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Determining the angle of a compound miter

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Blog entry by clazman posted 02-16-2012 05:48 AM 6745 reads 0 times favorited 9 comments Add to Favorites Watch

I realize that there is a lot of info on determining the angle in a compound miter. However, whilst reading some comments on this topic I was taken aback as to how many readers felt that 3D CAD was the only way of determining that angle.

That is simply not true. This angle can be determined, with the use of a pencil and paper and mild drafting skills.
2D CAD can replace the drafting table and improve the computational accuracy of the joint.

The method relies on creating several auxiliary views from the standard orthographic views.

Step one, is to create a true view of one of the sides (or faces). This will show the true angle to set the taper jig to. It will also show the joint in true length. To do this, a view is created that is perpendicular to the face in question.

Step two, is to create a view showing the joint as a line. This is the view that will show the true angle of the joint, the angle that the saw blade is set to. To do this, a view is taken perpendicular to the joint that is shown in true length. This view will now show the true angle of the joint for the view will be looking right down the joint.

As I stated earlier, accuracy of the manual method utilizing a drafting table is poor. Especially for small angles. To improve the accuracy the joint can be drawn, say, 10 times the original size. 10 is chosen to simplify calculations. The measurements are simply a factor of ten larger than the actual.

I have submitted screen dumps of a drawing project that has four sides that are angled out at 10 degrees.

The first shows the overall project. The second view shows the joint enlarged to improve clarity.

For reference only, I have dimensioned the opposing joint, WHICH IS NOT CORRECT for it is NOT in true view. I hope this isn’t confusing.

This article is THE way in which any joint angle is determined. ANY tables or calculations, even solid modeling, are only derived from the procedure that I have presented here.

I only present this procedure to show that without ANY modern systems (confusers) the the problem can be solved.

I hope this hasn’t been too confusing, for auxiliary views are created THE SAME WAY that the “standard orthographic views are created. Its just that many do not realize this and consequently have an aversion to auxiliary view creation.



9 comments so far

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clazman

19 posts in 2470 days


#1 posted 02-16-2012 05:50 AM

Why are my images being cropped? The images appear to be un-cropped at photobucket.

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BritBoxmaker

4607 posts in 2497 days


#2 posted 02-16-2012 05:07 PM

Whilst I agree with you that 3D CAD is not the only way it is by far the simplest method as only one drawing (a 3D model) needs be done. The angle measurement tools are there for you too.

I learnt technical drawing with a pencil and used a slide rule or tables to calculate angles when I started. I can still do it but I can’t for the life of me see why I should.

Oh well I suppose people still make things using only hand tools. Each to their own.

-- Martyn -- Boxologist, Pattern Juggler and Candyman of the visually challenging. http://www.theartofboxes.com

View clazman's profile

clazman

19 posts in 2470 days


#3 posted 02-17-2012 08:30 PM

Britboxmaker,

I am sad of the insinuations to my character you made here. I have done very many descriptive geometry problems without the aid of a computer. In my first year in college, 1966, I was taught descriptive geometry by a very wise instructor. This instructor was the bane of many a student handing out very few “B’s”. I earned an “A” in that class.
I am also well versed in finite element analysis which requires solid modeling capability.

Please be careful when you make insinuations to the technical capability of those you degrade.

You missed the whole idea! You do not realize that I was presenting a graphical solution to show that 3D is not necessary. A computer is not necessary. Solid modeling simply utilizes the computational power of the computer to solve descriptive geometry mathematically. Not everyone has 3D capability.

I am sad that you cannot believe why you should belittle yourself by doing it the old fashioned way.

To say that 3D is the “end all” is naive to say the least. 2D construction is still required in the development of solids. Consequently, some problems can be better solved with 2D or pencil and paper.

As in this case it took very little time to come to the solution in 2D. Yes, I did first do it in 3D. But, I wanted to refresh my mind with the descriptive geometry.

And … when did “learnt” become a tense of the verb learn?

View Jorge G.'s profile

Jorge G.

1537 posts in 1936 days


#4 posted 02-17-2012 08:41 PM

I kind of agree with BritBoxmaker, your post itself is ironic in many ways. You did not want to go to the trouble of taking out your pencil and paper, protractor, rulers, etc. So you state, using 2D CAD is the same. I don’t think so, learning to use a CAD program takes a steep learning curve, why didn’t you do it on paper? simple, it was more convenient to make it on the computer.

So, on the one hand you say “3D and computers are not needed” and on the other hand you take advantage of the convenience of the same instrument you eschew. As BritBoxmaker stated, you could use a slide ruler instead of a calculator, but then you won’t be doing any woodworking that day.. :-)

-- To surrender a dream leaves life as it is — and not as it could be.

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BritBoxmaker

4607 posts in 2497 days


#5 posted 02-17-2012 09:06 PM

I made no insinuations about your ability whatsoever. You are being overly sensitive. Please re-read the last sentence. Each to their own. Which means that I accept that anyone is free to do things in the manner in which they wish. Being able to do anything from first principles is an admirable ability. I know that a computer is not necessary but if its freely available I’ll use it.

-- Martyn -- Boxologist, Pattern Juggler and Candyman of the visually challenging. http://www.theartofboxes.com

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clazman

19 posts in 2470 days


#6 posted 02-17-2012 11:33 PM

I should have gotten the drafting board out, the tee square, the protractor. Oh yes, a #6 pencil? A Pink Pearl eraser. Then how do I submit the drawing? Use a digital camera? Maybe I should use a film camera so that I could take a picture of my drawing and then wait several days for the developer then paste the picture where? Maybe I should chisel it in stone and throw it at the modem.

Why is everyone so literal? Give some leniency.

Oh my, where should I draw the line (pardon the pun)

View DIYaholic's profile

DIYaholic

19172 posts in 2136 days


#7 posted 02-17-2012 11:52 PM

Scanner!!!

-- Randy-- I may not be good...but I am slow! If good things come to those who wait.... Why is procrastination a bad thing?

View Jorge G.'s profile

Jorge G.

1537 posts in 1936 days


#8 posted 02-18-2012 12:59 AM

DIYaholic beat me to it, presumably you can draw all this on an 8×10 sheet. Even my cheap Epson scanner comes with a scanner.

-- To surrender a dream leaves life as it is — and not as it could be.

View RickRinger's profile

RickRinger

92 posts in 1412 days


#9 posted 12-06-2013 10:39 PM

Here’s a very valuable resource that I found.

http://woodgears.ca/miter/

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