How might I make a tetrahedron?

B

Bill Kahn

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OK. I got making a cube now basically figured out. I have a a PM25MV mill. And some extra stuff (vise, end mills, caliper, clamps, angle plate, rotary table...). And I finally can make a 2" cube that is good to .005 on any measurement. I am thrilled. (Was talking to my machinist brother-in-law over Thanksgiving--he mass produces to .0002" so he wasn't impressed. I think he said he was doing .005" when he was 12 years old. Did not dampen my excitement though.)

How might I machine a tetrahedron? (4 identical equilateral triangles as the four sides). I am a good enough mathematician to work out any of the angles I may need. But geometrically, how do you grab hold of it to machine it? I don't want a hold down threaded hole in one side. I can make an "extruded" triangle--e.g. --a triangular "cylinder." So, I have one of the four triangles. Then I can grab the two parallel sides in a small vise along just the edges, angle it up, and get the second side milled.

I just can't think of how to hold it from there.

Any thoughts/suggestions/references/youtubes?

Thanks.

-Bill
 
Make the outside of a cavity, bolted together, cast one in the cavity.
 
Are you trying to make a tetrahedron just because, or is it meant to serve some purpose?

Personally I would start with a bit of round stock and machine the top three sides of the tetrahedron on the end forming a pointy stick effectively. This can be done by setting the work at the appropriate angle then cutting, rotating 120 degrees, cutting again and rotating/cutting one last time.

I would cut the sides all the way out to the bounds of the round stock the part it off at the appropriate "height" Preferably this is done on a lathe, but it is also possible to "part off" on a mill.
 
Bill Kahn said:
OK. I got making a cube now basically figured out. I have a a PM25MV mill. And some extra stuff (vise, end mills, caliper, clamps, angle plate, rotary table...). And I finally can make a 2" cube that is good to .005 on any measurement. I am thrilled. (Was talking to my machinist brother-in-law over Thanksgiving--he mass produces to .0002" so he wasn't impressed. I think he said he was doing .005" when he was 12 years old. Did not dampen my excitement though.)

How might I machine a tetrahedron? (4 identical equilateral triangles as the four sides). I am a good enough mathematician to work out any of the angles I may need. But geometrically, how do you grab hold of it to machine it? I don't want a hold down threaded hole in one side. I can make an "extruded" triangle--e.g. --a triangular "cylinder." So, I have one of the four triangles. Then I can grab the two parallel sides in a small vise along just the edges, angle it up, and get the second side milled.

I just can't think of how to hold it from there.

Any thoughts/suggestions/references/youtubes?

Thanks.

-Bill
Click to expand...
My approach would be to machine all but one side on the end of a larger piece and cut it off creating the final side. Then make a 3 sided "v block" jig to hold it in a vertical position (cut end up) and machine off the saw marks. You could use strong magnets in the "v block" to hold the work. Curious, Is this to show-off to your brother in law at Christmas dinner?
 
You can easily machine all but one side. For the last side/face, make a vacuum pod to hold the thing so you can machine the last surface…Dave.
 
Take a 6 sided collet holder big enough for the raw stock of the tetrahedron.
Take a 30º triangular reference and use it to position the 6-sided collet holder in the milling vise holding the raw stock.
Knock off 3 sides with this on the mill.
Take the 6 sided collet holder to the lathe and part off the tetrahedron.
 
This is an interesting problem in work holding. I would machine three faces, leaving a long handle on the forth face. If you are not concerned with final size, any cut for the fourth side will work as long as it is perpendicular to a line through the apex and equidistant from the first three sides. Holding the work to make the cut could be an issue though. You could hold by the handle to part off the work. I guess that I would make a cylindrical handle, set up in the mill to cut the three faces, and part in the lathe. This should get you within a few thousandths of your final size.

I would make a fixture for the tetrahedron out of plaster of Paris, epoxy, or similar castable material. I calculate the taper angle to be 19.471º which is not locking taper so some means of hold down clamp would be required. I would face one half, move the clamp(s), and face the second half.

If you are going to use a secondary operation for finishing (e.g.. lapping), it would eliminate the need for the fixture.

Let us know how it turns out!
 
I have a solid or wire frame model for your project.
Your welcome to both , let me know.
Good luck
Jerry
 
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