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Codex OuroborusBy Karl Lautman 1/01 - 6/01

Copyright 2001 Karl Lautman

Ouroboros: emblematic serpent of ancient Egypt and Greece represented with its tail in its mouth continually devouring itself and being reborn from itself. A Gnostic and alchemical symbol, O uroboros expresses the unity of all things, material and spiritual, which never disappear but perpetually change form in an eternal cycle of destruction and...

Description A circle of 40 dominoes, approximately 13 in diameter, arranged atop a square base approximately 6 high. A single cord provides wall power (110V AC). There is a single momentary pushbutton on the front of the base. Pressing the button causes an activation mechanism to topple the first domino, triggering the familiar chain reaction. When half the dominoes have fallen, the initial ones begin to right themselves, in order, creating a continuous wave of falling and rising dominoes. After five cycles all the dominoes are righted, ready to go again with the next press of the pushbutton.

Principle of Operation Each domino has two holes drilled in its base. Into each hole are attached the ends of a loop of polyester thread. Each loop is threaded through a corresponding hole in the surface on which the dominoes stand. The two loops are attached to the plunger of a solenoid directly beneath each domino (one solenoid per domino). After waiting a few moments after starting the cascade, a circuit stored in an FPGA energizes the solenoid for the first domino, pulling on the loops, standing it up. A short time later the solenoid for the second domino is fired, and so on until the 40th solenoid. A counter within the FPGA keeps track of each cycle. When it gets to five, the unit turns itself off by opening a normally closed relay, killing power to the rest of the machine; the pushbutton activates a normally open relay which powers the unit up, and is wired so as to bypass the pushbutton, latching itself on.

In the event all the dominoes are lying down at start-up (due to transportation, nudging, etc.), the unit will simply right them all on the first cycle, then hum as it completes the remaining four cycles, and turn itself off, reset and ready to go. Development and Implementation There were a number of questions at the start of the project: 1. What material should be used for the loops? It must be strong, flexible, and wear-resistant due to friction caused by rubbing against the holes it would pass through. Fishing line was tested first as this is readily available in a wide variety of strengths. It was soon apparent, however, that line that was strong enough to not stretch was too stiff to allow a domino to fall naturally. Kevlar was found to be sufficiently flexible and strong. 2. What adhesive should attach the loops to the dominoes? It, too, must be strong, but low viscosity, to flow into the holes. Epoxy was adequate for one or two dominoes, for experimentation, but its viscosity led to lots of mess requiring too much cleanup to be practical for dozens of dominoes. UV-curable adhesive was considered but dismissed since the holes it would be injected into, at .0625 diameter by about .5 deep, would be too narrow and deep for the UV to penetrate sufficiently. Loctite 401 super glue was adopted after being recommended by Loctite. The glue is injected into a hole using a fine tip attached to the glues squeeze bottle, and then the ends of the loop are inserted and held in place for a few seconds. A light tug tests the bond, which, while strong right away, reaches full strength in 24 hours.

The photo above shows the jig used to hold a domino while drilling the two holes in its base.

3. How much force is required to right a domino? This would determine the solenoids to be used. Two holes were drilled in a small board allowing one domino to be set up, with its loops threaded through, and tipped over to rest on an adjacent domino as would be the case in the ouroborus (considerably more force would be required to right a domino lying flat). A small container was attached to the loops and washers added one by one to the container. When the domino finally stood up, the container was weighed. The weight was the required force. 4. How would the dozens of holes through which the loops would pass be drilled with the requisite precision? A jig using a lazy susan would be bolted to the stage of a drill press, with the board on which the dominoes would stand screwed to, and centered on, the lazy susan. A pencil would be placed in the chuck of the drill press and the stage raised until the board was in contact with the pencil. Then the board would be slowly spun through 360 degrees, causing a circle to be drawn on it. A second, concentric circle, with .5 greater radius (the holes in the dominoes in which the loops are glued are .5 apart, drilled with the aid of the jig, below) would be drawn in the same way. Radials would be drawn with a straight edge out from the center to intersect the circles. The intersections would mark where to drill, after replacing the pencil with a .0625 bit. Two limits arise from this approach. One is the size of the board, since the corners of a sufficiently large board would contact the pillar supporting the drill press, preventing the board from turning (see figure on next page). The other is the number of radials (which is the number of dominoes). This number must be a simple divisor of 360, since dependence on a protractor for odd angles is unreliable over the distances and quantities of radials envisioned. E.g., its easy to divide a circle into four parts with just a straight edge and square (and knowledge of the center). Its not so easy to divide it into five parts.

Drill press pillar

Drill press stage

1.625Base of jig attached to stage

5

1

7 x 16 7.5

Lazy susan

The above figure shows the relationship of the board, lazy susan drilling fixture, and drill press, from above.

19 .62 Do 5 min x o 19 bo .62 ar 5 d x (.7 5)

The above photo shows the lazy susan tool attached to the drill press.

This photo shows drilling in progress, with the inner circle barely visible.

5. How many dominoes should be used, and how far apart should they be spaced? This would determine the final size of the machine. Based on the considerations from 4., above, 32, 40, and 48 radials were tested on circles with diameters of 11.51, 14.057, 17.265, and 17.571; these diameters result from the selection of domino spacings of .75 and 1. The circles were drawn concentrically on a large sheet of paper, along with the radials, and dominoes set up by hand on one circle and radial set at a time. They were then knocked over and their falling timed and videotaped. The tape was later watched to see if there might be any problems with the patterns the dominoes made as they came to rest. Nothing came from these tests that definitively argued in favor of one layout over another. The design was fixed at 40 dominoes as a compromise between size (the bigger the better) and cost (solenoids are about $10 each). A 14.057 circle was chosen as this would result in the largest board (after adding margin) that would fit under the drill press. This also results in the closest possible spacing between the dominoes (.75) due to the width of the solenoids and their associated mounting brackets..87 x 1.125 14.888 dia., 46.772 circ.

15.888 dia., 49.914 circ.

8.5 x 8.5

PCB 6 x 4.625

5V DC

19.625 x 19.625 x (.75)

Inner radius = 7 7/16 = 7.438a

7.438 4.5 deg.

Dist. from one inner hole to the next = 1.168 = 1 11/64

9 deg.

7.438

sin (opp./hyp.) 4.5 deg. = .0785, so a = 7.438 x .0785 = .584 = 1/2 of distance to next hole. Total distance = 2 x .584 = 1.168.

The above figure show the arrangement of the dominoes (small rectangles) on the board, with the two outermost circles indicating where the loop holes will go. Also shown are the solenoids (squares with solid circles at their center), the solenoid mounting brackets (large rectangles), and starting solenoid in the upper left.

This photo shows a lone solenoid mounting bracket, as well as one installed in the jig used for precisely drilling holes in its long (solenoid mounting) and short (board attachment) legs. The jig is bolted to the drill press stage when in use.

This photo shows a test fixture used to determine the effect of the weight of a solenoid plunger (washers) pulling on each domino on the speed at which the dominoes fall, as well as their resting orientation.

6. How durable should the machine be? A minimum life expectancy of 10,000 up/down cycles/domino (corresponding to 2,000 button pushes) was arbitrarily selected. How would this limit be tested? A test stand with one domino and two solenoids was built. One solenoid knocked the domino over (see 7., below) and the other stood it up again, as described earlier; a complete cycle took about 1.5 seconds. An optical sensor attached to the solenoid plunger detected when the domino fell. A Basic Stamp microcontroller was used to control the solenoids and monitor the sensor. Unfortunately, this piece of equipment was cannibalized for parts before being photographed. The first test ran for 22 cycles before one of the reed relays driving one of the solenoids fused due to being over powered. Suitable MOSFET transistors were located to drive the solenoids and the test repeated. This time it ran for 872 cycles when the Kevlar thread used for the loops wore out due to abrasion with the holes in the board. The Kevlar was replaced with polyester thread and the test repeated. It ran for 9,687 cycles when a piece of the thread retaining the plunger in the starter solenoid gave out. Since this greatly exceed the life requirement for the starter, and the loops were holding up well, th