Tetrahedron Machines 1992-current     (return to home page)

Frank Hausman

The Tetrahedron Machine is the simplest Platonic solid brought to life as a dynamic mechanism. Its four corners, four sides, and six edges form a tetrahedral shape. The edges are made of air cylinders, connected to each other by flexible joints. Extending and contracting these cylinders changes the shape and volume of the Tetrahedron Machine.

Locomotion is achieved in several ways: flipping, lean/sliding, hopping, leaping, and other combination moves.
When fully retracted, the machine can simply flip over onto a new face by extending and retracting one vertical cylinder, or horizontal cylinder. This shifts the center of gravity; inertia continues the motion to completion. With high air pressure and good timing, the machine will neatly flip onto any desired new face.
Lean/sliding moves the Tetrahedron's center of mass toward one face; as a result, one foot will have less friction with the ground than the adjacent feet. This foot slides away from the others when the adjacent edges are extended. This works best with low air pressure.
When two or more upright edges are simultaneously extended, the machine will hop.
If the machine is nearly flat, and "top-down", and if the "top" edges extend simultaneously, the Prime Tetrahedron will leap into the air a distance greater than its own height. The machine has a natural top, which is also the least massive corner - where three shafts are joined, as opposed to the other corners where one, two, or three cylinder bases connect.
Reduced gas pressure and flow moves the machine gracefully, almost sinuously, like an amoeba or a dancer under water.
When two adjacent edges are simultaneously extended, the machine can enter a degenerate planar state, fully collapsed on the ground. With high enough gas pressure, the machine will escape this state with a nice hop into the air. Low gas pressure will not allow any escape. This mode strains the corner joints and bends the cylinder shafts. Volunteer operators seem to enjoy this mode, however, as I cannot talk them out of it.

Construction details Three cylinders are joined at a corner by a three-axis 180-degree hinge. The corner joints also protect the cylinders from ground strikes. The volume of space enclosed by the tetrahedron can shrink to nearly zero (flat), and expand to 0.117 cubic units when all edges are one unit long. This prevents practical inclusion of a gas source on the tetrahedron chassis. A button box or computer controls an electrically-actuated pneumatic valve bank, which actuates the cylinders to extend or retract. Participants can control the Tetrahedron with a remote button-box or computer. The Prime Tetrahedron uses 1/2" diameter cylinders and is optimized for high speed and power-to-weight ratio. Its 1/8" I.D. hose provides adequate air flow and pressure to allow wild leaping behavior. The Skinny Tetrahedron's 3/8" diameter cylinders and 1/16" I.D. hose optimize it for low gas usage and gentle motion; it is still surprisingly agile. The Big Tetrahedron uses 3/4" diameter cylinders and isn't really optimized for anything except looming over children and animals. Pneumatic cylinder manufacturers only make cylinders this long and skinny under protest, and offer absolutely no warranty for any use. The Human Scale Tetrahedron (5 10 tall) is planned for completion for live performance. Its initial incarnation will be PVC Schedule 40 pipe with end travel dampeners and flow metering.

History The Prime Tetrahedron (11"-19" tall) was conceived in 1992 and assembled in 1994. The first corner joint system was duct tape which lasted 20 minutes - one full performance. The Skinny Tetrahedron (12"-21"tall ) and first Big Tetrahedron (31"-54" tall) were constructed in May 2000. All three machines received new reliable corner joints based on the original design drawings from 1992. These were realized in machined aluminum, brass and stainless steel components, and polyethylene hose.

Performances

• 1994. Prime Tetrahedron with Amorphic Robot Works in The Merge of the Children into Dream State at the Marin Headlands Center for the Arts, CA. Directed by Chico MacMurtrie.
  
• 2000. All three Tetrahedra at the San Francisco Museum of Modern Art Rebellissance Ball , a Surrealism-themed event for their Magritte Exhibition.
  
• 2001. All three Tetrahedra at The Amorphic Farewell to San Francisco party.
  
• 2002. Skinny Tetrahedron at The Amy Show , a benefit, SomArts Cultural Center, San Francisco.
  
• 2007. Skinny and Prime at the Blue and Green Ball , a benefit for Todd Blair at SomArts Cultural Center, San Francisco.
• 2010. Skinny Tetrahedron at the TV of Tomorrow Show 2010 Interactive Media Conference at Yerba Buena Center for the Arts, San Francisco.

Site requirements: Compressed gas, power, space, and light. Summary:

• Gas: compressed air at 110 P.S.I (12 bar), compressed nitrogen cylinders, or liquid CO2 cylinders. The Tetrahedron kits possess all necessary adapters and regulators.
• Power: 110V or 220/240V AC, 2 amperes.
• Area: small Tetrahedra need a 2x2 meter area for minimal operation. Two or more adjacent folding tables will suffice. Big Tetrahedra require 3x3 meters.
• Surface: should be approximately level and reasonably smooth. Tetrahedra typically will not damage durable flooring. The aluminum corner "feet" can be covered with rubber, felt, or teflon, as agreed upon in advance. Wild leaping behavior may require a thin (¼") protective surface such as carpet or plywood.
• Light: at least one dedicated lighting instrument appropriate to the venue.

Gas type and consumption tradeoffs:

• 20-lb cylinder of liquid CO2: highly available and portable. Can freeze under high flow.
• 70-lb cylinder of compressed nitrogen: requires a rack-equipped truck for transport; high flow; freezing unlikely.
• Motorized air compressor: portable but provides low flow; very noisy.

• Skinny Tetrahedron: Slowest, safest, lowest flow. CO2 cylinder lasts 2 hours. Nitrogen cylinder lasts 6 hours.
• Prime Tetrahedron: Acrobatic. CO2 cylinder lasts 20 minutes, can freeze. Nitrogen cylinder lasts 1 hour, no freezing.
• Big Tetrahedron: Lumberingly big. Nitrogen cylinder lasts 20 minutes.

Safety Matters:

• There is a slight hand-pinch hazard if the machine is grabbed near a corner.
• No hazardous or toxic materials are consumed or generated by the Machine.
• Temperature of exposed operating parts does not exceed ambient +10°F.
• Noise emitted does not exceed 70 dB at one meter (loud conversation).
• Air pressure is limited to 110 P.S.I.
• Electrical power to valvebank is low voltage, low current; (< 24 volts, <1 ampere).
• Machine proper is insulated electrically from any power source.
• No radio-frequency communication equipment is used.

Images:

• Prime Tetrahedron's first movie - tetra.ram (42k) or tetra.rm (42k) (get Real player) or tetra.avi (500k).
• Large Tetrahedron at San Francisco Museum of Modern Art
• Prime and Large Tetrahedra at SFMOMA.
• Large Tetrahedron balanced on edge.
• Skinny Tetrahedron hops a little.
• Prime Tetrahedron balanced.

Contact Information:

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