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Controversial Origins of Tensegrity

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p. 1642-1652 Tensegrity is a developing and relatively new system (barely more than 50 years old) which creates amazing, lightweight and adaptable figures, giving the impression of a cluster of struts floating in the air. The intention of this paper is to explain the origins of tensegrity, original patents included, and shed light on some polemic aspects about the authorship, enquiring personally to its discoverer, the sculptor Kenneth Snelson. Finally, the history and progress of this kind of structure will be revised, tracing a line of the time and pointing out the most relevant authors, specialists and publications, which could serve as a guide for further investigators.
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Proceedings of the International Association for Shell and Spatial Structures (IASS) Symposium 2009, Valencia
Evolution and Trends in Design, Analysis and Construction of Shell and Spatial Structures
28 September – 2 October 2009, Universidad Politecnica de Valencia, Spain
Alberto DOMINGO and Carlos LAZARO (eds.)
Controversial Origins of Tensegrity
Valentín GÓMEZ JÁUREGUI*
*www.tensegridad.es
Urb. Los Robles, 39706, Santullán, Cantabria, SPAIN
tensegridad.es@gmail.com
Abstract
Tensegrity is a developing and relatively new system (barely more than 50 years old) which
creates amazing, lightweight and adaptable figures, giving the impression of a cluster of
struts floating in the air. The intention of this paper is to explain the origins of tensegrity,
original patents included, and shed light on some polemic aspects about the authorship,
enquiring personally to its discoverer, the sculptor Kenneth Snelson. Finally, the history
and progress of this kind of structure will be revised, tracing a line of the time and pointing
out the most relevant authors, specialists and publications, which could serve as a guide for
further investigators.
Keywords: Tensegrity, structures, origins, history, tension, floating compression, Kenneth
Snelson, Buckminster Fuller, David Emmerich, patents.
1. Introduction
Tensegrity is a developing and relatively new system (barely more than 50 years old) which
creates amazing, lightweight and adaptable figures, giving the impression of a cluster of
struts floating in the air. As it is explained in Gómez Jáuregui [1], it is not a commonly
known type of structure, so knowledge of its mechanism and physical principles is not very
widespread among architects and engineers. However, one of the most curious and peculiar
aspects of tensegrity is its origin; controversy and polemic will always be present when
arguing about its discovery.
The intention of this paper is to explain the origins of tensegrity, original patents included,
and shed light on some polemic aspects about the authorship, enquiring personally to its
discoverer, the sculptor Kenneth Snelson.
Finally, the history and progress of this kind of structure will be revised, tracing a line of
the time and pointing out the most relevant authors, specialists and publications, which
could serve as a guide for further investigators.
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Evolution and Trends in Design, Analysis and Construction of Shell and Spatial Structures
2. The origins.
Three men have been considered the inventors of tensegrity: Richard Buckminster Fuller
[2], David Georges Emmerich [3] and Kenneth D. Snelson [4]. (As a precaution, these
names have been mentioned in chronological order of their granted patents: Fuller-13 Nov
1962; Emmerich-28 Sep 1964; Snelson-16 Feb 1965).
Although all of the three have claimed to be the first inventor, R. Motro [5] mentions that
Emmerich [6] reported that the first proto-tensegrity system, called
"Gleichgewichtkonstruktion", was created by a certain Karl Ioganson (some authors call
him Johansen) in 1920 (figure 1.a). As Emmerich explains:
"Cette curieuse structure, assemblée de trois barres et de sept tirants, était manipulable à
l'aide d'un huitième tirant detendu, l'ensemble étant déformable. Cette configuration labile
est très proche de la protoforme autotendante à trois barres et neuf tirants de notre
invention."
Figure 1: Comparison between the "Gleichgewichtkonstruktion" or “Structure-Sculpture”
by Karl Ioganson, first proto-tensegrity system (1.a), and the Simplex by Snelson, simplest
tensegrity system (1.b).
This means it was a structure consisting of three bars, seven cords and an eighth cable
without tension serving to change the configuration of the system, but maintaining its
equilibrium. He adds that this configuration was very similar to the proto-system invented
by him, the "Elementary Equilibrium", with three struts and nine cables (figure 1.b). All the
same, the absence of pre-stress, which is one of the characteristics of tensegrity systems,
does not allow Ioganson's “sculpture-structure” to be considered the first of this kind of
structures.
The most controversial point has been the personal dispute, lasting more than thirty years,
between R. B. Fuller (Massachusetts, 1895-1983) and K. D. Snelson (Oregon, 1927). As
the latter explains in a letter to R. Motro, during the summer of 1948, Fuller was a new
professor in the Black Mountain College (North Carolina, USA), in addition to being a
charismatic and a nonconforming architect, engineer, mathematician, cosmologist, poet and
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Evolution and Trends in Design, Analysis and Construction of Shell and Spatial Structures
inventor (registering 25 patents during his life). Snelson was an art student who attended
his lectures on geometric models, and after that summer, influenced by what he had learnt
from Fuller and other professors, he started to study some three-dimensional models,
creating different sculptures (figure 2).
Figure 2: "X-column" by Snelson, his first tensegrity art piece. Illustration donated by the
artist.
As the artist explains, he achieved a new kind of sculpture, which can be considered the
first tensegrity structure ever designed. When he showed it to Fuller, asking for his opinion,
the professor realized that it was the answer to a question that he had been looking for, for
so many years. In Fuller’s [7] words:
“For twenty-one years, before meeting Kenneth Snelson, I had been ransacking the
Tensegrity concepts. (…) Despite my discovery, naming and development of both the multi-
dimensional vectorial geometry and the three dimensional Tensegrity, I had been unable to
integrate them, thus to discover multi-dimensional four, five and six axes symmetrical
Tensegrity.”
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Evolution and Trends in Design, Analysis and Construction of Shell and Spatial Structures
Figure 3: Comparison of three details of the three patents: Fuller-13 Nov 1962; Emmerich-
28 Sep 1964; Snelson-16 Feb 1965
In contrast to other authors, and serving as an illustration of how important it was
considered, he always wrote “Tensegrity” starting with a capital T.
At the same time, but independently, David Georges Emmerich (Debrecen-Hungary, 1925-
1996), probably inspired by Ioganson's structure, started to study different kinds of
structures as tensile prisms and more complex tensegrity systems, which he called
"structures tendues et autotendants", tensile and self-stressed structures (figure 3). As a
result, he defined and patented his "reseaux autotendants", which were exactly the same
kind of structures that were being studied by Fuller and Snelson.
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Proceedings of the International Association for Shell and Spatial Structures (IASS) Symposium 2009, Valencia
Evolution and Trends in Design, Analysis and Construction of Shell and Spatial Structures
3. The controversy
Even though at the beginning Fuller mentioned Snelson as the author of the discovery, after
some time he started to consider it as “my Tensegrity”. Actually, he coined this term in
1955 as a contraction of “Tensional-Integrity”, so by calling these structures with the
denomination he chose, he let people think that it was his invention. “Creating this strange
name was his strategy for appropriating the idea as his own”, quotes Snelson in various
publications (Coplans [8] and Schneider [9]).
Obviously, his art student was certainly confused; at the end of 1949 Fuller wrote to
Snelson saying that his name would be noted in history, but some years later he changed his
mind, asking his student to remain anonymous for some time. This situation pushed
Snelson to insist on acknowledgement during an exposition of Fuller’s work in 1959, at the
Museum of Modern Art (MOMA) in New York. Therefore his contribution to tensegrity
was credit and recognized publicly.
A couple of years later, Fuller [7] referred to Snelson again:
“(…) an extraordinary intuitive assist at an important moment in my exploration of the thus
discovered discontinuous-compression, continuous-tension structures was given me by a
colleague, Kenneth Snelson, and must be officially mentioned in my formal recital of my
"Tensegrity" discovering thoughts.”
Figure 4: Kenneth Snelson working in his studio in 1961. Illustration donated by the artist.
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Evolution and Trends in Design, Analysis and Construction of Shell and Spatial Structures
However, he always thought that if he had not catalyzed Snelson’s discovery, Tensegrity
would have never been invented as a new structure. In fact, he never mentioned Snelson in
one of his most important and renowned books about tensegrity, “Synergetics” (Fuller [10])
and failed to do so again in his correspondence with Burkhardt [11].
The accuracy in reporting (expression suggested by Snelson instead of battle of egos) by
both men continued furthermore, when in 1980 Fuller wrote a 28-page letter to Snelson, in
answer to a Snelson’s one-page letter. According to Vesna [12], in those letters they tried to
clarify the authorship of the discovery, and not the inventor, because Fuller affirmed that
inventors can’t invent the eternal principles-cosmic laws of the universe. Paradoxically, he
had patented those universal laws in 1962.
Who invented tensegrity? It is evident that the answer is not evident. In the author’s
opinion, the synergy (a word so often used by Fuller) created by both the student and
professor, resulted in the origin of tensegrity. As quoted by Stephen Kurtz’s [13]:
“If Fuller acknowledges his debt to Snelson for the invention of the tensegrity principle,
Snelson likewise acknowledges his own debt to Fuller's visionary work”.
Although acknowledgement is very important for the two of them, especially for Snelson
(the only one still alive), perhaps it would be better to pay more attention to the possibilities
of these structures than to the past controversy.
4. The evolution.
After the brief moment of acknowledgment in the MOMA, Snelson was once again keen to
continue working with tensegrity as an essential part of his sculptures, which he has been
creating until the present day. Even though he commenced studying the fundamental
concepts of tensegrity, gathered and summarised in his web page [14], he focused his work
on the sculptural and aesthetic aspect. He avoided very deep physical and mathematical
approaches, due to his artistic background and his opinion in relation to the difficult
application of tensegrity systems. This process provided him the facility to develop very
different configurations, asymmetrical and non conventional, applying his intuitive
knowledge and achieving impressive sculptures that are spread all over the world.
Moreover, the construction of tensegrity systems requires a fine and delicate technique that
he has been improving over the years. The actual process whereby Snelson erects his works
is a science and an art in itself; actually, as it is stated by Fox [15], he is the only person
capable of engineering his constructions.
On the other hand, Fuller and Emmerich took a different approach, studying the different
possible typologies of tensegrity, mainly spherical and one-dimensional systems: masts.
They did it using models and empiric experiments as their main tools, and in contrast to
Snelson, they looked for possible applications to architecture and engineering.
Just after viewing Snelson’s sculpture, the inventor from Massachusetts studied some
simple compositions, and produced a family of four Tensegrity masts characterised by
vertical side-faces of three, four, five and six each, respectively (Fuller [7]). He also
discovered the “six-islanded-strut icosahedron Tensegrity” (expanded octahedron).
Subsequently, this work was developed by other people, creating such Tensegrity systems
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as the “vector equilibrium” (cubo-octahedron), the “thirty-islanded Tensegrity sphere”
(icosahedron), the “six-islanded Tensegrity tetrahedron” (truncated tetrahedron) and the
“three-islanded octa-Tensegrity” (all quotation marks are Fuller’s denominations).
Consequently, a hierarchy of premier Tensegrity structures was created and the
comprehensive laws of universal tensegrity structuring were completed.
Thus, Bucky (as Buckminster Fuller was also known), kept on looking for new designs,
applications and methods of construction. He made several attempts to design geodesic
tensegrity domes (figure 5) (although they lacked of stability due to the absence of
triangulation), and patented some of his works connected to this subject (Fuller [16] and
[17]). However, the final application of Tensegrity was not as successful as he thought it
would be; he was never able to produce the Tensegrity dome which could cover a whole
city, as he intended; and, in addition, he was forced to build the Montreal bubble at Expo
’67 as a geodesic dome but without using Tensegrity principles due to time and budget
reasons.
Figure 5: “Geodesic Tensegrity Dome” by Fuller in 1953. Illustration taken from
Gengnagel.
Henceforth, some people who were influenced by Fuller’s work, started to explore this new
structural system, looking for any application to architecture and engineering. For instance,
J. Stanley Black [18] wrote an unpublished study which tried to recall the main concepts
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Evolution and Trends in Design, Analysis and Construction of Shell and Spatial Structures
known at that time and to figure out some possible systems and configurations. Although it
was a good attempt, the basis of tensegrity were not very clear at that moment, and his final
design was not a reflection of a true tensegrity system, but something more similar to Levy
and Geiger’s works (Geiger [19], Goosen et al. [20] and Setzer [21]). After some first
attempts of tent-shaped structures by Frei Otto during the 60s, tensile structures became
more popular in the 1970s, e.g. the Olympic Stadium of Munich by Fritz Leonhardt, Frei
Otto and Jörg Schlaich in 1972.
René Motro, probably one of the most important specialists in tensegrity at present, started
to publish his studies on the subject in 1973: “Topologie des structures discrètes. Incidence
sur leur comportement mécanique. Autotendant icosaédrique”. It was an internal note for
the Laboratory of Civil Engineering of the University of Montpelier (France) about the
mechanical behaviour of this kind of structure. From this time forth, this laboratory and
engineer became a reference in terms of tensegrity research.
Some years later, in 1976, Anthony Pugh [22] and Hugh Kenner [23], both from the
University of California (Berkeley), continued this work with different lines of attack. On
the one hand, Pugh wrote the “Introduction to Tensegrity”, which is interesting for the
variety of models that it outlines and his strict classification and typology. On the other
hand, Kenner developed the useful “Geodesic Math and How to Use It”, which shows how
to calculate “to any degree of accuracy” the pertinent details of geodesic and tensegrity
regular structure’s geometry (lengths and angles of the framing system), and explores their
potentials. Even though the latter work is more explicit in geometric and mathematic
subjects, it also lacks the treatment of behaviour of tensegrity under load. Nevertheless,
both of the authors realized that, apart from some of Fuller’s writings, little reliable
information had been published on the subject. It is important to note that there is
conflicting information in both books: Kenner affirms that Snelson’s work was “unknown
to Tony” (pg. xi), while Anthony Pugh refers to Snelson in several paragraphs of his book
(pgs. ix, 3,…).
During the 1980s, some authors made an effort to develop the field opened by their
predecessors. Robert Burkhardt started an in-depth investigation and maintained a
correspondence with Fuller [23] in order to obtain more details about the geometry and
mathematics of tensegrity. The final result, 20 years later, is a very complete, useful and
continuously revised Practical Guide to Tensegrity Design (Burkhardt [11]). Other
important investigators have been Ariel Hanaor [25], who defined the main bi-dimensional
assemblies of elementary self-equilibrated cells and Nestorovic [26] with his proposal of a
metallic integrally tensioned cupola.
Recently, several works have been adding to the body of knowledge. Since it is not always
possible to read all the publications that are appearing in relation to a specific field, only the
most relevant will be pointed out in the next paragraphs.
Connelly and Back ([27] and [28]) have aimed to find a proper three-dimensional
generalization for tensegrities. Using the mathematical tools of group theory and
representation theory and the capabilities of computers, they have drawn up a complete
catalogue of tensegrities with detailed prescribed types of stability and symmetry, including
some that have never been seen before.
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Evolution and Trends in Design, Analysis and Construction of Shell and Spatial Structures
Other authors (S. Pellegrino, A.G. Tibert, A.M. Watt, W.O. Williams, D. Williamson, R.E.
Skelton, Y. Kono, Passera, M. Pedretti, etc.) have also studied the physics, mathematics
(from geometrical, topological and algebraical points of view) and mechanics of tensegrity
structures. However, apart from the authors mentioned above, and Motro and his group in
Montpellier, there have not been many works seeking to apply this new knowledge to any
field in particular. The most recent works will be referred to again in other papers.
Acknowledgement
I received invaluable help from Kenneth Snelson, the discoverer of the tensegrity
structures. He personally answered some of my questions and doubts about the origins of
floating compression, replying to all of my endless e-mails and checking some of the
chapters concerning his experience. I feel really thankful to him.
References
[1] Gómez Jáuregui V. Tensegridad. Estructuras Tensegríticas en Ciencia y Arte.
Servicio de Publicaciones de la Universidad de Cantabria, Santander, 2007.
[2] Fuller, R.B. Tensile-Integrity Structures, U.S. Patent No. 3,063,521, November 13,
1962.
[3] Emmerich, D.G. Construction de réseaux autotendants, French Patent No. 1,377,290,
September 28, 1964
[4] Snelson, K. Continuous tension, discontinuous compression structures, U.S. Patent
No. 3,169,611, February 16, 1965.
[5] MOTRO, R. (2003) Tensegrity: Structural Systems for the Future, London: Kogan
Page Science.
[6] EMMERICH, D. G. (1988) Structures Tendues et Autotendantes, Paris: Ecole
d'Architecture de Paris la Villette.
[7] FULLER, R.B. (1961) “Tensegrity”, Portfolio and Art News Annual, No.4. pp.112-
127, 144, 148. Also available in
http://www.rwgrayprojects.com/rbfnotes/fpapers/tensegrity/tenseg01.html
[8] COPLANS, J. (1967) "An Interview with Kenneth Snelson", Artforum, March 1967.
pp.46-49.
[9] SCHNAIDER, A. (1977) “Interview with Kenneth Snelson”, Nationalgalerie Berlin
Exhibition Catalog. March-May 1977. Also available in
http://www.kennethsnelson.net/icons/art.htm
[10] FULLER, R.B. (1975b) Synergetics: Explorations in the Geometry of Thinking, New
York: MacMillan Publishing Co., Inc. Also available in
http://www.rwgrayprojects.com/synergetics/synergetics.html
[11] BURKHARDT, R.W. (1994-2004) A practical guide to tensegrity design, [on-line],
Cambridge (USA) http://www.channel1.com/users/bobwb/tenseg/book/cover.html
Accessed December 2003-August 2004.
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[12] VESNA, V. (2000) Networked Public Spaces: An Investigation into Virtual
Embodiment. Unpublished PhD thesis. University of Wales College, Newport. Also
available in http://vv.arts.ucla.edu/publications/thesis/official/tensegrity.htm
[13] KURTZ, S.A. (1968) “Kenneth Snelson: The Elegant Solution”. Art News. October,
1968. Also availabe in http://www.kennethsnelson.net/icons/art.htm
[14] Snelson, K. Kenneth Snelson, [on-line], New York (USA).
http://www.kennethsnelson.net/ Accessed December 2003- July 2004.
[15] FOX, H. N. (1981) “Portrait of an Atomist”, Catalog Essay for Kenneth Snelson
Exhibition at Hirshhorn Museum and Sculpture Garden, Smithsonian Institution,
Washington, D.C., June - August 1981. Also available in
http://www.kennethsnelson.net/icons/art.htm
[16] FULLER, R.B. (1967) Octahedronal building truss, U.S. Patent No. 3,354,591,
November 28, 1967.
[17] FULLER, R.B. (1975b) Synergetics: Explorations in the Geometry of Thinking, New
York: MacMillan Publishing Co., Inc. Also available in
http://www.rwgrayprojects.com/synergetics/synergetics.html
[18] BLACK, S.J. (1972) Cords and countercords. Proposal for a tensile building system.
Unpublished BArch dissertation. School of Architecture, Queen’s University Belfast.
[19] GEIGER, D.H. (1988) Roof structure, U.S. Patent No. 4,736,553, April 12, 1988.
[20] GOSSEN, P.A., CHEN, D., AND MIKHLIN, E. (1997) The First Rigidly Clad
"Tensegrity" Type Dome, The Crown Coliseum, Fayetteville, North Carolina, [on-
line], USA: Geiger Engineers.
[21] SETZER, S.W. (1992) Georgia Dome. Raise High the Record Roof, [on-line], New
York: Columbia University.
http://www.columbia.edu/cu/gsapp/BT/DOMES/GEORGIA/g-raise.html Accessed
June 2004.
[22] PUGH, A. (1976) An Introduction to Tensegrity, Berkeley, California: University of
California Press.
[23] KENNER, H. (1976) Geodesic Math and How to Use It, Berkeley, California:
University of California Press.
[24] FULLER, R.B. (1982) Correspondence with Robert Burkhardt, January 29 - March
18, 1982. Also available in http://www.bfi.org/burkhardt/section1.html
[25] HANAOR, A. (1987) “Preliminary Investigation of Double-Layer Tensegrities”, in
H.V. Topping, ed., Proceedings of International Conference on the Design and
Construction of Non-conventional Structures (Vol.2), Edinburgh, Scotland: Civil-
Comp Press.
[26] NESTOROVIC, M. (1987) “Metallic Integrally Tensioned (Tensegrity) Cupola”, in
H.V. Topping, ed., Proceedings of International Conference on the Design and
Construction of Non-conventional Structures (Vol.2), Edinburgh, Scotland: Civil-
Comp Press.
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[27] CONNELLY, R. and BACK, A. (1998a) “Mathematics and Tensegrity”, American
Scientist. Vol.86, No.2, March-April 1998.
[28] CONNELLY, R. and BACK, A. (1998b) Catalogue of Symmetric Tensegrities, [on-
line], Cornell University, Ithaca (USA).
http://mathlab.cit.cornell.edu/visualization/tenseg/in_progress/short_top.html
Accessed May-August 2004.
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... (Enciclopedia Treccani on-line-http://www.treccani.it/enciclopedia/tensegrita/) rivendicata nello stesso periodo, con rispettivi brevetti, da Richard Buckminster Fuller (1962), David Georges Emmerich (1964) e Kenneth Duane Snelson (1965). A questi si deve aggiungere, come antesignano, lo scultore avanguardista lettone Karl Ioganson , che nel 1920 creò una struttura-scultura (Gleichgewichtkonstruktion) che può essere considerata una anticipazione dei sistemi tensegrity sviluppati una quarantina d'anni dopo (Gómez Jáuregui, 2009). ...
... rivendicata nello stesso periodo, con rispettivi brevetti, da Richard Buckminster Fuller (1962), David Georges Emmerich (1964) e Kenneth Duane Snelson (1965). A questi si deve aggiungere, come antesignano, lo scultore avanguardista lettone Karl Ioganson , che nel 1920 creò una struttura-scultura (Gleichgewichtkonstruktion) che può essere considerata una anticipazione dei sistemi tensegrity sviluppati una quarantina d'anni dopo (Gómez Jáuregui, 2009). Forse la versione più probabile è che il concetto di tensegrity sia dovuto agli sforzi sinergici di Snelson (scultore) e Fuller (architetto, ingegnere, matematico, cosmologo, poeta e futurista). ...
... Fuller era noto per le sue idee non convenzionali ed è quindi probabile che il concetto di tensegrity sia nato proprio dai suoi studi architettonici strutturali che si ispiravano all'idea che, contrariamente alle costruzioni dell'uomo costituite da elementi solidi impilati l'uno sopra l'altro sottoposti soltanto a sforzi di compressione, il mondo naturale fosse pieno di strutture non convenzionali che mantengono la loro stabilità, o integrità, attraverso forze di tensione pervasive. Da qui il termine tensegrity, fusione delle parole tension e integrity, coniato da Fuller soltanto nel 1955 (Gómez Jáuregui, 2009) anche se -a detta di Fuller stesso -egli avrebbe cominciato a concepirlo fi n dal 1920 (Ingber e Landau 2012), probabilmente proprio ispirandosi alle sculture create da Ioganson. ...
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... The term tensegrity [1] is a crasis of the two words tensile and integrity [2]. Such systems have attracted the attention of the researchers in many different fields [3][4][5] due to their peculiar features and advantages. ...
Article
Tensegrity structures are an intriguing kind of structures by virtue of their deployability, scalability and high stiffness to mass ratio. Fraddosio et al. recently proposed a family of five innovative V-Expander elementary tensegrity cells, characterized by an increasing degree of geometrical complexity, and designed as a morphological evolution of a concept originally proposed by Motro and Raducanu. Here, we study the mechanical behavior of these innovative V-Expander elementary tensegrity cells by referring to different topologies; in particular, we analyze for such cells the feasible self-stress states in the cases in which the components in compression are composed of 2, 3, 4 and 6 struts, respectively. In addition, we evaluate the minimal mass of the cells taking into account the buckling strength of members in the self-equilibrium states according to the indications of standard building codes.
... Wśród pomysłodawców układów tensegrity powszechnie wymienia się trzech autorów; są to: David Georges Emmerich, Richard Buckminster Fuller i Kenneth Snelson. Każdy z nich przypisuje sobie status pierwszego wynalazcy tensegrity [Gómez Jáuregui: 2009]. Niezależnie od tego wszyscy trzej opatentowali m.in. ...
Thesis
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Idea tensegrity po raz pierwszy została opisana około 50 lat temu. Dotyczy specyficznych struktur, w których elementy ściskane oraz rozpierane przez nie elementy rozciągane wzajemnie stabilizują się, mimo że w strukturach występują mechanizmy. W rozprawie postawiono pytanie o to, czy i w jakim stopniu możliwe jest wykorzystanie idei tensegrity w konstrukcjach budowlanych, a w szczególności w obiektach mostowych. Aby na nie odpowiedzieć, podjęto rozważania zarówno na temat podstaw teoretycznych, jak i aspektów praktycznych projektowania tego typu konstrukcji. Bazując na mechanice konstrukcji sformułowano autorskie definicje „czystych tensegrity” i „konstrukcji o cechach tensegrity”. Określono najważniejsze cechy tensegrity, takie jak występowanie mechanizmów infinitezymalnych oraz stanów samonaprężenia, co pozwoliło na opracowanie opisu matematycznego tego typu konstrukcji oraz podanie własnej propozycji sposobu poszukiwania formy tensegrity. Wybrano metody obliczeniowe adekwatne do wspomnianych cech konstrukcji. Posługując się nimi, przeanalizowano właściwości statyczne i dynamiczne podstawowych modułów tensegrity. Podjęto rozważania na temat możliwości łączenia modułów pod kątem ich wykorzystania w konstrukcjach mostowych, a także wpływu sposobu łączenia na właściwości otrzymywanych w ten sposób struktur. Omówiono najważniejsze zagadnienia technologiczne związane z wykorzystaniem tensegrity w mostownictwie. Zbadano odpowiedź wybranych konstrukcji na obciążenia statyczne i dynamiczne w kontekście ich zastosowania jako ustroje nośne kładek dla pieszych. Dokonano oceny i klasyfikacji istniejących projektów oraz realizacji obiektów mostowych pretendujących do miana tensegrity. Przedstawiona analiza pozwoliła na sformułowanie wniosku mówiącego o możliwości zastosowania tensegrity w mostownictwie, głównie w zakresie ograniczonym do konstrukcji o cechach tensegrity. Zastosowanie „czystych tensegrity” może być uzasadnione w przypadku konstrukcji o specjalnym przeznaczeniu, takich jak mosty sterowane i rozwijane. / The concept of tensegrity was first described about 50 years ago. It refers to a particular type of structure, in which the compression and tensile components stabilize each other, despite the existence of mechanisms in the structure. A question, whether and to what extent it is possible to use the idea of tensegrity in building constructions, especially in bridges, was raised in the dissertation. To answer it, the author elaborated on both theoretical basis and practical aspects of the design of this type of structures. Two own definitions, based on mechanics of structures are presented. These are “pure tensegrities” and “structures having tensegrity features” definitions. The main features of tensegrity, such as the existence of infinitesimal mechanisms and self-stress states were defined. This made it possible to develop a mathematical description of this type of structures and to propose a new form-finding method. Computational methods appropriate for aforementioned properties were chosen. Static and dynamic properties of the basic tensegrity modules were analyzed using the selected methods. The possibility of combining modules for the use in bridge structures was discussed, as well as the impact of connection type on the properties of thus obtained structures. The most important technological issues associated with the use of tensegrity in bridges were discussed. The response of selected structures on the static and dynamic loads was examined in the context of their use in construction of footbridges. Existing projects and realizations of bridges called tensegrity were classified and evaluated. The analysis allowed to conclude, that there is a possibility of using tensegrity in bridge structures, limited mainly to the structures having tensegrity features. The use of “pure tensegrities” may be justified in the case of special-purpose structures, such as adaptive and deployable bridges.
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Buckminster Fuller dedicou sua vida a resolver problemas globais de habitação, transporte, educação, energia, destruição ecológica e pobreza, problemas que repercutem até os dias atuais, sua metodologia se baseava em compreender o espaço físico, limitações dos materiais e características da sobrevivência humana para introduzir artefatos que melhorassem a vida das pessoas, portanto o objetivo desta pesquisa é identificar a produção arquitetônica de Buckminster Fuller de forma cronológica e a associar a seus princípios de design antecipatório compreensivo, sinergia e efemerelização, através disso pode se identificar que seus conceitos embora fossem abrangentes eles estavam interconectados e continuam presentes até os dias atuais, seu objetivo mais notório era de se fazer mais com menos, mais espaço com menos material, energia e tempo investidos, Fuller certamente atingiu esse objetivo quando construiu uma de suas maiores invenções que foi o domo geodésico, embora a grande ambição de Fuller ele nunca conseguiu construir um domo que cobrisse uma cidade inteira, mesmo assim suas ideias e princípios de design continuam influenciando novas gerações de designers, arquitetos, cientistas e artistas a criarem um mundo mais sustentável.
Article
There is a growing need for new alternatives of long-span roof structures with high level of transformability and structural robustness. This led to the development of deployable cable-strut structures, which are composed of a continuous net of struts and another continuous net of cables. Subsequently, a special type of these systems was pioneered and given the term deployable tension-strut structures (DTSSs). The motivation beyond this new concept was the lack of structural efficiency and form flexibility of conventional space trusses that are usually employed for covering large spaces. Typically, DTSSs are roof structures consisting of multiple modules put together to form the roof system. This paper is mainly concerned with developing new robust modules for DTSSs. The technique that was adopted for this purpose is a form-creation methodology previously introduced in the literature. A few modules were already developed based on this shape grammar. However, its potential to develop multiple efficient modules has not been sufficiently investigated. In this current work, the afore-mentioned algorithm was utilized to form 16 new modules. A comparative study based on a nonlinear finite element technique was conducted to investigate the efficiency of the novel modules as compared to that of the previously proposed in the literature. The results show that some of the new proposed modules are far more efficient than those presented in previous researches. Based on this comparative study, the most two efficient modules among the novel ones were picked for further study. Parametric studies were conducted on these two systems under gravity loads and wind loads considering the following parameters: no. of modules, span/depth ratio, and cables’ pre-stress level. For each parameter, the optimal range of values were determined to be used as a guide for the design of such systems.
Article
There is still no consensus on the mechanisms regulating the formation and maintenance of morphological structures in the individual development of living organisms. The hypothesis that the mechanical forces are important for biological morphogenesis was put forward more than 100 years ago. In recent decades, studies indicating the regulatory role of mechanical stresses at different levels of organization of life have appeared. The signaling mechanisms that are responsible for the reception of mechanical influences and reprogramming of the properties of cells and tissues are studied. Since the mid-1970s, the principles of selfstressed structures or the tensegrity (tensional integrity) theory have been applied to understand the structure and functions of living structures in statics and dynamics. According to this standpoint, the cell can be represented as a self-stressed structure in which microtubules function as rigid rods and microfilaments serve as elastic threads. Such a system is anchored to extracellular matrix through cellular contacts, since it is adjusted to the external patterns of mechanical stresses. The notion of living systems as self-stressed structures provides a fresh look at the mechanotransduction, developing organism integrity, and biological morphogenesis. Although the application of the ideas of tensegrity to biological systems has not yet received broad support among biologists, the influence of these ideas on the formation of modern mechanobiology and understanding the crucial role of cytoskeletal structures in cellular processes should be mentioned.
Chapter
In this paper we describe a tensegrity ring of innovative conception for deployable space antennas. Large deployable space structures are mission-critical technologies for which deployment failure cannot be an option. The difficulty to fully reproduce and test on ground the deployment of large systems dictates the need for extremely reliable architectural concepts. In 2010, ESA promoted a study focused on the pre-development of breakthrough architectural concepts offering superior reliability. This study, which was performed as an initiative of ESA Small Medium Enterprises Office by Kayser Italia at its premises in Livorno (Italy), with Università di Roma TorVergata (Rome, Italy) as sub-contractor and consultancy from KTH (Stockholm, Sweden), led to the identification of an innovative large deployable structure of tensegrity type, which achieves the required reliability because of a drastic reduction in the number of articulated joints in comparison with non-tensegrity architectures. The identified target application was in the field of large space antenna reflectors. The project focused on the overall architecture of a deployable system and the related design implications. With a view toward verifying experimentally the performance of the deployable structure, a reduced scale breadboard model was designed and manufactured. A gravity off-loading system was designed and implemented, so as to check deployment functionality in a 1-g environment. Finally, a test campaign was conducted, to validate the main design assumptions as well as to ensure the concept’s suitability for the selected target application. The test activities demonstrated satisfactory stiffness, deployment repeatability, and geometric precision in the fully deployed configuration. The test data were also used to validate a finite element model, which predicts a good static and dynamic behavior of the full-scale deployable structure.
Book
Las estructuras tensegríticas son realmente asombrosas: constan de barras que están flotando en el aire, tan sólo sujetas mediante cables a otras barras... ¡que también flotan en el aire! Quizás sea precisamente esto lo que a la gente le entusiasma de la Tensegridad, contemplar este fenómeno "mágico" que son incapaces de entender. What’s tensegrity? “Food for thought.” Jörg Schlaich Diversas definiciones han sido establecidas por diferentes especialistas en la materia. Pero se podría definir así: La Tensegridad es un principio estructural basado en el empleo de componentes aislados comprimidos que se encuentran dentro de una red tensada continua, de tal modo que los miembros comprimidos (generalmente barras) no se tocan entre sí y están unidos únicamente por medio de componentes traccionados (habitualmente cables) que son los que delimitan espacialmente dicho sistema.
Construction de réseaux autotendants, French Patent No
  • D G Emmerich
Emmerich, D.G. Construction de réseaux autotendants, French Patent No. 1,377,290, September 28, 1964
Networked Public Spaces: An Investigation into Virtual Embodiment Unpublished PhD thesis Also available in http://vv.arts.ucla Kenneth Snelson: The Elegant Solution
  • V Kurtz
VESNA, V. (2000) Networked Public Spaces: An Investigation into Virtual Embodiment. Unpublished PhD thesis. University of Wales College, Newport. Also available in http://vv.arts.ucla.edu/publications/thesis/official/tensegrity.htm [13] KURTZ, S.A. (1968) " Kenneth Snelson: The Elegant Solution ". Art News. October, 1968. Also availabe in http://www.kennethsnelson.net/icons/art.htm [14] Snelson, K. Kenneth Snelson, [on-line], New York (USA).
The First Rigidly Clad "Tensegrity" Type Dome, The Crown Coliseum
  • P A Chen
  • D And Mikhlin
GOSSEN, P.A., CHEN, D., AND MIKHLIN, E. (1997) The First Rigidly Clad "Tensegrity" Type Dome, The Crown Coliseum, Fayetteville, North Carolina, [online], USA: Geiger Engineers.
Portrait of an Atomist Catalog Essay for Kenneth Snelson Exhibition at Hirshhorn Museum and Sculpture Garden Also available in http
  • D C Fuller
FOX, H. N. (1981) " Portrait of an Atomist ", Catalog Essay for Kenneth Snelson Exhibition at Hirshhorn Museum and Sculpture Garden, Smithsonian Institution, Washington, D.C., June - August 1981. Also available in http://www.kennethsnelson.net/icons/art.htm [16] FULLER, R.B. (1967) Octahedronal building truss, U.S. Patent No. 3,354,591, November 28, 1967.
Tensile-Integrity Structures, U.S. Patent No. 3,063
  • R B Fuller
Fuller, R.B. Tensile-Integrity Structures, U.S. Patent No. 3,063,521, November 13, 1962.