How to Make a Parabola with a CNC


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A parabola is not an easy thing to make, or at least it isn’t if you don’t have a CNC. With a CNC its actually pretty easy. This tutorial will show you how to make a parabola using Sketchup. Once created, you can export it from Sketchup to an STL file, load it into Meshcam (or another program like it), and generate the G-code.

You will need to have the Su2stl.rb Plug-in installed in Sketchup to export the parabola to STL.

You can get it here along with quite a few other Plug-ins if you want them.

As you may find out, the export to STL Plug-in sometimes doesn’t work. However, it doesn’t take very long to make a parabola in Sketchup. If it doesn’t come out right, just start over from scratch. It will usually work the second time around.(or at least it has for me)

This parabola is designed to be cut out of two 13″ x 13″ x 3/4″ MDF boards glued one on top of the other. The total thickness will be 1.5″. If you actually make one with these dimensions, I recommend that you cut a circle with a 3 3/4″ radius out of the center of the top board to reduce the amount of waste/dust.

Update: 4/11/10
Make sure to scroll down to the bottom of this page to find out how you can make a parabola which is more accurate than the one I originally made here.

Finding the Focal Point of a Parabola

It is useful to know where the focal point will end up when making a parabola. If your going to use your parabola as a solar reflector, keep in mind that it is safer for the focal point to be in close to the parabola.

Here is the formula for finding the focal point.

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F = focal point
D = diameter
d = depth

These are the dimensions I will be using for this parabola.

D = 12″
d = 1 3/8″ which is 1.375 in decimal form.

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So the focal point will be about 6.5″ away from the bottom of the parabola.

Drawing the Parabola

1. First, select the Arc tool and, starting at the origin, draw a line 12″ long with 1 3/8″ bulge.

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b.  ^^^ That’s what the Arc button looks like.

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2. Next, draw a line 1 1/2″ down from both ends.

Connect the bottoms of those ends to create a face.

Now, draw a line straight up from the midpoint of the bottom line to the bottom of the arc.

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3. Erase the right half.

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4. Draw a circle from the inside of the arc to the outside.

Next, click the middle of the circle so that it’s highlighted.

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5.       Select the Follow Me tool and click anywhere on the face with the arc. This should create the parabola.( I turned on the hidden geometry so that you can see the parabola’s shape easier. It’s under the view tab on the menu bar. )

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b.    ^^^ That’s what the Follow Me tool looks like

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6.      The next thing you should do is build a box around it so that MeshCam won’t end up cutting out anything other than the parabola. The one below is 13″ x 13″. After you’ve done that, it’s finished!

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7.    The only thing left to do is export to STL. This parabola exported correctly on the first try. If it doesn’t for you, just try rebuilding it. Hopefully it will work the second time.

Making the Parabola more Accurate

(Backtrack to step 4)

On one final note, you can increase the accuracy of the parabola by right clicking the circle and selecting divide from the menu that pops up. Red dots will appear on the screen, and their number will either increase or decrease depending on where you move the cursor along the circle. It’s also possible to divide the arc into smaller segments as well.

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You can divide a curve into as many as a hundred segments, but if you do too many Sketchup will most likely crash when you use the Follow Me tool. I generally divide the circle into 100 segments and the arc into 25. If you have a slowish computer, you may not want to bother with this step.

Pictures of the Finished Parabola

[bad]

Update: 4/11/10

Someone e-mailed me recently to give me a heads up about a potential problem with my parabola. Basically, Sketchup’s arc tool doesn’t draw parabolas so much as it draws sections of circles. The shape is parabola-ish, but not a true parabola. This is something that I had half realized on my own sometime after I wrote this tutorial, but never got around to correcting. Since somebody finally called me out on it though, so I decided it was time to add to the tutorial. :)

If you look at the picture below, you can get an idea of how accurate a parabola drawn with the arc tool is. The vertical black lines represent the sun’s rays and the dashed black lines represent those same rays after they have reflected off the surface.

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Here is the same picture after zooming into where the sun’s rays are the most concentrated. Notice how they don’t really meet up at the same focal point. The shape still concentrates the sun’s rays, but not as accurately as a true parabola does. As mentioned in the e-mail I received, this is more of a “spherical dish reflector” than a parabolic dish reflector.

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Update Continued: Making an Accurate Parabola

If you want to make a more accurate parabola with your CNC than the one that I made, here’s how you can do it.

First, go to this page http://mscir.tripod.com/parabola/ and download the Parabola Calculator program (It’s free!). Below you can see a picture of this awesome program in action. A big thanks to the individual(s) who wrote it!

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Just type in your desired diameter and depth and hit calculate to get your parabola. Notice that it automatically calculates the focal point too. Also notice how there is an option to either add or remove segments. More line segments will make the parabola created by the program more accurate. Of course, if you have too many you may run into problems when you use the follow me tool as described in the original part of this tutorial.

After you’ve finished designing your parabola, go to “file” on the menu bar and click “Save Data to DXF (.dxf) File” and choose where you would like to save your file.

Next open up Sketchup, go to “File” on the menu bar, click “Import” and go to the file you saved in the Parabola Calculator program. (Note: I am using Sketchup 7 and am unsure if all of the older versions will import DXF files. You may need to upgrade if using an older version.)

If successful, your parabola should appear inside of Sketchup. From here, you can basically just follow the original tutorial. Note: You will probably want to rotated the parabola 90 degrees along the x-axis so that it is facing the right direction.

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With this parabola, you can see how the rays from the sun are concentrated much more accurately than they were with the one I had originally made.

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Here is the same parabola after using the follow me tool on it.

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