Origami Side Table

I created a table based on five intersecting tetrahedrons.

It was inspired by an origami model shown to me by my son, Kirk Meier. He created it from the instructions in the book The Origami Handbook: The Classic Art of Paperfolding in Step-by-Step Contemporary Projects. According to the book the design was devised by Tom Hull using a module created by Francis Ow.

Geometry

I wanted to make it from hardwood. So my first step was to understand how the geometry worked. Here's a  short video which shows the concept for how the parts relate (created in Rhino with Grasshopper):

Here are some screen captures of the computer model, baked after everything was positioned correctly in Rhino/Grasshopper:

It's constructed from five different species of hardwood: Maple, Cherry, White Oak, Mahogany, and Tulip Poplar. These woods were chosen to provide a variety of textures, grain patterns, and colors to make each tetrahedron individually distinguishable.

The parts slide by one another a teeeeeny bit. There's about 1/16" of space between adjacent members. It's locked pretty tight - with a very small amount of play. This is actually very useful because placing it on the floor aligns the points on the top (for the glass) equally flat.

Material

I had enough material in my existing wood supply to use for the table.

After some work between the joiner, table saw, band saw, and chop saw I had the material sized. Each piece is about 1.5"x1.5"x24". Some were a bit thinner, some shorter, based on the material I had. As long as the parts weren't less than 1.3" high and 23.25" long they were fine.

This large block of Cherry was broken up on the band saw into 4 parts.

Fixturing

Like any CNC project how you hold the workpiece during cutting is very important. Because I was cutting all the way through the parts I needed a small spoil board for each piece. The spoil board can be cut into (usually about 0.05"). The spoil board was held to the router table on pods using vacuum pressure.

I attached the pieces to the spoil board using fiberglass reinforced carpet tape. This adheres tenaciously but can be pried free with some rolling, forceful, hand pressure. Any residue left on the workpiece can be removed with paint thinner (mineral spirits wouldn't do it).

The stock is attached to scraps of MDF or MDO I had.

It's also important to note that brief clamping pressure must be applied between the stock and the spoil board. Without that the tape does not develop enough adhesion. I clamp the stock at each end, and in the middle to press them firmly together, just for a few seconds. That creates a very strong hold.

Test Cuts

To see if the parts fit together I made some extra blanks from Poplar. Over the course of several cuts I refined the toolpaths. It took a bit of iteration to get it just right but I got it so the parts would come out really nice each time. 

Okay they look good. How's the fit? Here are some parts dry fit: 

The initial clamping was nothing more than painter's tape. The joints were so tight, and geometrically they nest so well, it was very easy to glue up. Some tension across the joints was enough force. 

With the tape removed the finished tetrahedron looks great. 

Toolpath Programming

The key to cutting these parts successfully is thoughtful, tested, toolpath programming. It was critical to make sure the wood fibers were fully supported during the cut - in particular on the fragile mitered edges. By default router bits rotate clock-wise. Given this it is necessary to sometimes climb cut, and other times conventional cut to always cut "down hill". That is, to cut in the direction from shorter fibers to longer fibers.

A 1/2" 3 flute down-shear bit was the only tool used. Solid carbide and very sharp.

Final finish pass on the back edge. This cut is 0.05" thick.

The second of three depth cuts of the top during the roughing pass. You can also see the pockets cut to clear material from the mitered ends:

Final roughing pass of the mitered end:

Finish pass of the mitered end. This slice is 0.05" thick.

The finished piece: 

Cleaning up mid-cut. Things were starting to get a little deep. What lovely shavings!

Achieving Accuracy

What allowed the cutting to be accurate and error free?

• Careful Toolpath Programming: As discussed above this is critical. Refining the toolpath as you watch it cut is a basic part of CNC craftsmanship. I changed the programming at least five times as I watched more and more parts being cut. For instance what worked in forgiving Poplar didn't work as well it splintery Cherry. I had to revise the cut to eliminate it. 
• Sharp Tools: There is no substitute for sharp router bits. They cut more cleanly and accurately with less force on the work than dull tools. 
• Good Fixturing: The parts have to be held securely. In this case the right type of tape was critical. The spoilboard has to be consistent as well. It needs to be measure carefully as this affects the depth of cut. If it changes you need to adjust the origin of the stock. Using the double-sided tape was also very helpful to ensure the fibers did not tear free. The tape reinforced the fragile fibers at the end of each piece
• Stock Setup: The parts have to be milled dead flat so they don't move. The tape is strong but it needs a very flat surface to hold. 
• An Attentive CNC Operator: I was adjusting the speed with each change of species of wood. For example it was easy to move faster than normal on the Mahogany. It cuts so beautifully and is relativity soft. By contrast the White Oak had to be cut much slower. It is tough! I was cutting at half speed when swarf cutting the miters - otherwise there'd be chatter and a poor finish to the part. 

Finishing

Any tear out was scraped out. Actually, the only tear out was from the original planing which was taped down and couldn't be milled on the router. The sharp edges were slightly rounded by hand sanding at 80 grit.

Everything was sanded up to 220.

The parts after final sanding. Left to right - White Oak, Maple, Cherry, Mahogany. The Poplar parts are already assembled.

The parts after one coat of finish. After a second coat assembly began.

Assembly

The first tetrahedron was easy because it could be assembled alone. The second one was not too bad as there weren't many parts in the way. Once I got to the third one I realized I needed something to help with the alignment of the parts. They have to be fed one at a time through the already assembled others so all six members have to be glued up at once. And getting them all just right, with 10 minutes of glue setup time, was problematic.

To help I made some simple fixtures, one for each corner of the tetrahedron. These were cut from from some plywood scraps on the 5-axis router.

They are tapered at the correct angle so inserting the parts assures they get aligned correctly.

This makes it MUCH easier!

Finished Table

Here are some photos of the finished table:

The table sits on the floor on five points and the table top rests on five points:

The table was on display at the 92nd Annual All Media Exhibition at the Ann Arbor Art Center:

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