Threading to a shoulder, external or internal, on a lathe can be a tricky operation. Many times, threading away from the shoulder makes things easier. Puzzling out the correct setup can be tricky. I did it once, covering all the possibilities, and put together this chart so I would never have to think about it again.
Perhaps some of you might find it useful...
A - Threading tool upright, point toward lathe back
B - Threading tool inverted, point toward lathe back
C - Threading tool upright, point toward lathe front
D - Threading tool inverted, point toward lathe front
L - Direction of feed = Left
R - Direction of feed = Right
f - Forward Spindle Rotation
r - Reverse Spindle Rotation
To Cut Right Hand External Threads: Lf(A/D) Rr(B/C)
To Cut Left Hand External Threads: Lr(B/C) Rf(A/D)
To Cut Right Hand Internal Threads: Lf(B/C) Rr(A/D)
To Cut Left Hand Internal Threads: Lr(A/D) Rf(B/C)
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