Thanks everyone, those have been the pushes I need to get it done
For posterity, how it made sense to me was – ignore actual gear train initially, just work with lead screw tpi and a 127/100 compound pair. I.e.
- Convert tpi to pitch (between teeth) in decimal inches
- Divide by ratio of translation gear (127/100)
- Multiply by 25.4
= metric pitch given by that translation
Here, with an 8tpi lead screw, we get:
((1/8)/(127/100))*25.4 = 2.5mm pitch
So with sliding gear in, lever to B, front slider dogged to 1, and a 127/100 compound gear in the train, the lathe will cut a 2.5mm thread
Turning all this around, you have the equation that lets you see what tpi (lever/dog combination) you need to set the lathe to for it to cut a given metric pitch.
Worked through for a 0.7mm pitch:
1/((0.7/25.4)*(127/100)) = tpi needed =28.5 tpi
C8 is the nearest setting available (=0.714mm)
If I want to get closer to 0.7mm, I need to mess with the gear train – finding one that changes the gear ratio coming into the gearbox such that one of the gearbox ratios spits out “28.5tpi”