So using those figures, screw pitch is .2", and it takes 4000 counts to move 1 revolution, or 0.2", so that means it takes 20'000counts (4000 x 5 revolutions) to move 1".Yes... that is correct. 2000 counts on the servo motor axis (pulley) will move the ball-screw axis One-Half of a revaluation, which is 100".
So, the Servo Motor Axis moving 2 revaluation to a count of 4000 will rotate the Ball-Screw 1 revaluation, which is .200" (on a dial-indicator).
Which then means it takes 20'000/1000(thousands per inch) or 20 counts to move a thou.