For the leadscrew drive on my lathe I have a 77mm center distance on the shafts with very little adjustment. If need be I can make an idler to push in on the belt, so it needs to be a type that tolerates bending backwards.
I want to do a 2:1 reduction from motor to screw. The motor has a 3/8" shaft while the screw has a 10mm shaft. Oh the joys of surplus components! I can put one pulley in a lathe and ream it out to 10mm.
Right now the rest of the specs for the motor and screw don't matter, Linux CNC can take care of how far each 1/2 step moves the lathe carriage. I just need a cogged belt and matching pulleys that will provide the 2:1 ratio and fit the center distance. Metric, Imperial, tooth profile, doesn't matter. Any of the available types should be more than strong enough to handle driving a carriage leadscrew on a 9x20 conversion.
If you really must know, the motor says 450oz holding torque, 200 steps. The leadscrew is a 16 mm per turn linear actuator enclosed ball screw. Happened to be exactly the right length to bolt onto the front of the 9x20 bed and I milled an aluminum motor plate which bolts to both the drive end of the actuator and the headstock end of the bed. The drive system isn't going to shift any which way.
So driving the motor 1/2 step = 400 per revolution. 2:1 ratio = 800 1/2 steps to turn the screw once. Thus 16/800 = 0.02 mm linear motion per motor 1/2 step. The Slo-Syn part number data sheet says 5% accuracy so trying for 1/16th stepping to get 0.01 mm movements is likely an exercise in impossibility with this motor. Not going to be building an interferometer or atomic force microscope with the lathe...