Marv, I'll try and do another drawing later that shows what is actually happening, but in words:
The X axis tool slide holds a tool turret with driven tooling. The selected tool will be a spiral end mill cutting on it's flank, not its end, and it's axis of rotation will be parallel to the main lathe spindle.
As this tool can only move in towards the lathe axis, or away from it (ie not up and down) it cannot cut a flat, unless the main spindle rotates slowly as the tool slide slides in and out. It is the mathematical relationship between the work rotation (represented by the angle of the line L) and the movement of the tool slide (represented by the length of line L) that I am trying to build into my algorithm.
When there are less grandchildren crawling over me I'll try and get a sketch drawn up