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Definition and Classification of Tensegrities

by Bob Burkhardt
Last revision: October 20, 2011

Preface

In my book, I reference three different ways of defining the word tensegrity. Each of these definitions recommended itself to me for one reason or another, but I found none completely satisfactory. This being the case, I've decided to formulate my own definition, and my latest effort appears below. The definitions referenced in my book are listed below in the References.

Definition

A tensegrity is a pattern integrity which has purely-tensile portions which are essential to its integrity.

Subsidiary Terminology

A "pattern integrity" is a description of a system whose instances maintain a stable pattern in space and time in a variety of situations (see Synergetics, Section 505.01). "purely-tensile portions" means portions which are at least sometimes in tension and are not required to sustain non-tensile loads. "essential to its integrity" means that in general the instances of a pattern integrity are not able to maintain their stable patterns without the presence of certain purely-tensile portions.

Discussion of the Definition

I'm trying to be very broad here and include any pattern integrity whose instances can take advantage of the tensegrity advantage. The tensegrity advantage is the potential use of light-weight tensile materials in the purely-tensile portions of the pattern integrity. Typically these tensile materials are much less material-intensive than the materials that are used to fabricate the portions of an instance that are in compression or exhibit other complex stresses. Beyond this, I also want to include pattern integrities whose instances might use gravity, electrostatic forces or other force-at-a-distance phenomena as the purely-tensile portion.

At the same time as being broadly inclusive, I also want to exclude pattern integrities for which the tensile portions are not purely tensile (meaning they could be in compression depending on the instance), are present only as an inessential side effect or used only to reinforce an instance whose essence does not depend on their presence (though perhaps engineering wisdom may dictate their use). I also want to exclude structures where the purely-tensile component which coheres the structure is not part of what is generally understood to be the structural system.

It is worth emphasizing that in speaking of a purely-tensile component I am talking about the effects it has on other components rather than its internal stresses and strains. A purely-tensile component is either pulling other components together or having no effect at all. It never pushes other components apart. Internally to achieve any effects, the component will exhibit compressive and tensile forces, but how these are distributed within the component and their magnitudes are irrelevant to the definition; only the effect the component has on other components matters.

Finally, I deal in terms of pattern integrities rather than instances since a particular instance generally has peculiarities which are not typical of the pattern as a whole and should not be used to categorize it. It should also be noted that this definition is just a way of categorizing pattern integrities and not a measure of structural superiority in any sense. The question of what pattern integrity to apply in a particular situation is more of an engineering question and depends on a host of other issues.

I've debated back and forth about including prestress in this definition, and now it does not include prestress as I do not think this is essential to tensegrity phenomena. Many tensegrities will retain their structural integrity (albeit in a somewhat loose way, like the sand bag example below) when prestress is removed. In some applications, like say a balloon-shaped lunar rover, a lack of prestress may actually be a feature that is useful, for example for gaining traction. Prestress also does not seem very useful for classifying tensegrities, though prestress is certainly highly useful in most tensegrity applications. Perhaps the potential for being prestressed is a definitive quality of tensegrity structures.

One thoughtful criticism I received from Tim Tyler is that a non-tensegrity space frame might be held together by purely tensile rivets at its joints. Perhaps the answer there is that another fastening system, like dove-tailing or welding, could be imagined for the pattern where the fasteners were not purely tensile. Once the members being joined come in contact, things like rivets and hinges and u-joints pass into the realm of hub joinery and can be neglected when considering the pattern in an abstract way. Certainly, this criticism touches what I see as one of the boundaries of tensegrity, since some tensegrity patterns can be arranged in a sequence such that the limit of the pattern is not a tensegrity. This is the case with deresonated structures which are mentioned below, where a deresonated structure can be looked upon as a limiting pattern of a type of tensegrity based on geodesic subdivisions of the sphere.

Classification of Tensegrities

The presence of various additional properties can be used to classify tensegrities. Such distinguishing properties include:

Some researchers have made some of these items requirements for being a tensegrity. To me the non-fulfillment of any of these requirements is not a reason for excluding a pattern integrity from the tensegrity category, but only a way of differentiating it from other tensegrities. The first item in the list, "continuous tension", seems to be present in just about every tensegrity, and for several years I had seen discontinuous tension only in a couple designs I had developed which incorporated my tensegrity-prism-as-joint technology. Later Kenneth Snelson shared with me the experimental "Sprawl Piece" he had developed in 1974. But still I would say discontinuous tension is very uncommon. For the rest of the categories, examples and complementary examples exist abundantly.

 
Tensegrity Examples
 
bow As in bow and arrow (or bow and violin). Structurally its instances are not very efficient since a portion bends. The tension in the bow and the string (or horsehair) is continuous and makes a loop.
prestressed concrete This is concrete that has internal reinforcements that are always in tension. The reinforcements preserve the concrete from crumbling under tensile loads which are its weakness and allow it to contribute its compression resistance which is its strength.
kite Kites of the standard diamond shape which are bowed using a string in back, or with the bow string omitted. This structure is listed in Val's book as one of the three primitive sorts of structures (cometa along with rueda de radios -- spoked wheel -- and estructuras pneumáticas -- pneumatic structures) which people use as analogies when coming to grips with tensegrity (see pp. 75-77).
bicycle wheel The spokes are the purely-tensile portions. The rim seems like it must be purely compressive, like an arch in the round. The hub must undergo complex stresses. This is not as general a category as spoked wheels in general since cart wheels I would exclude.
floating compression
This is a term Kenneth Snelson has used to label many of the structures he has built. The compression and tension portions are all linear and typically connected end to end. None of the compression members touch each other. Typically the member forces are purely axial; however, it is possible to build structures like this that have tendons connected to the middle of a strut, and for these there may be some bending component in the member force in that strut so the member force would not be axial. Snelson prefers the purely axial approach for his structures.
Skylon This is a non-self-sufficient tensegrity. It is anchorage dependent.
circus tent This is a non-self-sufficient tensegrity. It is anchorage dependent. Here we're imagining poles which are not rigidly attached to the ground which are held in place by tent fabric and ropes which are staked into the ground. Without the purely-tensile components, the whole thing would fall over. Camp Elsewhere's Tensegrity Shade Structures fall in this category. Other tent strategies would need to be examined on a case-by-case basis.
spider web This is a non-self-sufficient tensegrity. It is anchorage dependent.
suspension bridge This is a non-self-sufficient tensegrity. It is anchorage dependent. When it is supported by pylons which are rigidly connected to the ground, the pylons should be considered part of the anchorage, and the bridge should be considered a composite structure, only the non-pylon part of which is a tensegrity. If the proper function of the bridge depends on the gravity field coming from one way rather than another, as seems likely given the adjective "suspension", perhaps I should be cautious here since the bridge would be force-field dependent, as in the not-a-tensegrity Roman arch below. But some local fastenings working with gravity, as might be desirable for wind and earthquake resistance, would firmly restore its tensegrity-hood; and a suspension bridge would not completely vulnerable to disintegration in the absence of gravity, as opposed to the case of the Roman arch below which would be.
balloon The balloon's skin is the purely-tensile portion.
sand bag The sand bag's skin is the purely-tensile portion. Sand does not distribute pressure as evenly as air, and many instances are not prestressed, but overall it seems to fit the balloon model.
ball of yarn The ball of yarn needs to be tightly wound to keep it from unraveling. The winding puts tension on the yarn and the resulting compressive reaction presses the threads together and keeps them from unraveling.
human body The muscles, tendons and ligaments are the purely tensile components which bind together the bones and cartilage. These statements could probably use the attention of someone better versed in anatomy. Plants, fungi, single-cell creatures and other animals should be considered for inclusion in the tensegrity category on a case-by-case basis.
living cells Using floating-compression models as his primary analogy, Donald Ingber has made a good case for many cells of living tissue fitting the tensegrity model.
solar system Gravity coheres the components while rotational momentum keeps them apart.
atoms Electrostatic forces cohere the components while rotational momentum (or something like that?) keeps them apart. I must be thinking of something like the Bohr model of the atom.
Earth Without the presence of gravity, I imagine the spinning of Earth on its axis would cause it to disintegrate, likewise for most of the other large members of the solar system.
 
Not-a-Tensegrity Examples
 
Roman arch The purely-tensile phenomenon of gravity is essential to its coherence, but is really not part of the system under consideration. In a zero-gravity environment, the components of the arch would float apart. The Earth-Roman-arch structural system could be considered a tensegrity. Here the purely-tensile component would now be internal to the system. Egyptian pyramids and New England stone walls could be analyzed similarly. Other bridge-like designs besides the Roman arch should be considered on a case-by-case basis for inclusion in the tensegrity category.
geodesic
domes and spheres
These are typically not tensegrities. There are no purely-tensile components. The member forces present in an instance of a geodesic dome or sphere depend on environmental conditions. A component which is in compression when gravity or the wind comes from one direction may be in tension when gravity or the wind come from another direction. An instance of a geodesic dome or sphere in an environment with no gravity or acceleration forces impinging on it will maintain its pattern without any of the members being in tension. There are some atypical geodesics that fit, or come close to fitting, the tensegrity category. The seedpod foldable geodesics seem to fit the category, and the design for the American Society of Metals structure in Cleveland, Ohio, must come close to fitting the category if it does not strictly fit in. A single-layer hexdome where the compression hexagons are stabilized by internal stars of tensile cables is a tensegrity that looks much like a geodesic.
deresonated
domes and spheres
Although these pattern integrities are based on patterns used for geodesic types of floating-compression structures, the apparently purely-tensile stress in an instance can be relieved by permanently bending the struts appropriately and is not essential to the pattern integrity. Indeed the purely-tensile and purely-compressive portions can exchange places by permanently bending the struts more than is necessary. Rotegrities can be analyzed similarly. This is not to say the tension generated by forcing slightly out-of-kilter components to fit does not play a valuable reinforcement role in instances of these pattern integrities. These statements are working hypotheses based on experiences with geodesic sub-networks. I have not worked directly with deresonated or rotegrity models.
Empire State Building Its system of girders give it great strength, but there are no purely-tensile portions which are essential to its structural integrity.
compressed
gas cylinder
When full, the cylinder's shell must be tensile, but when it is empty it functions rather like a geodesic sphere. Though its tensile components are valuable reinforcement for the extreme environmental situations the cylinder must operate in, they are not essential to its basic structural integrity.

Language

Val Gómez Jáuregui thinks "tensegrity" as an adjective and as a noun needs separate words in Spanish. "Tensegridad" is already established as the noun, and he invented "tensegrítico" for the adjective. He also capitalizes "tensegridad" when he wishes to refer to the principle of tensegrity and leaves it lower case to refer to instances of the application of the principle. For more information, see Val's book on tensegrity in Spanish (cited in References below).

In English, Rene K. Mueller (in an email to the Geodesic listserv on July 7, 2007) says, "I wondered, is there an adjective for Tensegrity? Tension: tensile, Integrity: integral = tensigral?" And Val's procedure in Spanish as to capitalizing tensegrity when referring to the principle could be applied in English as well -- who knows, maybe I'm already supposed to be doing this. Phil Earnhardt (in an email to the Geodesic listserv on November 10, 2004) has suggested "tensegrous" has an adjective describing the relationship between systems.

References

Fuller, R. Buckminster, Synergetics: Explorations in the Geometry of Thinking, New York: MacMillan Publishing Co., Inc., 1975.

Gómez Jáuregui, Valentín, Tensegrity Structures and their Application to Architecture, Master's thesis, Belfast, Northern Ireland: Queen's University, School of Architecture, 2004. Much of this has been incorporated into Val's book (in Spanish): Tensegridad: Estructuras Tensegríticas en Ciencia y Arte, Santander, Spain: Servicio de Publicaciones de la Universidad de Cantabria, 2007.

Kanchanasaratool, Narongsak and Darrell Williamson, "Modelling and control of class NSP tensegrity structures", International Journal of Control, Vol. 75, No. 2 (January 20, 2002), pp. 123-139: "A tensegrity system is a stable connection of axially-loaded members. A Class k tensegrity structure is one in which at most k compressive members are connected to any node." ("Connection" does not seem like quite the right word here and could be a typographical error. Substituting "continuously-connected collection" yields a better description I think.)

Pugh, Anthony, An Introduction to Tensegrity, Berkeley, California: University of California Press, 1976, p. 3: "A tensegrity system is established when a set of discontinuous compressive components interacts with a set of continuous tensile components to define a stable volume in space."

Wang, Bin-Bing, "Cable-strut systems: Part I - Tensegrity," Journal of Constructional Steel Research, Vol. 45 (1998), No. 3, pp. 281-289 identifies the following characteristics of a tensegrity structure:

  1. It is composed of compression and tension elements.
  2. The struts (compression elements) are discontinuous while the cables (tension elements) are continuous.
  3. The structure is rigidified by self-stressing.
  4. The structure is self-supporting.

Acknowledgements

I would like to thank Phil Earnhardt, Dick Fischbeck, Spencer Hunter, Tim Tyler and other participants in discussions on the Geodesic listserv and the bit.listserv.geodesic newsgroup for criticisms and remarks on this definition and the accompanying examples which have helped me to formulate them. The comprehensive and thoughtful outlook of Val Gómez Jáuregui's master's thesis in architecture and, more recently, his book in Spanish based on that thesis (see References above), made reading through them very useful as well. No endorsement of the definition and my conclusions on their part is implied.

Contact Information

I am interested in your comments and questions. If you are not hooked up to the above-referenced Geodesic discussion groups, please direct your comments and questions via email to bobwb@juno.com or via Postal Service mail to me at Box 426164, Cambridge, MA 02142-0021.

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