Hi,
a rotary axis is tuned to so many 'steps per degree'. Thus if you have your stepper set for 8 microsteps or 8 x200 =1600 steps/ motor revolution.
With a belt reduction of 4:1 then 4 motor revolutions or 4 x 1600 = 6400 steps per A axis revolution or 6400 / 360 = 17.77 steps per degree. You will have to round to
18 steps per degree but that would result in an error of 1.2%. Not bad.
If you work backwards you may be able to reduce that error a bit. If you assume 18 steps per degree then a full A axis rotation would reuire 360 x 18 =6480 steps.
With the same 1600 steps per motor rev you would require a belt reduction of 6480 / 1600 =4.05. Thus if you have a belt reduction of 4.05:1 instead of 4:1 your steps
per degree would be perfect.
A pulley of 20 an a pulley of 81 teeth would do the trick.
Craig