Tables for Talk
Why These Tables Were Built and the Design Principles Behind Them
        In 1901 Frank Lloyd Wright addressed the Chicago Arts and Crafts Society on March 6 and the Western Society of Engineers on March 20. His address was entitled The Art and Craft of the Machine. Around 1972 I was about to be saddled with a physics degree and while I love physics and math I thought then and think now that humans have a greater need for wisdom than technology and cleverness. I thought then and think now that I could build things fit for a free people and that these things could nurture wisdom better than our present surroundings. I built tables because that was what I could afford. I tried to fit tools, material, and design together. I used modern tools and materials because they are generally abused and I wanted machines working for people and not vice versa.

        Because the tools were going to be machine tools and because machines are good at duplicating pieces there were going to be repeated parts. Now - if a part went through the center there would be a collision if its repeated part also went through the center. Although I didnít consider this problem when designing the columbine table (my first design) with hindsight it can be seen that the "arms" of the columbine table meet at the center at a different elevation of where the legs would meet if they werenít capped off.
        The end tables show clearly how the collision problem can be solved by having parts go through the center at different elevations.
The coffee table has an additional twist to having parts go through the center at different elevations - the coffee table also has the parts go around the center. If you watch the assembly animation for the coffee table you will notice that the very first piece has a square hole in the center. The coffee table does not have any part go through the center. All parts go around the center plus the legs play the elevation game.
        The dinner table has additional thinking to its design. For the dinner table I wanted the leg room of a pedestal table but the strength and stability of a regular table. Where oneís knees are there is a pedestal but where there is a heavy off-center load there are legs. The first dinner table design had five legs going around a massive pedestal.
The five legged table required extensive and precise machining. The parts fit together only because the abilities of the machine tools involved were considered in the design. Precise angles were needed. A milling machine measures lengths very precisely but doesn't measure angles at all. A triangle of precise lengths is also a triangle of precise angles. There are 5 leg-arm-brace triangles. Having both a leg and an arm helps spread the load. The brace makes things strong.
The pedestal required several jigs to hold it while being machined. The precise angles were obtained by precisely locating reamed holes and using dowel pins.
After the extensive machining required for the five legged table I wanted a table that was built of stock size material, I didn't want to build a bunch of jigs, and I wanted different size tops to be held by the frame.The table I came up with was the six legged table where aluminum legs and arms thread through a pedestal made of six hexagonal brass bars.
This table frame easily accommodates different size tops but the tops are way too heavy for a woman to handle.

        The latest dinner table design (which has yet to be built) uses leafs that a woman can handle. The latest dinner table design has (to me) a fabulously interesting design. I was messing with the idea of having the pedestal reach out to the legs instead of running the legs to the pedestal. While messing around with complicated vector algebra I realized I was working with octagons and hexagonal bars. I then realized I was using an interesting theorem from projective geometry which states " Any two ____ determines a ____. In the blanks one inserts the words "point", "line", or "plane". The particular version of the theorem I was using was "Any two lines determines a plane." With this insight I was able to fairly quickly design a dinner table. The table has leafs that are light enough for a woman to easily handle. The leafs have shiny copper plugs and shiny brass rods beneath clear glass and above smoked lexan. The ends of the brass rods are threaded into bicycle spoke nuts. The sandwiched "spider web" holds the patined brass border against the glass and lexan.
The leafs are conveniently stored below the main top on shelves. When looking down through the main top you will see layers of spider webs below. The leafs can be used in different arrangements.
In the final design for the dinner table with leaves the symmetry of the perfect octahedron in the middle was broken. This led to another collision problem where eight aluminum bars were going to the same point. This collision problem was solved by butting the eight bars into the eight faces of brass pieces that are half scale copies of the middle brass piece. This solution was a pleasant surprise in the design process.
Along the way I got matching chairs.

        (Projective Geometry has an interesting history. One of the 800,000 some soldiers of Napoleonís Grande Armee that invaded Russia was a Frenchman named Poncelet. Poncelet was captured and to wile away the time while starving in prison camp he would take charcoal and try to recreate old geometry lessons. While Napoleon was running back to Paris to further his wars Poncelet was inventing Projective Geometry. In this geometry the words "points", "lines", and "planes" can be interchanged at will. I find this symmetry fascinating.)

Another design problem for which I had a helpful insight involved a chandelier. I had a flat frame for stained glass.
Stained glass generally goes into flat windows and depends on sunshine for light. A chandelier uses light bulbs for light so I thought something intrinsically 3 dimensional was possible. I thought I could lay the frames along the edges of a tetrahedron and poke the spikes into the center.

As usual there was going to be collision problems. In the next picture is a tetrahedron drawn from the top with the vertices labelled 1,2,3,4. Next is an isometric view of the tetrahedron. The frame that lies on edge 1-2 has a spike poked into the tetrahedron. That spike needs to sidestep the center. The two possibilities for sidestepping the center are drawn as circles. The frame that lies on edge 3-4 has a similar problem and its possibilities are drawn as squares.
Notice that the circles and squares if connected with lines would form a square. It can be seen that the sum of all the possibilities of all six frames (a tetrahedron has six edges) lie on the edges of a cube. However you cannot color 6 edges of a cube without having some of the colored edges collide at a vertex. The solution is to bend 3 of the 6 frames out of their plane half the distance the flat frames sidestep the center. The possibility chosen for frames 1-2 and 3-4 now looks like
The collision problem is solved by 2 concentric cubes, each with 3 edges occupied.
The unwired chandelier looks like
And when the chandelier is wired for four 110V bulbs and ten 12V Radio Shack bi-polar lamps it looks like
        
C.B. Jamison