I had a pretty inconsequential project the other day, and decided that it would be nice to make it in the shape of an ellipse. It was to be about 5" major axis and 3" minor axis. I also wanted to round over the edge, and put a rounded groove in from the edge. I knew that you could create an ellipse in one of several ways: with two pins and a string and a pencil, OR, with an ellipse mechanism. The mechanism is traditionally used for cutting elliptical mats for art in a picture frame. The pins and string would work, but that involves cutting and sanding, and it seemed like there should be a better solution. Since this was to be made out of plastic, I wanted to cut this out with a milling machine or a router.
I found an ellipse jig on the Rockler web site http://www.rockler.com/product.cfm?page=17282. Aside from the fact that it cost $90, it would not allow me to cut an ellipse small enough for my project. However, after tching the video to see how the jig works, and giving it a LOT of thought as to how I could use the principle, I came up with the following.
I needed to have a pair of intersecting grooves to run some sliders in. I decided that I could tolerate small grooves in the back side of my parts, so I decided to do that. You could also have the grooves in another piece that is double-sided taped or screwed to the part. I cut grooves 0.150" deep x 0.250" wide in a test piece of MDF. I made up two aluminum sliders, each 0.125" x 0.248" (boy, it's hard to hold onto those small parts!), with a 1/8" hole in the middle. On the milling machine, I set up a plywood platform, with a series of 1/8" holes 1/2" apart, so I could play with the distance between them. These holes were a little undersized so that the steel pins had to be pressed into the plywood.
I could now put the sliders on the pins on the platform, and put my test piece over the sliders, one slider per groove. I was elated to find that I could indeed rotate the piece by hand and see that an ellipse would actually be cut by a straight cutter positioned along the pin line over the part! I set the major axis to be about 5", and fired up the mill. It cut easily, without any real danger of the part getting away from me. It did not try to lift up or run away, but this is probably mostly because the material is so soft and easy to cut. The following link is to a movie showing how the ellipse cutting works:
(Sorry, but I couldn't get a linked image or an embedded player to work right.)
By merely changing the cutter from a straight cutter to a core box bit, and moving the spindle toward the ellipse's center, I was able to easily cut the rounded groove on the part inset from the edge. I saw that the little sliders never did emerge from the slot in the side of the ellipse, so decided that I could cut the underneath slots only long enough to accomodate the sliders, so they wouldn't show on the edge of the finished part. Since I was rotating the part by the scrap that would be cut off, I could cut only most of the way through, then come back with a router pattern bit to clean up the rest of the material thickness. I could also use a router to round over the edge. Easy.
You can make ellipses as small as you'd like using this setup, by just moving the cutter closer to the center. You change the aspect ratio of the ellipse by adjusting the spacing between the pins in the platform.
It's a pretty crappy graph, but it seems like the aspect ratio is quite sensitive to pin spacing, especially at larger spacings.
I doubt that this will work well at all with any metal or other difficult-to-machine materials, as it would be too hard to manually feed the part into the cutter. If desired, you could set up a hold-down provision to keep the part on the platform, using an overhead caster or roller to apply downward pressure.
I then got thinking about how the sliders run in the grooves to produce the final ellipse. I wondered what shape you would get if the grooves were not perpendicular to each other. So, I made up another test piece with one groove 30 degrees off of perpendicular, and ran it. Interestingly enough, there was no visually noticeable difference, although it is probably no longer a true ellipse.Then, when I couldn't sleep one night and I got to thinking what would happen if one, or both, of the grooves were curved. This was a little tougher to set up, but the rotary table made it possible to cut curved grooves and some curved sliders to match. The only noticeable difference was with two curved lines it produced a very slightly more egg-shaped oval. See this photo of a variety of test runs.
The thick blue lines are the groove locations marked on the top surface so you can see what grooves made what shapes.
You can also vary the angle of the ellipse on the block by moving the location of the cutter with respect to the line of the pins. I found that if you have the cutter in line with the line connecting the two pins, the major axis of the ellipse will be parallel to that line. If you have the cutter off the line, perpendicular to the approximate center between the pins, the ellipse will be inclined 45 degrees to the line.
Plenty of other interesting (to some people) things to think about. For example, the ellipse has a center (where the major and minor axes intersect), but what is the shape of the path that this point traces as the ellipse is being rotated to be cut? So far, I don't know, but somehow suspect it is a circle. Any other opinions?