Locating A Corner on a Mill

[mklotz]

Well, disliking the term "geek", I prefer to describe myself as a math enthusiast, On that basis, let me make a stab at deriving Rick's equations...

The (presumed straight) line running from x3 to x2 has the equation...

x32 = [(x2 - x3)/z1] * z + x3

and the (presumed straight) line running from x2 to x1 has the equation...

x21 = [x1/z1] * z

When these two lines cross at (x0,z0) it must be true that x32 = x21, so

[(x2 - x3)/z1] * z0 + x3 = [x1/z1] * z0

which leads, after a bit of algebraic gymnastics (an exercise for the student) to

z0 = x3 * z1 / (x1 + x3 - x2)

plugging this result into the equation for x21 above, we have

x0 = (x1 *x3) / (x1 + x3 - x2)

consistent with Rick's result.

Rick's equation for z0 follows immediately.

Well done, Rick. There aren't many folks out there who appreciate how helpful math can be in the shop; and I'm not just talking about learning the basic trig relationships.