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Thread: Workshop Geometry Angles... again

  1. #1
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    Question Workshop Geometry Angles... again

    I need another formula. This time I'm making a splayed shop stool. Here's a 2D graphic of what it will look like (loosely).

    The legs are splayed 10° out BOTH directions. The legs are also tapered; 5" wide at the top and 2" wide at the bottom. The height of this stool (not including the seat) will be 23". I want to make one compound cut at the top and bottom of each leg to achieve the 10° splay and also have the ends of the legs parallel with the floor. Each of the 4 legs will be "L"s with the ends. I'll make the ends 3/4" narrower so the "L" is symmetrical. (All material is 3/4" thick)

    How is this figured?

    Also, since the legs are tapered, what would be the angle of the rail ends where they meet the inside of the legs?

    Thanks, Todd.
    Attached Images Attached Images

  2. #2
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    I guess your drawing program doesn't give you angles?

    I've been involved with cutting legs like this once...and with any kinda luck, it won't happen again. And we were only dealing with the compound cut at the top and bottom...no taper involved.

    Unless the taper changes things, I don't think all four legs will be alike. It makes sense to me that you could cut them all the same way and just turn them end for end...but for whatever reason we had to cut two pair of two...couldn't cut them all at once without changing the saw. Seems like it would also be easier to make the compound cuts before cuting the taper.

    You don't mention whether these are not these are for sale...but if they are you'll probably wanna just go ahead and make a hundred of them when you get jigged up. If they're for the missus, I might suggest a trip to Barstools Unlimited or Chair King as a cost saving (and frustration) measure.

    KC

  3. #3
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    I know that playing with numbers and computer programs can be fun. But in this case I would simply cut a piece of plywood into a rectangular shape that looks just like your drawing. I would cut it 23" long, I would then lay out the lines that you have done on your drawing. This would be my template to build the stool. I would take a ruler and an angle gage and take the dimensions off of the plywood and cut the pieces to match.

    If you were building boats, this would be called "lofting". So for want of a better name, just loft the stool design.

  4. #4
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    Quote Originally Posted by Mac McAtee
    I know that playing with numbers and computer programs can be fun. But in this case I would simply cut a piece of plywood into a rectangular shape that looks just like your drawing. I would cut it 23" long, I would then lay out the lines that you have done on your drawing. This would be my template to build the stool. I would take a ruler and an angle gage and take the dimensions off of the plywood and cut the pieces to match.

    If you were building boats, this would be called "lofting". So for want of a better name, just loft the stool design.

    I would also add. You would cut the four leg blanks an inch or two longer than the finished product. Cut the taper on the blanks. Lay the blanks on the plywood lofting template so they are properly oriented to the lofting lines with both ends hanging over the template. Take a pencil and draw the cut off line on both ends of the leg using the end of the plywood as your straight edge. Mark one leg at a time and put each one in exactly the same spot on the template and they all will be identical. Or, mark one leg, set up what ever saw you will be using for the end cut, put a stop to set the distance from the end of the leg to the blade. Make that cut on all four legs. Turn one leg around set up again for that cut, set a stop for the distance from the end of the leg to the blade and then cut all four legs on the other end. All four legs would then be identical.

    You then could put a blank that will be the cross piece at the top on the lofting template, put two legs in the proper place on the template and draw lines on the cross piece to set it's angle and length. Make both blanks exactly the same dimensions. Stick them both together with double stick tape. Set up your saw for the end angle cut and cut both pieces at the same time. They will be identical if you do your work carefully.

    When you are done. Drill a hole in the lofting template and hang it on the wall somewhere. Ten years from now you can still build an exact match to the stool with the lofting template. Make any construction notes on the template and you'll have them as long as you keep the template.

  5. #5
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    Mac, taking your suggestions, perhaps this could even be done easier:

    Cut the legs oversize as you say, taper, glue & nail them all together into the "L"s, lay the assembly with the joint up on the miter, bevel the blade 10° and have at it. Could also be done on the tablesaw - if the blade were tall enough.

    But, actually - while this would be close, and rough, there is still a problem. If the legs are joined at 90°, when splayed to 10°, they will no longer be 90° on the inside corner (when measured with a square that is parallel with the ground) - they will be something < 90°. This is what is called a dihedral angle. I need to know the angle to bevel the outside edges of each leg (the non-tapered side). Probably a degree or two... I made a cradle several years ago. The splay on each side was 15°. and the bevel cut was 43.5°.

    If this were not done, the outside face of the rails (the show side) would have a gap, whereas the inside (to the stool) face would be nice and tight.

    Thanks for the introduction to the term "lofting".

    I like math. Anyone else?

    Todd.

  6. #6
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    Todd.[/QUOTE]

    "dihedral angle"

    Right, you go for it! Let us know if you get there.

    Back in the good old days when ships were wood and the men who sailed them iron, every boat yard had a big wooden building with an upper floor, wood, that was set aside for nothing but laying out the lines of a ship, or parts there of. It was called a loft. The ships carpenters used the wood floor like a big template, laying out the lines to cut timbers, figuring angles in real dimensions. The process was and is called "lofting the lines" or just "lofting".

    Sails are sometimes as big as your house and they also are laid out and cut to size on a very large floor in real dimensions, (least ways they used to be). Hence the term "Sail Loft" as the place where you went to have the sails made for your vessel.

  7. #7
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    Angles are

    The angles on the ends of the cross pieces are 107.4314 degrees measured from the top to the side against the inside of the leg. The angles on the bottom ends of the legs should be 80 degrees from the outside edge to the bottom. The angle on top of the leg from the out side edge to the top is 100 degrees.

    I drew this up on autocad in just a few minutes.
    Lee Schierer
    USNA '71
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  8. #8
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    Thanks Lee!

    One last angle - the miter where the legs meet (not shown in drawing) to form the "L" - what's that? It's something > 90°...

    Any roofers in our midst? I'm thinking my grandfather and a good framing square could tackle this on a napkin...

  9. #9
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    107.4314 degrees

    I want to see the saw that you set that cut angle on!

  10. #10
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    "L" pieces

    Quote Originally Posted by Todd Burch
    Thanks Lee!

    One last angle - the miter where the legs meet (not shown in drawing) to form the "L" - what's that? It's something > 90°...
    I would make the "L" shaped piece first and then cut the ends to the angle needed. The two sides of the "L" shaped piece are 90 degrees to each other. Once I had the ends trimmed to the correct angles, then cut the tapers.

    Cutting the top end of the log to 107 in both directions will be a challenge to figure out. I would mark each piece with a pencil and then attempt the cuts, making sure I lined up with all the marks before actually making the cuts

    Hope you have an accurate miter gage.
    Lee Schierer
    USNA '71
    Go Navy!

    My advice, comments and suggestions are free, but it costs money to run the site. If you found something of value here please give a little something back by becoming a contributor! Please Contribute

  11. #11
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    Need dimention

    Quote Originally Posted by Todd Burch
    Thanks Lee!

    One last angle - the miter where the legs meet (not shown in drawing) to form the "L" - what's that? It's something > 90°...

    Any roofers in our midst? I'm thinking my grandfather and a good framing square could tackle this on a napkin...
    Todd, what size is the square formed by the outside edge of the top of the legs under the seat, the 10 degrees gives you 4.055" of splay per leg. the difference in the two triangles formed by the splay from the square at the top of the legs to the square at the floor level will give you the angle of change on the leg "L" of the 90 degree angle. I think. Its been many a year since Trig and I were on speaking terms, my Machinist Handbook is the Nineteenth Edition, that will date me.

  12. #12
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    The seat, a rectangle, will be 13" wide and 16" long (speaking in grain terms). In seat terms, 16" wide and 13" deep.

    Lee, if I make the 90° (BTW, the degree symbol is ALT+0176) first, when I splay it 10° one way and then 10° the other way, a framing square laid on the floor would not fit to the inside of the "L" any more. Try it, you'll see.

    These trash cans are splayed 15° each direction. The miters are 43½°, not 45°



    Todd.

  13. #13
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    Wrong again

    Quote Originally Posted by Todd Burch
    The seat, a rectangle, will be 13" wide and 16" long (speaking in grain terms). In seat terms, 16" wide and 13" deep.

    Lee, if I make the 90° (BTW, the degree symbol is ALT+0176) first, when I splay it 10° one way and then 10° the other way, a framing square laid on the floor would not fit to the inside of the "L" any more. Try it, you'll see.

    These trash cans are splayed 15° each direction. The miters are 43½°, not 45°

    Todd.
    Todd I was wrong and went hunting, found this, check it out.
    http://mathworld.wolfram.com/Trihedron.html Could this be what we have here, three plane ? I'll check out my idea.

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