Introduction: Origami Furniture Case Study: a Table
This "Origami Table" represents further refinements on the fabrication techniques developed for the preceding folded plate chair Instructable. Unlike the preceding chair design, this table needed to be stiff enough to comfortably seat a glass of water or write a letter. I tried a couple physical prototypes and computer models before this was satisfactory.
To me there is something about plywood's use as a furniture medium that is similar to paper's use in origami. Plywood and paper are often associated with more pedestrian uses. Plywood as a building substrate and paper for office work and towels.
A central goal of these hinged furniture pieces is to see how far a thin sheet of pedestrian material can expand. I want it to do something normally excluded from our collective understanding of the material's structural performance and functional use. This is also what has always drawn me to both the ancient art of Origami and the contemporary cardboard furniture of Frank Gehry. There is a sense with this kind of work, that mathematics has intervened so deeply into the making process as to effect a kind of alchemy that elevates the material to a new way of being. I love how the french engineer, LeRicolais, summarized his work: "Zero Mass, Infinite Span."
The virtue of these pieces is also that contemporary sheet goods can be milled on a CNC table with relative ease and great precision. This approach is not unlike the precision required to make the more sophisticated origami pieces. I spend a lot of time writing tool paths for my Shopbot objects but you can certainly build your own versions using a combination of more conventional wood working pieces. A router is probably essential for dapping the hinges but the rest of the cutting could be accomplished with a skill saw and a rip fence, a band saw or a handheld saber saw.
Step 1: The Pieces
There are many kinds of plywood out there but if you're actually going to make a nice piece of furniture without applying edge banding you really need to make the investment in a good sheet. One sheet of 1/2" latvian birch plywood ran me about $60 and this table will likely require at least three sheets of plywood.
The continuous hinges, which I use to make the folds, are a more cost driven decision. After experimenting with more costly hinges I settled on your garden variety 1 1/2" wide continuous hinges from the local hardware store. There availability and their ability to be modified with a pair of tin snips made them good choice. A 6' length runs about $15 to $20 dollars. I used a 3/8" button head screws for the continuous hinge. These are NOT the screws that come with the hinge. It would be nice if I could countersink the screws but it turns out continuous hinges typically countersink the opposite side from the face we use in this project. I've spoken with the manufacturers about reversing the countersink but at this point, big surprise here, it would kill the economy of the project.
The most expensive part of the table was the 3/8" tempered glass table top. This cost about $300. If you wanted to do a simpler version you could avoid the cutout on the tabletop and just let the top be solid plywood. With the glass, you should be able to make the table for less than $700 each. I'm planning on finishing mine in Tung Oil but you can certainly pick any number of finishes.
Step 2: Conceptual Sketches and Hinge Performance
The first step in designing this kind of furniture piece is to do some conceptual sketching and ascertain the performance characteristics of your hinges and your sheet goods. The range-of-motion associated with the folds will depend on the paired performance of your plywood and hinges. Certain dihedral angles will not be possible with this pairing and therefore it is necessary to do a dihedral angle analysis before going too far with your initial design. A theoretical model showing the dihedral angles you wish to accomplish is an essential first step in this making process. I find Rhino to be very helpful at this point.
Step 3: Hinging Methodology
In general it is simplest to confine the hinge placements to only one side of the material. This simplifies both the computer modeling and the fabrication process significantly. For the computer work it helps because the furniture can essentially be "indexed" to one face of the material. Thus far, this is the inside face of the sheet since it simplifies the look of the piece and discourage clothing from catching on the hinges. For fabrication it helps to be able to lay the facets on the ground and attach all the hinges at once. In general it tends to make the most sense to place the barrel of the hinge inside the plane of the sheet material, or "facing down". For specific locations it may be necessary to "flip" the barrel of the hinge to face upward. This complicates the geometric model a bit but not as much as placing the hinge on the opposite sheet face. This "flipped hinge" approach is usually only necessary in locations where the dihedral angle is extremely acute.
Step 4: Facet Grouping
With any "origami" furniture that is somewhat complicated, it will be necessary to break the assembly down into a few "facet groups". Assembling the entire collection of pieces needs to be choreographed. This is normally accomplished by simply screwing a free hinge leaf on one facet group to the other facet group.
Step 5: Joining Facet Groups
Proper shoring of the two facet groups needs to be considered while doing this. With the exception of the special case mentioned next, I found the connections fit together with the ease one would expect of the Shopbot's geometric precision.
Step 6: Cut the Hinges Where the Fold Angle Is Very Acute and Access Is Difficult
There are the scenarios where fastening two facet groups meet at an acute angle. The joint can be unreachable with a screw driver or screw gun. When this occurs, it is necessary to CNC "fastener holes" on one side of a fold and modify one of the two hinge leaves at intermittent hole locations. The thin gauge of the sheet metal used on the piano hinges in this design is easily cut at the knuckles. Each knuckle is 1/2" long and the holes are at 2" intervals so the math is relatively straightforward. Staggering the access holes in this way is intended to accommodate the folds need for both strength and fastener access.
Step 7: Locating the Fastener Holes at Acute Folds
In the case of this table, the table top and the adjacent facet groups met at very acute angles. The fastener holes for this joint were located on the underside of the table top as shown.
This "facetted" way of building is cropping up all over these days. For the last couple decades there have been a lots of biomorphic forms seen in design magazines that utilize CNC technology to "tile" or "panelize" complex surfaces. Certainly Frank Gehry's early work with Catia is one example of this.
It is my sense a next step in sophistication will be to capture the structural properties of these complex forms and even allow the forms to be generated according to their structural wisdom. It has been disappointing to me, when visiting some of the braver undulating architectural design projects published in magazines, to see a rather complex array of old school steel armatures lurking awkwardly behind some of these "zoomier" forms. In finalizing this particular table, it seemed apt to top it with a tempered glass square and preserve a kind of "esthetic of the folds." I hope this instructable might inspire others to try out this way of building.
Because I reworked earlier versions of this table, I'm afraid there is not yet a single complete cut file for a single clean build. I have attached the two main toolpath files I pulled my parts from. If there is sufficient interest, I will update these files with something more comprehensive and concise. Thanks for checking it out. If you enjoy the work please visit my Etsy shop,