS) - belt goes on outside of flywheel (not side towards machine) and it has a square needle plate. Needle hole is offset from presser bar. There are few other identifiers, and those aren't limited to Davis, but it helps narrow it down.
There are several that had the serial number stamped on the slide.
Here are several Davis machines, with different types of tension. If it's got a top tension like the first, look closely as they are also a way to identify the manufacturer.
