OK, so the original question was about 15 years ago, a WISEA$$ kid sitting in a geometry class (me) says, “this sucks, what are we ever going to use this for?!” Not sure what the answer was then, but can think of something now! This leads to the second question where I ask you guys and hope one of you paid attention. I am not great at explaining stuff and this will be hard to explain, but bear with me. I want to make a table that is in the shape of a capital D if looking down on it. So basically it has 3 sides of a rectangle with the forth side (in place of the second long side) there is an outward arc. I know the dimensions of, the overall length of the table, the width of the 2 smaller sides of the rectangle and I know the width of the widest part of the table which is the center of the arc. My question is how do I find out the radius of the circle that forms the arc? How would I make that? I am imagining some kind of huge compass type of jig that would guide a router to cut the arc? Am I close? Am I way off on this? If so how would you do it, if I am not way off, then how do I figure out that radius? If this isn’t clear, you can send me back to the drawing board and I can try to conjure up some images. Thanks a TON in advance and I know, I know, I know the teacher is always right! This is NOT one of the first 500 times I was a JACKA$$ and it came back to bite me! :P :P
Marc is correct in his drawing for an ellipse, however if you want a circle edge, use only the center point.
I just recently saw in one of the WW mags that shows how to construct a jig for your router for cutting a circle or an ellipse. If memory serves me correctly, it invloved two movable arms attached to blocks that moved in a frame in X and Y directions. If anyone remembers the mag (it was just in the past month or so) please post. In the meantime, I'll try to find it tonight and post it later.
Measure with a micrometer, mark with chalk, cut with an axe.
Actually, I don't know that I would mess with finding a center for a circle, and given your description, I don't know that a hard fast geometry equation, etc would be in order. By your explanation, the short sides are going to have some straight length before the beginning of the arc forming the rounded side and you know the distance from the center of the long leg to the center of the arc.
If it is a rather long smooth curve that you want, then the simplest method for laying it out would be to mark the straight edges out onto you template material, then tap a finish nail at the termination point of the two short edges and a third one at the apex of the curve. Using those nails as anchors, bend a long enough piece of scrap cut thin enough to bend but still be strong enough to maintain tension and not break from the inside of one nail at the end of one short side, around theoutside of the nail at the apex, then back to the inside of the nail at the other short side. Trace along that piece of scrap to get your arc. Cut it out on the template and proceed in the normal method of using a template.
You said that you have three sided of a rectangle and you want the fourth side to be an arc.
Lets start with the smallest possible arc and then get bigger. When looking at a "D" the smallest possible arc has the sides of the rectangle TANGENT to the arc. That is if you were to draw a circle, the diameter would be the distance between the two sides of the rectangle. That arc would be a half circle and the table would be sort of squarish. (If that's a word.) For a table, that would be a bit too much of a curve for my tastes. What is important about this exercise is that the CENTER point of the arc is half way between the sides of the rectangle. For your purposes, the center of the arc will always be equidistant between the two sides of the rectangle.
For larger raidus arcs, no further measurement or geometry is necessary. Put a small pin or nail at each point where the arc starts on the sides of the rectangle. Put a strip of cardboard or thin wood against the pins or nails. Grasp the strip at the point where center of the arc from the above paragraph and gently pull until you get the desired arc for the table. Draw a line along the strip and you'll have the desired arc.
Isn't that what I said in my first post quoted here?
"If it is a rather long smooth curve that you want, then the simplest method for laying it out would be to mark the straight edges out onto you template material, then tap a finish nail at the termination point of the two short edges and a third one at the apex of the curve. Using those nails as anchors, bend a long enough piece of scrap cut thin enough to bend but still be strong enough to maintain tension and not break from the inside of one nail at the end of one short side, around theoutside of the nail at the apex, then back to the inside of the nail at the other short side. Trace along that piece of scrap to get your arc. Cut it out on the template and proceed in the normal method of using a template."
Thank you guys so much for the help so far. I like Jerry’s idea about the scrap and I think that is how I will do it. So if I figure out my points, run the piece of thin scrap between 3 nails that I put at the end points of the short sides of the rectangle and the widest part of the circle. I am clear with that part. Now I understand that I want to trace that arc and that will be my arc. How do I cut that arc out so it is perfectly rounded? Do I have to cut it freehand on a bandsaw or jigsaw and then try to get it perfect sanding it down? Or can I find a way to use the new arc as a guide for a router to cut the jig? That is what I want to do with the jig is run a router along the arc to cut the final arc. Do I need to make the arc on the jig a little smaller then the arc that I want as a final product to make up for the distance between the edge of the router base and the bit? That couple of inches will actually make a larger arc, will it matter?
Thanks again in advance!
I would lay the arc out onto some MDF, cut it out on a bandsaw or jigsaw . . . just outside of the line and use a rasp or whatever to take it down to the line and get it perfect, then use that as a template. As to whether the template needs to be the exact size, or a little smaller will depend on whether you use a flush cut bit wit a bearing or a template bushing like those here:
Sorry to be a little thick headed here, but I am not sure what we are looking at in that link? How do these bushings work? How would you do it if you wanted to make this? I guess I had a vision of laying out the arc and using it as a guide to run the router base along. That method creates a problem with the couple of inches between the edge of the base and the bit though. Also, is there anyway to do the first cut (on the MDF or whatever) without having to smooth it freehand?