Hmmm...
I just don't get half of the small, plan view diagrams on p122 of the excellent Vardex catalogue, with particular reference to what they convey about the sign of the helix angle.
Here's my problem: if I look at the topmost case (RH thread, RH tooling) and imagine I swap the workpiece and tooling into an identical lathe, except with the headstock on my right and tailstock on my left, obviously the tooling and directions won't need to change. With the exact workpiece shown I'll have to start the thread further up the workpiece to miss the chuck, but that's surely immaterial to the tooling's handing and helix angle?
If I now walk around to the back side of the lathe, it seems to me I'm seeing the seventh case down. The rotation is as shown, as is the direction of tool travel. And the thread is still RH, as per the diagram.
So why do they tell me I now need a LH tool, with the opposite helix angle? (remembering that case seven is still a RH thread)
I have the same problem understanding three other cases. I would have thought the helix angle was purely a function of whether the thread was RH or LH.
Can anyone pinpoint what's wrong with my argument? Clearly they must be correct, I just can't see my error.
(Please don't anybody feel they should go to any great trouble devising a different explanation if mine doesn't do it for you - by all means do so if you want to, but it's unlikely to help me with my problem, which is that I seem to have an apparently sound argument which gives the wrong answer.
This is something which should strike deep feeligns of unease in a thinking, technical mind. It's not a sound basis for confidence in one's reasoning. What I'm hoping for help with is discovering the mis-step in my joining of the dots.)