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Pneumatics is a branch of technology that deals with the study, application and use of pressurized gas in structures and manufactured devices, usually to affect mechanical motion.

Pneumatics in Tensegrity Structures

In tensegrity studies, the pneumatics of pressurized, inflatable, flexible membranes are considered as an ideal model of a prestressed tensegrity structure. The membrane plays the role of the tension network while the isolated, rapidly moving molecules of the compressed gas play the role of the compression struts. The two classic examples are balloons and pneumatic tires. Pneumatics are also used in dynamic tensegrity structures to extend and collapse adjustable length struts.

Balloon as a Tensegrity Structure

Fuller found the balloon comparison so central to comprehending tensegrity, he opens with that discussion in his Synergetics. He wrote that tensegrities are "'hollowed out' balloons, discarding their redundantly 'solid' air core." [1]

Wilken wrote, "When we examine an inflated balloon as a system, we find that the rubber skin of the balloon continuously pulls while the individual molecules of air are discontinuously pushing against the inside of the balloon keeping it inflated. All external forces striking the external surface are immediately and continuously distributed over the entire system. This makes the balloon very strong. Molecules of air discontinuously pushing against the continuously pulling rubber skin of the balloon." [2]

In more detail, Fuller wrote, "The pressurized internal liquid or gaseous molecules try to escape from their confining enclosure. The outward-bound molecules impact evenly upon all the inside surface of the enclosure__for instance, upon all of the football's flexible inside skin when it is kicked in one spot from outside. Their many outward-bound impactings force the skin outwardly and firmly in all directions, and the faster they move, the more powerful the impact. This molecular acceleration is misidentified as pressures and firmness of the pneumatic complex. This molecular acceleration distributes the force loads evenly. The outward forces are met by the comprehensive embracement of all the tensile envelope's combined local strengths. All locally impacting external loads, such as the kick given to a point on the football's exterior, are distributed by all the enclosed atmospheric molecules to all of the skin in the innocuously low magnitudes." (Synergetics 703.05)

Illustration of a pneumatically inflated balloon, by Timothy Wilken""

Fuller wrote and lectured extensively about the balloon model of tensegrity, motivated by a variety of concerns. A partial list of these is discussed below.

Chords resist compression along the membrane

Fuller found it important to stress that, due to our experience of traditional architecture (or kindergarten wooden blocks) we expect that a structural element resisting compression will always be a strut oriented in parallel with the force being resisted. For example, when we press down on a table, it is the legs that oppose our pressure, pushing back up with an equal force. The pressure is borne by tension around the table legs' girth; see strut for a fuller explanation.

Fuller wrote, "Every action has a reaction. For a molecule of gas to be impelled in one direction, it must "shove off from," or be impelled by, another molecule accelerated in an opposite direction. Both of the oppositely paired and impelled action and reaction molecules inside the pneumatically expanded domes will impinge respectively upon two chordally opposed points on the inside of the skin. The middle point of a circular chord is always nearer the center of the circle than are its two ends. For this reason, chords (of arcs of spheres) impinge outwardly against the skin in an acutely glancing angular pattern." Synergetics 703.09

Synergetics by R. B. Fuller, Fig. 762.01, Chordal Ricochet Pattern in Stretch Action of a Balloon Net.""

The membrane is full of holes

The balloon membrane, when viewed microscopically, is composed mostly empty space. How then does the balloon both cohere structurally and resist compression? The answer is clear to anyone that has held a tensegrity sphere in their hands: compression is resisted by omnidirectional dispersion of the compressive force around the pre-stressed tensegrity network of struts and tension elements.

Synergetics by R. B. Fuller, Fig. 761.02 Function of a Balloon as a Porous Network.""

The center of gravity is still

As a result of the chordal dispersal of forces mentioned above, the gravitational center of the balloon plays no role in its membrane's structural integrity. This is a non-intuitive correlation, as most people expect the center to play a "central role." In contrast, tensegrity structures, like hurricanes, have centers that are still, non-moving and at rest. Fuller argued that the center cannot be involved. "When two molecules accelerate opposingly from one another at the center of the sphere, their outward trajectories describe a straight line that coincides with the diameter of a sphere. They therefore impinge on the skin perpendicularly, i.e., at 180 degrees, and bounce right back to the sphere center. It is experimentally evidenced that all but two of the myriad molecules of the captive gas do not emanate opposingly from one another at the center of the sphere, for only one pair can occupy one point of tangent bounce-off between any two molecules. If other molecules could occupy the nucleus position simultaneously, they would have to do so implosively by symmetrical self- compression, allowing the sphere to collapse, immediately after which they would all explode simultaneously. No such pulsating implosion-explosion, collapse-and-expand behavior by any pneumatic balls has been witnessed experimentally." Synergetics 703.10

Tire as a Tensegrity Structure

Wilken wrote, "The automobile tire is one of the strongest most durable inventions in the history of humankind. And few of us are aware that it is a tensegrity. It is the power of tensegrity in each tire that protects us from failure and blowout despite high speeds and long miles." [2]

The pneumatic tire is a tensegrity tube, not to be confused with the wire spoked wheel.

Pneumatics as Dynamic Struts

Pneumatic control units are implemented in tensegrities that implement struts with changing lengths. Changing the gas pressure changes the strut length, hence the morphology of the tensegrity structure. Sterk wrote about pneumatic pistons, "by understanding the typical way pneumatic pistons are controlled, we can also understand how [a]] wall [may be]] actuated by distributing air pressure between two different pneumatic chambers (within the body of a piston) in different combinations to allow the piston to extend, to contract, or alternatively jitter in a mode that enables it to extend and contract very rapidly. A computer... [may]] fire each piston sequentially in order to produce a series of patterns that responded to environmental stimuli."

References and Links

[1] Tensegrity by Fuller, from Portfolio and Art News Annual, No.4, 1961. [2] Explanation of tensegrity focusing on balloons, by Timothy Wilken,