Thanks Fastest1. This explains the coordinate systems, but I guess I'm still a bit confused. I was corrected before that the X and Z axis are the table planes and the Y is the vertical plane. Looking in Mach3 turn, it solidified that in my mind because it only has X and Z since the lathe only has the table movements. The Cad reference you showed here, even on a mill on the first link shows it the way I am used to picturing it where the X and Y would be the flat plane the tables move on, and the Z the vertical plane as the first link shows on the mill. That is why I wanted to pose this question once more here to ensure I had it engrained in my thick brain before I set my machine up. I know that with a home machine, I can do it what ever way I want and make it work anyway I want. I'd rather do it in a standard way, or the most standard way in machining so when I get into conversations with someone who works in the profession, we don't have to spend the first part of the conversation getting on the same page.
Looking at the first link you presented, it's obvious that there is more than one way the profession views the axis, or is it different between the lathe and the mill? Right now I have my DRO plugged in so it matches the mill in your first link and I only have used it that way for a very short period of time, and only to do some minor things. I was hoping to fix it now, so I'm learning it "right" if there is such a thing.
Again, I thank you for answering this question. Now I'd ask for clarification on a couple things, such as which axis is which, and when looking at the lathe spindle, moving the tool toward the chuck, is that "-", and moving it from side of the machine I stand on to the opposite side of the machine, is that also "-"?
My objective here isn't to start a debate. I just want to do it "right" the first time, and continue this pattern.
Again, many thanks
Ed (teaman)