Locating A Corner on a Mill

This work was inspired by a very clever tool presented by Marv Klotz on
Homemadetools.net (http://www.homemadetools.net/forum/one-tool-two-uses-
27184 ).

Given a block held at an arbitrary angle in a mill vise, how do you locate the top corner? Marv's tool is elegant. Of course, I'm always looking for other ways to do the same thing. Here is a method that uses no special tools. It assumes the faces of the block are flat but not necessarily perpendicular.

If you are interested, please see

http://rick.sparber.org/LACOM.pdf


Your comments are welcome. All of us are smarter than any one of us.

Thanks,

Rick

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.

Marv,

Thanks for checking my work :-)

Here is another challenge - when using the edge finder, do you have to account for its radius. Given that we touchdown on both sides of the corner, I would not be surprised it this radius doesn't matter.

Rick

over my head

Quote:

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Originally Posted by rgsparber

Marv,

Thanks for checking my work :-)

Here is another challenge - when using the edge finder, do you have to account for its radius. Given that we touchdown on both sides of the corner, I would not be surprised it this radius doesn't matter.

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Should be easy to test. Simply add a constant 'r' representing the radius of the probe to each of the 'x' measurements and see if the equations reduce to the result you published. You may have to introduce an 'x0' measurement to replace the zero you assumed. [In general, it's good practice to never set a zero before deriving relationships; assign a variable and let it go to zero after the algebra is done.]

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.

https://s3-us-west-1.amazonaws.com/f...he/97016-1.jpg

I agree with Marv and Rick. Algebra and Trig are indispensable solutions for converting 'abstract' figures into factual articles. The problem many face stem once again, from removal of vocational electives from public schools. Theory and rote memorization never make the point of utility better than usage in real situations, reinforced by visual results. Math was my biggest adversary in classes, but a breeze in shop! With 45 years machining, and 26 navigating my attention is better than predictions indicated. My solutions tend along with Rick, using different means. I respect Marv's ability to illustrate sophisticated calculations, I'm restricted to smaller bites.
I prefer trig overall for various solutions. I probably use algebraic techniques unknowingly, by reasoning out digits to work with over letters.
But tell algebra this; quit asking us to find your X; she's long gone and not coming back!

I salute you guys who still posses your math skills. I lost a large portion of mine years ago when I had a severe blood flow discrepancy to my brain that I didn't even realize was happening until one day I woke up and thought I was having a heart attack. It turned out to be 90% Arterial blockage to my LAD the artery that supplies the Heart caused by scar tissue build up pressing on the outside of the artery which was most likely caused by a missed fragment of Shrapnel dating circa 1971 or 2 . A stint solved the problem but I had already spent nearly a year without a decent new coherent design thought. That was about the time I decided it best that I retire and put my shingle in a drawer
Toolmaker 51 Never underestimate the power of "n" when looking for "X" or you will wind up having to cosign the tangent.

Depending on the height I have my mill table cranked to I have always found it easy to locate the corner with either my knee, hip or elbow with very little difficulty

Quote:

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Originally Posted by 12bolts

Depending on the height I have my mill table cranked to I have always found it easy to locate the corner with either my knee, hip or elbow with very little difficulty

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Pretty easy to find all of the movement handles as well, especially in the sark

Quote:

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Originally Posted by 12bolts

Depending on the height I have my mill table cranked to I have always found it easy to locate the corner with either my knee, hip or elbow with very little difficulty

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Pretty easy to find all of the movement handles as well, especially in the dark

Thanks Rick! We've added your Corner Locating Method for a Mill to our
Measuring and Marking category, as well as to your builder page: Rick's Homemade Tools. Your receipt:

<div id="blocks"> <div class="block b1 pngfix"> <div class="bimg"> <div> <a href="http://www.homemadetools.net/homemade-corner-locating-method-for-a-mill"><img src="http://www.homemadetools.net/uploads/203220/homemade-corner-locating-method-for-a-mill.jpeg"/></a></div> </div> <div class="head pngfix"></div> <div class="left pngfix"></div> <div class="right pngfix"></div> <div class="blockover b1 pngfix"> <div class="title"> <a href="http://www.homemadetools.net/homemade-corner-locating-method-for-a-mill">Corner Locating Method for a Mill</a> <span> by <a href="/builder/Rick+Sparber">Rick Sparber</a></span> </div> <div class="tags">tags: <a href="http://www.homemadetools.net/tag/measurement">measurement</a>, <a href="http://www.homemadetools.net/tag/edge-finder">edge finder</a></div> </div> </div> </div>

I suspect that I suffered in the same manner, always having a hard time in math class concentrating on what was being taught. Part of that was sitting next to with e window (it was always more interesting outside) and part due to abstract ideas with no relation associated with the real world. In a nut shell you combine a bad student with difficulty linking the abstract to the real and you have problems.

Recently I wanted to plot some holes on an archimedes spiral and spent some time relearning (or maybe learning stuff I never really got) a bit of math. What a reward though to actually get results you want after many false starts. While I've yet to apply this to the project I have in the shop, I did the math via a programming language Called Python and plotted the results immediately. I really think that, that plotting helped immensely with understanding the math and getting the right result. The visuals are very important in grasping some of this strange math.

Quote:

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Originally Posted by Toolmaker51

I agree with Marv and Rick. Algebra and Trig are indispensable solutions for converting 'abstract' figures into factual articles. The problem many face stem once again, from removal of vocational electives from public schools. Theory and rote memorization never make the point of utility better than usage in real situations, reinforced by visual results. Math was my biggest adversary in classes, but a breeze in shop! With 45 years machining, and 26 navigating my attention is better than predictions indicated. My solutions tend along with Rick, using different means. I respect Marv's ability to illustrate sophisticated calculations, I'm restricted to smaller bites.
I prefer trig overall for various solutions. I probably use algebraic techniques unknowingly, by reasoning out digits to work with over letters.
But tell algebra this; quit asking us to find your X; she's long gone and not coming back!

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Quote:

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Originally Posted by wizard69

I really think that, that plotting helped immensely with understanding the math and getting the right result. The visuals are very important in grasping some of this strange math.

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That's probably why, after arithmetic, geometry is the oldest form of mathematics. It deals with relationships between objects that can be drawn and seen.

Unfortunately, when one gets a bit farther along in math, drawing a picture becomes very difficult. Consider the fact that many infinite series (sum of an infinite number of terms) have finite sums. How do you draw a picture to visualize that?

Another idea for a centering tool on every angle value.(it's a bad picture but I'm really not a graphist…)
Attachment 19252

Have you tried this out? I'm not sure how it works.

Rick

In order for it to work the angle to be measured must contact the edges of BOTH slots. A sufficiently obtuse angle will not do that, so I can't see it working on "every angle value". Also, very acute angles will penetrate too far and not contact both slot edges.

Sorry for my too shorter explanation, it goes on all angles but you need to have multiple widhts, it's not a single universal tool, but each time you need one and make it you can use it on different angles, and often i open more until it's no more usable.
It is not an universal tool as described on the original post, just another way in the same manner to simplify the job.:rolleyes:
I try to make a short video for a better explanation.