Although I am by no means knowledgable of Atlas machines, I do remember where at least one had an undermount motor. In the days this was common, a variable speed motor was actually a variable ratio pulley arrangement. While I am "old school" and fully support rebuilding such an arrangement, finding the parts to begin with is going to be like searching for a treasure chest full of gold. Almost impossible this day and age, and expensive if you do find one. (assembly)
For all intents and purposes, my choice would be either a 3 phase motor with a VFD or a strong DC motor with speed control. Either one can be mounted below the machine as desired, or behind and/or above if suitable. I personally would build it behind the machine, below would serve just as well.
Starting with the footprint of a NEMA-56 motor, (single or 3 phase) that would provide all the relevant dimensions, including shaft size. At this point in the design stage, NEMA-56 dimensions would be all that is required to devise most any under or behind mount. There are 1 HP NEMA-56 motors, although for such a small machine 3/4 HP would be more suitable. Opting for a larger motor, the only dramatic change would be the frame size, its' NEMA specification. I run a much older Craftsman 12" (Atlas 10"). That machine was supplied with a 1/2 HP motor, I currently run a 1/3 HP NEMA-56 with no stalling. But I do light weight, mostly non-ferrous work.
One major consideration is some sort of countershaft in the drive system. Whether you opt fo 3 phase with a VFD or a DC motor, speed control will be in the range of 50-150% of motor base speed. Any operation outside those parameters will require some sort of gearing, most likely with belting.
I support any effort to find and use an OEM speed control, but the likelyhood is low.
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