Five cut method on MFT3 explained

[tbellemare]

Wait a minute...

Nobody solved the "Impact" equation. (3rd order differential)

I suspect this thread had a lot of impact on who was watching it.

Tom

 

[wow]

Does this mean there will be no fisticuffs to watch?

Darn...

Tom

Don't know, but can somebody stream it if there is one? I would watch...and I'll put $5 on Rick Christopherson.

[popcorn]

 

[paulhtremblay]

Actually, I'd argue that we do have a right triangle here. Keep in mind that you are not measuring the length of the the ends of the offcut; rather you are measuring its thickness. If you place your calipers with the jaws pointing down the length of the offcut, the calipers themselves will create a right angle, and thus the right triangle.

That might force a right angle, but it wouldn't prove the formula in the Kapex manual.

The formula is in fact a simplification. It will work for small angles, but it will actually create a math error for large errors. For the sake of argument, imagine that your error were 60 degrees. The equation will actually cause a math error.

As I have said before, there is nothing wrong with simplifying equations, as long as you understand that the simplification and know it will not cause a serious error in practice. I am actually trying to establish a proof that would do just that.

Remember, this discussion started because of the conflict of the two different methods of calculating the error for the final error. I was told the method in my original document was wrong (which it probably was), so I just wanted to establish the correctness of the favored method. In doing so, I stumbled upon the equation's imprecise nature.

 

[tjbnwi]

Why do we care what the angle is?

Tom

 

[paulhtremblay]

Why do we care what the angle is?

Tom

The angle implicitly the exact nature of the error. If we can't determine the angle, then really we can't say that the error is .6 mm over 500 mm, or whatever. We couldn't really move the fence or guide rail to correct the problem. By saying the error is a ratio of the length, we are saying we know the angle.

 

[Rick Christopherson]

The angle is correct and accurate. Your ability to measure it using linear tools is not. If you really, really want that extra 0.0001 degrees, then you should be measuring the angle using an angle measuring tool.

 

[paulhtremblay]

The angle is correct and accurate. Your ability to measure it using linear tools is not. If you really, really want that extra 0.0001 degrees, then you should be measuring the angle using an angle measuring tool.

The physical measure of the angle has nothing to do with the formula in the Kapex manual. The equation in the Kapex manual is based on trigonometry. It assumes a right triangle where there is not one.

 

[tjbnwi]

Why do we care what the angle is?

Tom

The angle implicitly the exact nature of the error. If we can't determine the angle, then really we can't say that the error is .6 mm over 500 mm, or whatever. We couldn't really move the fence or guide rail to correct the problem. By saying the error is a ratio of the length, we are saying we know the angle.

Every time I've set up an MFT for square I've always used the difference between fence and free end measurements. Could care less what the angle is, looking for 0.0000" difference between the ends on the 5th cut piece.

I set machines that worked with a tolerance of 0.0005" across a 3' travel in X, Y and Z, never cared what the angle was if it was out of tolerance.

If your 5th cut piece was out 0.250" in a 24" cut it is expressed as out 1/4" in 24". Makes no reference to the angle.

Tom

 

[wow]

The angle is correct and accurate. Your ability to measure it using linear tools is not. If you really, really want that extra 0.0001 degrees, then you should be measuring the angle using an angle measuring tool.

The physical measure of the angle has nothing to do with the formula in the Kapex manual. The equation in the Kapex manual is based on trigonometry. It assumes a right triangle where there is not one.

Yes, there is. See post #37 above.

We're working with wood here. The method in the Supplemental Manual is more than sufficient for that.

By the way, this whole conversation reminds me of what I was taught by my engineering teacher in high school - back in the slide rule days. He called it 'The progression of Accuracy'

1. Measure with micrometer
2. Mark with chalk
3. Cut with axe

[big grin]

 

[tjbnwi]

I find the angle measuring tools to be highly inaccurate. I had to send a new one out to a cal lab, it was out .3º out of the box.

Tom

 

[paulhtremblay]

If your 5th cut piece was out 0.250" in a 24" cut it is expressed as out 1/4" in 24". Makes no reference to the angle.

Tom

That will work because the error in the angles are small. But if you had a large error, it would not work, precisely because of the simplification of the formula.

I'm not saying anyone should be concerned about the angle. In fact, I have argued the opposite in earlier posts. Keep doing it that way; it makes more sense.

Again, I was just trying to establish the correctness of the method. In doing so, I realized you have to be able to determine an angle.

 

[paulhtremblay]

We're working with wood here. The method in the Supplemental Manual is more than sufficient for that.

Yes. I have said the same. For small angles, the formula will only result in an error less than can be measured by a caliper. Practically speaking, we will only use small angles. So the formula is good. Not only have I said this a number of times in a number of different ways, I even pointed that out in my proof.

 

[paulhtremblay]

Rather than trying to do a pure mathematical proof, I wrote a program that would calculate the error from the Kapex formula, and more generally, from the advice that you should correct your fence according to the difference in lengths of your off cut piece.

For example, suppose your setup was a full 10 degrees off. Let's suppose your off cut length is 500 mm, and your fence is also 500 mm. The difference between the top and bottom of your off cut pieces would be 371 mm. The common rule tells you to move your fence 371 mm/ 4, or roughly 93 mm. You should actually only move it 87 mm. (sin(10) * 500 mm.) The rule is off by 5 mm.

My example is obviously absurd. If your setup was a full degrees off, the resulting off cut would not fit between calipers. I only used it to explain what I mean by error.

Practically speaking, the rule produces no error. I have done dozens of tests, and the maximum difference I got between the top and bottom of my off cut was 2 mm, less than .1 degrees off. At this small angle, there is no difference between what you really need to move the fence, and what the general rule tells you--or at least no difference to a thousandths of a millimeter. In fact, if your difference between the top and bottom were a full 13 mm (about 1/2 a degree), you would still see no difference in the true measure and the approximation. At a full degree, the error from the test is 5 hundredths of a millimeter; but at a full degree, the difference between top and bottom is over 30 mm for the off cut, so it is unlikely you will ever see this in the shop.

 

[xtrememtnbiker]

I'll just say this, I'm not the brightest of fellows. Most of this math stuff is way over my head.

Tom's method for squaring the MFT is crazy simple. The second feather key and a set of feeler gauges simplifies it a ton. Which for me, is great.

I've read the whole thread, I haven't a clue what ya'll are talking about...  [smile]
But making it be a degree's issue when it can be a linear measurement seems to make it really complicated...

Carry on!!

 

[Len]

By the way, this whole conversation reminds me of what I was taught by my engineering teacher in high school - back in the slide rule days. He called it 'The progression of Accuracy'

1. Measure with micrometer
2. Mark with chalk
3. Cut with axe

[big grin]
[/quote]

Great quote!

 

[wrightwoodwork]

I'm watch this thread just for amusement. It appears to me as a way to complicate a simple task. The only practical and sensible advice has being with the feeler gauges. In all honest as long as the piece that is being cut is the right size and it all comes together nicely at the end. It truthfully doesn't matter how you got there. 

 

[paulhtremblay]

Sorry to have complicated the matter. I would not have introduced math except for the contradiction between the two methods one finds on the web. In the one method, you add all the sides of your original board to determine the error. The second method has you measure the off cut piece. The two methods will give you results different enough to see in your workshop. I wanted some real proof as to what method you should actually use.

It turns out one should use the method in my document, of measuring the off cut piece.

The five cut method (which can actually be achieved with *four* cuts!) achieves its power through simplicity. You don't need anything more complicated than a $20 caliper. You don't need any of the math in this thread. You can safely ignore any equation, sin formula, or geometry rule.

Best of all, you don't need an expensive square to gauge your accuracy. Jut follow the method in my document, or anywhere else found on the web.

I'm sorry that math hijacked this thread. My original document has no math. It has just simple pictures and a simple explanation. In fact, I try to avoid mentioning the angle at all, and instead show the error in woodworking terms: one width of the board is two sheets of paper wider than the other (for my test cut).

Anyone care to still review my document?

 

[teocaf]

I've tried to review your document but got lost between the 'before 4th cut' and 'after the 4th cut'.  Pictorially it is hard to follow--obtuse, one might say...  One would think with all the time you put into it with explanations, calculations and programming you might have used a straight edge, perhaps draw it to scale, you know, some more effective clearer ways to display your theory.  I'll have to draw it out myself to see what the heck is going on.

 

[paulhtremblay]

I've tried to review your document but got lost between the 'before 4th cut' and 'after the 4th cut'.  Pictorially it is hard to follow--obtuse, one might say...  One would think with all the time you put into it with explanations, calculations and programming you might have used a straight edge, perhaps draw it to scale, you know, some more effective clearer ways to display your theory.  I'll have to draw it out myself to see what the heck is going on.

Sorry about that. You are looking at the proof, not the actual document. Yes, the proof is terribly obtuse, even for if you were mathematically inclined.

The document I mean is the PDF on the first post. It uses just pictures.

 

[Rick Christopherson]

I didn't realize that was going to be your final version. Maybe you missed where I mentioned it earlier, but I would prefer that you don't use my name in the document.