In mechanics and biomechanics, tensegrity or tensional integrity is a property of objects with components that use tension and compression in a combination that yields strength and resilience beyond the sum of their components. Mechanics refers to: a craft relating to machinery (from the Latin mechanicus, from the Greek mechanikos, meaning one skilled in machines), or a range of disciplines in science and engineering. ... Biomechanics is the research and analysis of the mechanics of living organisms, pioneered by Professor Yuan-Cheng Fung. ... In physics, tension is a force on a body directed to produce strain (extension); it can be considered to be negative compression. ... Compression in material science, physics or structural engineering, is the stress state of materials where the volume tends to decrease (compaction). ...

Animals and other biological structures are made strong by their tensioned and compressed parts. Muscles and bones act in unison to strengthen the other. This kind of strength exists also at the cellular level, and it is a somewhat new understanding of biological structures.

Principles

Tensegrity is the pattern that results when push and pull have a win-win relationship with each other. The pull is continuous and the push is discontinuous. The continuous pull is balanced by the discontinuous push producing an integrity of tension and compression.

Buckminster Fuller explained that these fundamental phenomena were not opposites, but complements that could always be found together. Tensegrity is the name for a synergy between a co-existing pairs of fundamental physical laws; of push and pull, and compression and tension, or repulsion and attraction. In the U.S. postage stamp commemorating Buckminster Fuller and his contributions to architecture and science, some of his inventions are visible. ... A physical law or a law of nature is a scientific generalization based on empirical observations. ...

If one pushes a ping-pong ball on a smooth table with the point of a sharp pencil, the ball would always roll away from the direction of the push, first rolling one way then the other. Push is divergent. Regional competition level table tennis, showing table, net, and player getting ready to return the ball with a winning backhand topspin stroke. ... In mathematics, the concept of a limit is used to describe the behavior of a function, as its argument gets close to either some point, or infinity; or the behavior of a sequences elements, as their index approaches infinity. ...

On the other hand if attaching a string to the ping pong ball with tape, and pulling it creates convergence. No matter how other forces might influence the ball to roll away from you, the string would always bring it to you more and more directly. Pull is convergent. For a discussion of convergence and convergent series, see limit (mathematics). ...

Another example from common experience occurs when pulling a trailer with a car. When driving uphill, one is pulling against gravity, and a trailer will converge toward the same course behind the car. If the trailer begins to sway, increasing pull by increasing acceleration can dampen the swaying motion.

Driving downhill, however, the trailer may begin to push, and the trailer will begin to sway from side to side.

The human organism

Two tensegrities are easily recognizeable in systems of the human body. The muscular-skeletal system is a tensegrity of muscle and bone, the muscle provides continuous pull, the bones discontinuous push.

This forms the basis for all human physical mobility. The central nervous system can also be understood as using the analogy of tensegrity where motor neurons and sensor neurons, complement the other in a balance.

A more common example of a tensegrity is in a child's balloon. When examined as a system, the rubber skin of the balloon can be seen as continuously pulling (against the air inside) 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, meaning the balloon is very strong despite its thin material. In science, a molecule is the smallest particle of a pure chemical substance that still retains its chemical composition and properties. ...

The automobile tire works the same way. It is the tensional integrity in the tire that yields a low failure rate despite the wear of high speeds and long miles.

A tensegrity then is any balanced system composed of two elements – a continuous pull balanced by discontinuous push. When these two forces are in balance a stabilized system results that is maximally strong.

Larger structures

Tensegrity also refers to a means of creating structures.

Tensegrity was first explored by artist Kenneth Snelson to produce sculptures such as his 18 metre high Needle Tower (1968). The idea was adopted into architecture in the 1980s with David Geiger designing the first significant structure - a competition hall for the Summer Olympics of 1988. The Georgia Dome, which was used for the 1996 Olympics is a large tensegrity structure of similar design to the aforementioned competition hall. Kenneth Snelson (born 1927) is a contemporary sculptor whose works are designed using flexible and rigid components in a mutually supportive arrangement, according to the idea of tensegrity. ...

The term 'tensegrity' was coined for Snelson by Buckminster Fuller from tensional integrity. His famous geodesic domes are themselves tensegrities. In the U.S. postage stamp commemorating Buckminster Fuller and his contributions to architecture and science, some of his inventions are visible. ... The American Pavilion of Expo 67, by R. Buckminster Fuller, now the Biosphère, on Île Sainte-Hélène, Montreal A geodesic dome is an almost spherical structure based on a network of struts arranged on great circles (geodesics) lying on the surface of a sphere. ...

"The great structural systems of Universe are accomplished by islanded compression and omnicontinuous tension. Tensegrity is a contraction of tensional integrity structuring. All geodesic domes are tensegrity structures, whether the tension-islanded compression differentiations are visible to the observer or not. Tensegrity geodesic spheres do what they do because they have the properties of hydraulically or pneumatically inflated structures."

The larger the tensegrity the stronger it is. The geodesic dome at Disney World in Florida is an example. Theoretically, there is no limitation to the size of a tensegrity. Cities could be covered with geodesic domes. Planets and stars (Dyson sphere) could be contained within them. Diagram of an idealized Dyson shell of 1 AU radius A Dyson sphere is a hypothetical megastructure first described in 1960 by the physicist Freeman Dyson. ...

As Harvard physician and scientist Donald Ingber explains:

• "The tension-bearing members in these structures – whether Fuller's domes or Snelson's sculptures – map out the shortest paths between adjacent members (and are therefore, by definition, arranged geodesically) Tensional forces naturally transmit themselves over the shortest distance between two points, so the members of a tensegrity structure are precisely positioned to best withstand stress. For this reason, tensegrity structures offer a maximum amount of strength".

Build Your Own Tensegrity Structure

It is not difficult to build a tensegrity structure. From this first simple unit you can experiment and add other units to make it as complex as you like. Image File history File links 01_MaterialsNeeded. ...

You will need:

• 3 poles
• 6 rubber bands
• string
• tape
• ball

Image File history File links Download high resolution version (514x686, 42 KB) Summary Author: JHuberman Source: My picture modified with MS PhotoDraw 2 of instructions for building a tensegrity structure Licensing File history Legend: (cur) = this is the current file, (del) = delete this old version, (rev) = revert to this old...

Make a Three Legged Stool

The first thing to do is tape the poles to the ball to make a "three legged stool". this will hold the structure together while you attach the string.

If you try and assemble it without holding the poles somehow it will become a tangled mess and you will lose track of what goes where.

Remember the structure has no integrity until all the strings are adjusted and tight.

Image File history File links 04_TopTriangle. ... Image File history File links Download high resolution version (595x794, 62 KB) Summary Author: JHuberman Source: My picture modified with MS PhotoDraw 3 Instructions for building a tensegrity structure Licensing File history Legend: (cur) = this is the current file, (del) = delete this old version, (rev) = revert to this old version. ...

Attach the String

• In this step you use the rubber bands to attach the string to the top of the poles.
• Notice how long the loops of string are
• The easiest way to do this is to wrap the rubber band around the string with just a small amount showing, and then pull the loops out.
• Notice how the loops reach down to the bottom of the poles and have enough length to reach the bottom of the next pole.
• It is important to leave enough slack so you have enough string to adjust the finished structure.

Image File history File links 06_BottomStrings. ... Image File history File links 05_CutStrings. ...

Cut the Top Strings and Attach the Bottom Strings

• In these steps you cut the loops and attach the strings to the bottom.
• When you cut the loops, be sure to leave a couple of inches sticking out of the top so you have string for adjustments.
• Notice that the lines from the top go down to a bottom pole without crossing over any other poles, and then continue on to the bottom of the next pole (not back to itself).
• Follow the picture carefully for your first structure. After you get it working, then experiment with different arrangements to create your own works.

Image File history File links 07_RemoveBall. ...

Tighten the Strings and Remove the Ball

• You are almost done.
• Pull the strings snug.
• Carefully remove the ball.
• Adjust the strings to get the form you like

Image File history File links 08_SideView. ... Image File history File links 09_EndView. ...

Two Enhanced View of the Finished Structure

• Notice that there are two kinds of structural triangles.
  • Two are made of three strings and one of them is shown in blue.
  • Three are made of two strings and one pole. One is shown in black.
• It is difficult to see in the 2d pictures, but none of the poles touch each other.
• Experiment by putting several of these units together.
• Have fun building Tensegrity Sculptures.

References

• Donald E. Ingber, The Architecture of Life, Scientific American Magazine, January 1998
• Buckminster Fuller, SYNERGETICS—Explorations in the Geometry of Thinking, Volumes I & II, New York, Macmillan Publishing Co, 1975, 1979
• Seeking the Gift Tensegrity Dr. Timothy Wilken TrustMark 2001

Tensegrity was a term used by Carlos Castaneda to refer to the modernized version of some movements called magical passes (a series of meditative stretches, stances and movements) developed by Native American shamans who lived in Mexico in times prior to the Spanish conquest. Castaneda borrowed the term tensegrity from architecture because the magical passes combine tension and relaxation of the muscles, joints and ligaments in a way that yields a stronger, more flexible, and more "aware" physical body. 'Tensegrity' also refers to the flow of energy between people who are practicing the Tensegrity exercises together, according to Nyei Murez, one of the current teachers of Tensegrity. She is from Atlanta, home of the Georgia Dome. Carlos Castaneda (previously Castañeda) was born in Peru on December 25, 1925 and died in Los Angeles on April 27, 1998. ... A Hupa man, 1923 The scope of this indigenous peoples of the Americas article encompasses the definitions of indigenous peoples and the Americas as established in their respective articles. ... A shaman doctor of Kyzyl. ... Spanish colonization of the Americas began with the arrival in the Americas of Christopher Columbus in 1492. ...

See also

• Tensile architecture

Tensile architecture is a relatively new field of architecture devoted to lightweight membrane structures. ...

External links

Kenneth Snelson's site with an excellent article on the theory and development of tensegrity as well as pictures of his sculptures from desk top pieces to 90 foot towers.

Tensegrity in a Cell -- This interactive feature allows you to control a cell's internal structural elements. From the reseach department of Children's Hospital Boston.