Locating A Corner on a Mill

[mklotz]

OK, Rick, you made me do it. Here's the proof of your conjecture that the diameter of the edge finder doesn't matter.

You'll have to refer to the scan of my handwritten work. I didn't have the patience to convert all that math to typewritten text.

Instead of your "X=0 & Z=0", I labeled that point (x0,z0). With that notation I wrote the equations for the left line (xL) and right line (xR) in your diagram. By setting xL = xR, we arrive at equation (1) for "z", [By setting x0 = 0 and z0 = 0 this equation reduces to yours as it should.)

Now, if we want to include the effect of the edge finder, we need to make the replacements shown on the sheet. Imagine the x measurements being made with a DRO. When you touch off on x0, the DRO will read x0 - r, whereas when you touch off on x3 it will read x3+r.

Below the "replace", you see what equation (1) becomes when we make these replacements. When the equation containing the replacements is simplified, all the "r"s disappear and the result is equation (2) which, you will note, is identical to equation (1).

I think that proves your conjecture very nicely.