Definitions of Tensegrity
Read here a collection of definitions of tensegrity.
Sources
A comprehensive, definitive page on definitions is hosted by Burkhardt. See "Definition and Classification of Tensegrities"; some excerpts below. The article is modeled after Gerald Scarr's page of definitions (http://www.tensegrityinbiology.co.uk/definitions.html). Definitions are added as they are discovered.
Definitions of Tensegrity in English
“All structures, properly understood, from the solar system to the atom, are tensegrity structures. Universe is omnitensional integrity.” [3] -- by Buckminster Fuller
“Tensegrity describes a structural-relationship principle in which structural shape is guaranteed by the finitely closed, comprehensively continuous, tensional behaviors of the system and not by the discontinuous and exclusively local compressional member behaviours.” [4] -- by Buckminster Fuller
"An assemblage of tension and compression components arranged in a discontinuous compression system." -- by Buckminster Fuller
"To Fuller, tensegrity is nature's grand structural strategy. At the cosmic level, he saw that the spherical astro-islands of compression of the solar system are continuously controlled in their progressive repositioning in respect to one another by comprehensive tension of the system which Newton called 'gravity'. At the atomic level, man's probing within the atom disclosed the same bind of dicontinuous compression, continuous tension apparently governing the atom's structure." -- by Shoji Sadao
“Tensegrity describes a closed structural system composed of a set of three or more elongate compression struts within a network of tension tendons, the combined parts mutually supportive in such a way that the struts do not touch one another, but press outwardly against nodal points in the tension network to form a firm, triangulated, prestressed, tension and compression unit.” -- by Kenneth Snelson
"[Tensegrity]] is a structure that joins nodes (points) with inextendibile cables and incompressible struts. The cable can be made from string, wire, or rope, and struts can be made from tubes, dowel rods, or just sticks." -- by Robert Connelly
"[Tensegrity]] is a finite configuration of points, the nodes, in space or the plane where some pairs of the nodes are designated cables, constrained not to get further apart, and some pairs are designated struts, constrained not to get closer together. Note with this definition cables and struts are allowed to intersect and cross." -- by Robert Connelly
"A tensegrity is a pattern integrity which has purely-tensile portions which are essential to its integrity. 'Pattern integrity' is a description of a system whose instances maintain a stable pattern in space and time in a variety of situations. '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. -- by Robert Burkhardt.
“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.” -- by Anthony Pugh
"Internally prestressed, free-standing pin-joined networks, in which the cables or tendons are tensioned against a system of bars or struts." -- by Ariel Hanaor.
"Tensegrity systems are spatial reticulate systems in a state of selfstress. All their elements have a straight middle fibre and are of equivalent size. Tensioned elements have no rigidity in compression and constitute a continuous set. Compressed elements constitute a discontinuous set. Each node receives one and only one compressed element.... Extended definition: Tensegrity system is a system in a stable self-equilibrated state comprising a discontinuous set of compressed components inside a continuum of tensioned components.” -- by René Motro
"A tensegrity system is a system in a stable self-equilibrated state comprising a discontinuous set of compressed components inside a continuum of tensioned components." -- by René Motro
“Tensegrity is a structural principle based on the use of isolated components in compression inside a net of continuous tension, in such a way that the compressed members (usually bars or struts) do not touch each other and the prestressed tensioned members (usually cables or tendons) delineate the system spatially.” -- by Valentín Gomez-Jauregui.
“A tensegrity structure is a three-dimensional truss with numerous tension members and a smaller number of disjoint compression members, achieving a prestressed state at some funicular geometry.” by Oppenheim “A class k tensegrity structure is a stable equilibrium of axially loaded elements, with a maximum of k compressive members connected at the nodes.” -- by Robert Skelton
"In the absence of externalforces, let a set of rigid bodies in a specific configuration have torqueless connections. Then, this configuration forms a tensegrity configuration if the given configuration can be stabilized by some set of internal tensile members. A tensegrity system is composed of any given set of strings connected to a tensegrity configuration of rigid bodies." -- by Robert Skelton.
"A tensegrity system is a stable connection of axially-loaded members, being a Class k tensegrity structure if at most “k” compressive members are connected to any node. E.g., a traditional tensegrity structure is a class 1 structure because only one compression member makes a node -- by Robert Skelton, W.J. Helton and R. Adhikari [2]
"A tensegrity structure is any structure realised from cables and struts, to which a state of prestress is imposed that imparts tension to all cables." -- by Jan Marcus
"Compression is nature's way to keep everything from happening at the same place. Tension is nature's way to keep everything happening closely enough." -- by Phil Earnhardt
"A structure in which complex properties, patterns and behaviours arise through multicomponent mechanical interactions resulting in the object maintaining structural integrity, under continuous tension and discontinuous compression, is said to manifest a tensegrity (tensional integrity) state." -- by John Maina
“Tensegrity is a structural system based on geodesic geometry; where the forces of attraction (tension) and repulsion (compression) operate separately within distinct components, creating an isometrically tensioned structure that can be integrated into a hierarchy.” -- by Graham Scarr
"Systems in stable self-equilibrated state comprising a discontinuous set of compressed components inside a continuum of tensioned components." -- by Rhode-Barbarigos
"[Tensegrity]] is composed of compression and tension elements. The struts (compression elements) are discontinuous while the cables (tension elements) are continuous. The structure is rigidified by self-stressing. The structure is self-supporting." -- by Wang Bin-Bing
“A tensegrity structure is any structure realised from cables and struts, to which a state of prestress is imposed that imparts tension to all cables... as well as imparting tension to all cables, the state of prestress serves the purpose of stabilising the structure, thus providing first-order stiffness to its infinitesimal mechanisms.” -- by Miura Koryo and Sergio Pellegrino
"Tensegrity in the Tensegrity Wiki is not so much defined as discovered. These guidelines can be described. (1) structures are considered as tensegrities when they allocate highly significant functionality to tension-only components in a way unlike suspension bridges and guy-cabled tents; a primary differentiator is the direction of the deployed tension network--tension structures deploy linearly while tensegrity deploys tension globally (omnidirectionally) and not only linearly. This isolation of tension and its omnidirectional deployment applies to dynamic control systems, foldable models and robotics as well. (2) concepts and ideas that use the word tensegrity or of interest to the wiki when they truly resonate with tensegrity's unusual structural behavior, being radically different from classic lever/fulcrum, scale balance, etc, even though many of these usages grapple with subjects normally left out of classic, rational scientific discourse, such as meaning and truth." -- by TensegrityWiki
Compare and Contrast
Burkhardt posted this table on his "Definition and Classification of Tensegrities".
Tensegrity Examples
A list of structures that Burkhardt argues *are* tensegrities.
| 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
A list of structures that Burkhardt argues are *not* tensegrities.
| 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. |
Definitions of Tensegrity in Languages Other Than English
References
[1] Quoted by Jáuregui in his thesis, section 4, Definitions and principles
[2] "Mechanics of Tensegrity Beams", by Skelton, W.J. Helton and R. Adhikari UCSD, Structural Systems & Contr. Lab., Rep. No. 1998-1
[3] Synergetics paragraph 700.04 by Buckminster Fuller
[4] Synergetics paragraph 700.011 by Buckminster Fuller