I annoyed my HS geometry teacher by announcing I could trisect an angle.
True, a Carpenter's Square is illegal under the rules of "Geometric Construction", but I could easily prove that it worked.
There are other methods, using other tools, but a carpenter's square is probably the easiest to prove correct.
Hence the original masons used three tools: the straightedge, the compass, and the square. It's amazing what you can do with those tools and a little "secret" geometretic knowledge.
-- Jay
I had the same problem. You can solve (most) such problems with a CNC router; but it's a tad spendy if you're not serious about making it pay its own way.
I'm still a neophyte, but I'm increasingly reaching the conclusion that a little geometric knowledge is all you *want* to have. Because of a misspent youth, I can do a lot of what people tell me is fairly complex mathematics in my head. So I wind up designing furniture that contains 18.7457 degree angles, or better yet, angles that are arctan(5.75/11) or lengths that are (5+sqrt(7))/2 or something. I actually computed a fifth order polynomial approximation to the chair leg curve I wanted on a table I made for my mother-in-law last year.
Unfortunately, I have learned that I can do the math, but I can not cut these crazy dimensions accurately. From now on, it's 90 degrees or 45 degrees or re-design it because it's wrong.
That one I'd like to see.
Then your own designs are fairly simple. I admire people who do their own design. It's not the math, it's art. The math I can do easily, and often apply it in the shop, or on the computer or wherever, but the art? Stick people are beyond me. I need plans with numbers on them mostly. I did figure out how IKEA designed their neat folding table though.
Bill.
Plot your design. You can either superimpose it on a grid and scale it; or you can find a way to plot it full size. If necessary run it out on your printer in pieces, one piece per page, and then tape the printed pieces together...
Now you can transfer the design to the hardboard. Did you know that you can get hardboard with a slick white surface at the lumberyard?) I have a piece tacked to the wall that I sketch on with dry erase markers - lets me re-draw to my heart's content.
Practise makes (more) perfect. (-:
I knew the shape I wanted, but I can't draw (as you say, stick people are also beyond me), so the only way I could represent it was mathematically. I wanted the leg to be two inches wide at the top, one inch wide at the bottom and one-and-a-half-inch wide halfway down. I also knew I wanted the first derivative to be zero at the top and at the bottom, and I wanted the second derivative to be zero halfway down. That's enough to define a fifth order polynomial. The fun part was going to be to try to do it on two faces of the leg to get the three-dimensional shape I wanted.
So I got out Matlab and plotted the thing, then I tried to draw it on the leg with a pencil. Then I contemplated actually cutting it with my crappy jigsaw. Then I decided my mother in law would be very happy with a tapered leg. :)
It's not quite that my designs are simple. It's just that I have to take my original crazy designs and simplify them until they contain no parts that I can't make. Right now, that means it has to require no skill. I need a fence or guide or something to follow or the results are not pretty. I understand from my reading that people typically cut curves by following a hardboard template. I'm not sure how this solves the problem, since you first have to get the template right.
I have also learned that two or three hours with coarse sandpaper can make anything look good. :)
I won't dwell on it, but you still lose me. A 5th degree polynomial has [at most] four local max/min; i.e. the plot goes up/down/up/down/up. That's a strange shape for a leg. :-)
Matlab is a bit hefty for that sort of thing. Try Graphmatica for 2D plots: www,archives.math.utk.edu.
I find DeltaCad really helpful. A bit of a learning curve for a drawing klutz like myself, but I finally got the hang of doing spline curves.
Bill.
The trick is the "at most". I just wanted flat at both ends and the curve in between equally distributed. At the risk of dwelling on it: f(x)=6x^5 - 15x^4 + 10x^3 between x=0 and x=1 is the function I settled on. I think it'sa fairly standard chair leg shape, actually, although I don't know the name of it. The up/down/up/down/up part happens outside the range of interest.
It's not as strange as all that, and I probably could have achieved the same thing with a set of french splines. This way, I got to tell myself I was "woodworking" when what I was actually doing was playing with Matlab. I got to have similar fun when I sat down to plan the angle I needed to cut a desired cove on my table saw. As always, the doing was much harder than the math.
I did find myself a cheap (free) CAD package, but I found it very hard to use. My (minimal) CAD training is 15 years old, and at that time, you typed in the coordinates of the points you wanted and the machine drew it for you. These days, apparently, it's all about starting with blank shapes and doing cutting planes or rotations on them. This is not how my brain works at all.
Neat!!
I use Mupad for something more dramatic, but will stick to simpler programs, usually preferring to figure by hand. My brother in law was a draftsman, and left me some of his tools. One "French curve" is in the shape of a babe. I'm afraid to handle her too much ...too distracting, so she sits in a drawer.
Do try Deltacad. It's very intuitive. All have a learning curve, but this one is relatively slight. Recently I drew up a model of our front door that I have to rebuild. Just rectangles and a few lines and dimensions are figured automatically. The end product is infinitely neater than I could draw or sketch.
Bill.
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