The backgears are in no way coupled to the leadscrew of a lathe, that is entirely different, which is why I said that you can pick any set of gears that will fit in the space available with the minimum ammount of modifications.
You may have to make eccentric bushes, but at least the swing of the movable gear can be adjusted. An interesting project, which is quite rare, we look forward to hearing of your progress.
https://www.technobotsonline.com/gear-size-calculator.html
Edited By old mart on 24/04/2021 13:55:46
Edited By old mart on 24/04/2021 14:01:39