With change gears there are two terms that must be understood, spindle and stud.
Spindle refers to the shaft driven by the headstock spindle and is where the change gear driver gear goes. In the case of a compound gear train, the first driver gear.
Stud refers to the shaft that is on the end of the lead screw or the input shaft of a Quick Change (some times called "Norton") gear box and is where the driven gear goes. In the case of a compound gear train, the last driven gear.
If you are using a metric lead screw to cut inch threads or diametrical pitch worms or using an inch pitch lead screw to cut metric or metric module module worm threads, you must use your metric/inch transposing gears to in essence turn your lead screw from metric to inch or visa versa.
For an 8 threads per inch lead screw with metric transposing gears of 120 / 127
0.125 inch X 120 / 127 =
0.11811023622047244094488188976378 inch = 3mm
For a 3mm pitch lead screw with inch transposing gears of 127 / 120
3mm X 127 / 120 = 3.175mm = 0.125 inches or 8 threads per inch
When setting up the lead screw in the gear calculator and using metric - inch transposing gears enter the resulting pitch not the actual pitch of the lead screw.
If you do NOT have a Quick Change (Norton) gear box you can skip the rest of this page.
Most likely there is a ratio change in the gear box. The easy way to tell is by the spindle gear and stud gear teeth. If the number of teeth differ there is a ratio change. In my case 24 on the spindle and 48 on the stud. 24 / 48 = 1 / 2 (a ratio of 2 to 1). This means that when I set my quick change gear box to 8 threads per inch the lead screw is turning twice as fast as the gear box input shaft and I have to set the gear box to 16 threads per inch for a 1 to 1 ratio. Were it a 3mm pitch lead screw then setting for 0.75mm pitch would also give a 1 to 1 ratio.
This is an advantage because 10, 20 and 40 diametrical pitch or 2, 1 and 0.5 metric module can be cut with the same gears. Simply by changing the quick change gear box to 8, 16 or 32 threads per inch or 3, 1.5 or 0.75 mm pitch. The same would apply to other diametrical pitches or metric modules.