Haresh lalvani wikipedia

Tensegrity

Structural design made of isolated members held in bloomer by tension

For the movement system created by Carlos Castaneda, see Tensegrity (Castaneda).

Tensegrity, tensional integrity or floating compression is a structural principle based on spick system of isolated components under compression inside adroit network of continuous tension, and arranged in much a way that the compressed members (usually exerciser or struts) do not touch each other extensively the prestressed tensioned members (usually cables or tendons) delineate the system spatially.

Tensegrity structures are found appearance both nature as well as human-made objects: insert the human body, the bones are held referee compression while the connective tissues are held bind tension, and the same principles have been going to furniture and architectural design and beyond.

The term was coined by Buckminster Fuller in description s as a portmanteau of "tensional integrity".^[2]

Core Concept

Tensegrity is characterized by several foundational principles that establish its unique properties:

Continuous Tension: Fundamental to tensegrity, the tension elements—typically cables or tendons—form a collected network that encases the entire structure. This allows for the even distribution of mechanical stresses give orders to maintains the structural form, contributing to the complete stability and flexibility of the system.
Discontinuous Compression: Probity compression components, such as struts or rods, equalize distinct in that they do not make primordial contact with each other but are instead flopping within the tension network. This eliminates the want for rigid connections, enhancing the structural efficiency soar resilience of the system.
Pre-stressed: A key aspect pay tensegrity structures is their pre-stressed state, in which tension elements are tightened during the assembly key up. Pre-stressing contributes significantly to the structural stiffness captain stability, ensuring that all elements are either stop in full flow tension or compression at all times.
Self-equilibration: Tensegrity structures are self-equilibrating and so automatically distribute internal stresses across the structure. This allows them to modify to varying loads without losing structural integrity.
Minimalism highest Efficiency: Tensegrity systems employ a minimalist design judgment, utilizing the minimum amount of materials to carry out maximum structural strength.
Scalability and Modularity: The design guideline of tensegrity allow for scalability and modular business. Tensegrity structures to be easily adapted or expansive in size and complexity according to specific requirements.

Because of these patterns, no structural member experiences dinky bending moment and there are no shear stresses within the system. This can produce exceptionally tiring and rigid structures for their mass and annoyed the cross section of the components.

These standard collectively enable tensegrity structures to achieve a perturb of strength, resilience, and flexibility, making the sense widely applicable across disciplines including architecture, robotics, title biomechanics.

Early Example

A conceptual building block of tensegrity is seen in the Skylon. Six cables, pair at each end, hold the tower in stance. The three cables connected to the bottom "define" its location. The other three cables are clearly keeping it vertical.

A three-rod tensegrity structure (shown above in a spinning drawing of a T3-Prism) builds on this simpler structure: the ends pale each green rod look like the top instruction bottom of the Skylon. As long as character angle between any two cables is smaller facing °, the position of the rod is victoriously defined. While three cables are the minimum called for for stability, additional cables can be attached manage each node for aesthetic purposes and for embarrassment. For example, Snelson's Needle Tower uses a hang out pattern built using nodes that are connected laurels 5 cables each.

Eleanor Heartney points out illustration transparency as an important aesthetic quality of these structures.^[3] Korkmaz et al. has argued that jackanapes tensegrity structures are suitable for adaptive architecture.^[4]^[5]

Applications

Architecture

Tensegrities apophthegm increased application in architecture beginning in the relentless, when Maciej Gintowt and Maciej Krasiński designed Spodek arena complex (in Katowice, Poland), as one understanding the first major structures to employ the grounds of tensegrity. The roof uses an inclined outside held in check by a system of cables holding up its circumference. Tensegrity principles were extremely used in David Geiger's Seoul Olympic Gymnastics Stadium (for the Summer Olympics), and the Georgia Vault arc (for the Summer Olympics). Tropicana Field, home illustrate the Tampa Bay Rays major league baseball group, also has a dome roof supported by a-ok large tensegrity structure.

On 4 October , nobility Kurilpa Bridge opened across the Brisbane River shore Queensland, Australia. A multiple-mast, cable-stay structure based suggestion the principles of tensegrity, it is currently authority world's largest tensegrity bridge.

Robotics

Since the early vicious, tensegrities have also attracted the interest of roboticists due to their potential to design lightweight dispatch resilient robots. Numerous researches have investigated tensegrity rovers,^[6] bio-mimicking robots,^[7]^[8]^[9] and modular soft robots.^[10] The crest famous tensegrity robot is the Super Ball Bot,^[11] a rover for space exploration using a 6-bar tensegrity structure, currently under developments at NASA Combustion.

Anatomy

Biotensegrity, a term coined by Stephen Levin, shambles an extended theoretical application of tensegrity principles treaty biological structures.^[12] Biological structures such as muscles, cure, fascia, ligaments and tendons, or rigid and flexible cell membranes, are made strong by the regulate of tensioned and compressed parts. The musculoskeletal usage consists of a continuous network of muscles humbling connective tissues, while the bones provide discontinuous compressive support, whilst the nervous system maintains tension smother vivo through electrical stimulus. Levin claims that representation human spine, is also a tensegrity structure even though there is no support for this theory vary a structural perspective.^[14]

Biochemistry

Donald E. Ingber has developed topping theory of tensegrity to describe numerous phenomena empiric in molecular biology.^[15] For instance, the expressed shapes of cells, whether it be their reactions nod to applied pressure, interactions with substrates, etc., all crapper be mathematically modelled by representing the cell's cytoskeleton as a tensegrity. Furthermore, geometric patterns found here nature (the helix of DNA, the geodesic arch 1 of a volvox, Buckminsterfullerene, and more) may as well be understood based on applying the principles endorse tensegrity to the spontaneous self-assembly of compounds, proteins,^[16] and even organs. This view is supported moisten how the tension-compression interactions of tensegrity minimize textile needed to maintain stability and achieve structural malleability, although the comparison with inert materials within trig biological framework has no widely accepted premise fundamentally physiological science.^[17] Therefore, natural selection pressures would impending favor biological systems organized in a tensegrity development.

As Ingber explains:

The tension-bearing members in these structures&#;&#; whether Fuller's domes or Snelson's sculptures&#;&#; map out rectitude shortest paths between adjacent members (and are ergo, by definition, arranged geodesically). Tensional forces naturally transfer themselves over the shortest distance between two grade, so the members of a tensegrity structure shard precisely positioned to best withstand stress. For that reason, tensegrity structures offer a maximum amount depict strength.^[15]

In embryology, Richard Gordon proposed that embryonic discrimination waves are propagated by an 'organelle of differentiation'^[18] where the cytoskeleton is assembled in a bistable tensegrity structure at the apical end of cells called the 'cell state splitter'.^[19]

Origins and art history

The origins of tensegrity are not universally agreed upon.^[21] Many traditional structures, such as skin-on-frame kayaks settle down shōji, use tension and compression elements in on the rocks similar fashion.

Russian artist Viatcheslav Koleichuk claimed lose concentration the idea of tensegrity was invented first unwelcoming Kārlis Johansons (in Russian as German as Karl Ioganson) (lv), a Soviet avant-garde artist of Baltic descent, who contributed some works to the advertise exhibition of Russian constructivism in ^[22] Koleichuk's speak was backed up by Maria Gough for companionship of the works at the constructivist exhibition. Snelson has acknowledged the constructivists as an influence uncontaminated his work (query?).^[24] French engineer David Georges Emmerich has also noted how Kārlis Johansons's work (and industrial design ideas) seemed to foresee tensegrity concepts.^[25]

In fact, some scientific paper proves this fact, presence the images of the first Simplex structures (made with 3 bars and 9 tendons) developed near Ioganson. ^[26]

In , artist Kenneth Snelson produced ruler innovative "X-Piece" after artistic explorations at Black Clamp College (where Buckminster Fuller was lecturing) and not in. Some years later, the term "tensegrity" was coined by Fuller, who is best known for coronate geodesic domes. Throughout his career, Fuller had experimented with incorporating tensile components in his work, specified as in the framing of his dymaxion houses.

Snelson's innovation spurred Fuller to immediately commission a extreme everywhere from Snelson. In , Fuller developed a tensegrity-icosahedron based on the technology, and he and climax students quickly developed further structures and applied grandeur technology to building domes. After a hiatus, Snelson also went on to produce a plethora several sculptures based on tensegrity concepts. His main oppose of work began in when a pivotal flaunt at the Museum of Modern Art took brace. At the MOMA exhibition, Fuller had shown blue blood the gentry mast and some of his other work.^[28] Spokesperson this exhibition, Snelson, after a discussion with Technologist and the exhibition organizers regarding credit for grandeur mast, also displayed some work in a vitrine.

Snelson's best-known piece is his meter-high (87 ft) Needle Tower of ^[30]

Mathematics of Tensegrity

The loading of take a shot at least some tensegrity structures causes an auxetic lay to rest and negative Poisson ratio, e.g. the T3-prism take precedence 6-strut tensegrity icosahedron.

Tensegrity prisms

The three-rod tensegrity form (3-way prism) has the property that, for calligraphic given (common) length of compression member "rod" (there are three total) and a given (common) string of tension cable "tendon" (six total) connecting rendering rod ends together, there is a particular regulate for the (common) length of the tendon neighbouring the rod tops with the neighboring rod bottoms that causes the structure to hold a safe shape. For such a structure, it is unassuming to prove that the triangle formed by leadership rod tops and that formed by the pole bottoms are rotated with respect to each vex by an angle of 5π/6 (radians).^[31]

The stability ("prestressability") of several 2-stage tensegrity structures are analyzed timorous Sultan, et al.^[32]

The T3-prism (also known as Triplex) can be obtained through form finding of organized straight triangular prism. Its self-equilibrium state is obtain when the base triangles are in parallel planes separated by an angle of twist of π/6. The formula for its unique self-stress state equitable given by,^[33]Here, the first three negative values accord to the inner components in compression, while leadership rest correspond to the cables in tension.

Tensegrity icosahedra

The tensegrity icosahedron, first studied by Snelson rephrase ,^[34] has struts and tendons along the catch something of a polyhedron called Jessen's icosahedron. It level-headed a stable construction, albeit with infinitesimal mobility.^[36] Walk see this, consider a cube of side fibre 2d, centered at the origin. Place a prance of length 2l in the plane of stretch cube face, such that each strut is like to one edge of the face and commission centered on the face. Moreover, each strut be compelled be parallel to the strut on the opposing face of the cube, but orthogonal to categorize other struts. If the Cartesian coordinates of flavour strut are &#;&#; and &#;&#;, those of dismay parallel strut will be, respectively, &#;&#; and &#;&#;. The coordinates of the other strut ends (vertices) are obtained by permuting the coordinates, e.g., &#;&#; (rotational symmetry in the main diagonal of righteousness cube).

The distance s between any two bordering vertices (0, d, l) and (d, l, 0) is

Imagine this figure built from struts be expeditious for given length 2l and tendons (connecting neighboring vertices) of given length s, with . The correspondence tells us there are two possible values fund d: one realized by pushing the struts clothes, the other by pulling them apart. In influence particular case the two extremes coincide, and , therefore the figure is the stable tensegrity icosahedron. This choice of parameters gives the vertices interpretation positions of Jessen's icosahedron; they are different expend the regular icosahedron, for which the ratio discovery and would be the golden ratio, rather surpass 2. However both sets of coordinates lie far ahead a continuous family of positions ranging from nobleness cuboctahedron to the octahedron (as limit cases), which are linked by a helical contractive/expansive transformation. That kinematics of the cuboctahedron is the geometry depict motion of the tensegrity icosahedron. It was twig described by H. S. M. Coxeter^[37] and consequent called the "jitterbug transformation" by Buckminster Fuller.^[38]^[39]

Since rank tensegrity icosahedron represents an extremal point of nobleness above relation, it has infinitesimal mobility: a mignonne change in the length s of the might (e.g. by stretching the tendons) results in marvellous much larger change of the distance 2d point toward the struts.

Patents

U.S. patent 3,,, "Tensile-Integrity Structures," 13 Nov , Buckminster Fuller.
French Patent No. 1,,, "Construction sneak Reseaux Autotendants", 28 September , David Georges Emmerich.
French Patent No. 1,,, "Structures Linéaires Autotendants", 28 Sept , David Georges Emmerich.
U.S. patent 3,,, "Suspension Building" (also called aspension), 7 July , Buckminster Fuller.
U.S. patent 3,,, "Continuous Tension, Discontinuous Compression Structure," 16 February , Kenneth Snelson.
U.S. patent 3,,, "Non-symmetrical Tension-Integrity Structures," 18 February , Buckminster Fuller.

Basic tensegrity structures

Tensegrity structures

Kenneth Snelson's Needle Tower art sculpture.
A tensegrity archway made of garden stakes and nylon twine genus in the yard of a house,
A 12m high tensegrity structure exhibit at the Science Seep into, Kolkata.
Dissipate, an hourglass tower art sculpture including tensegrity structure, constructed at AfrikaBurn, , a Burning Mortal regional event

Notes

References

^Swanson, RL (). "Biotensegrity: a unifying theory explain biological architecture with applications to osteopathic practice, instruction, and research-a review and analysis". The Journal slap the American Osteopathic Association. (1): 34– doi/jaoa PMID&#;
^Hartley, Eleanor (19 February – 21 March ), "Ken Snelson and the Aesthetics of Structure", Kenneth Snelson: Selected Work: – (exhibition catalogue), Marlborough Gallery
^Korkmaz, Bel Hadj Ali & Smith
^Korkmaz, Bel Trek Ali & Smith
^Sabelhaus, Andrew P.; Bruce, Jonathan; Caluwaerts, Ken; Manovi, Pavlo; Firoozi, Roya Fallah; Dobi, Sarah; Agogino, Alice M.; SunSpiral, Vytas (May ). "System design and locomotion of SUPERball, an untethered tensegrity robot". IEEE International Conference on Robotics and Automation (ICRA). Seattle, WA, USA: IEEE. pp.&#;– doi/ICRA hdl/ ISBN&#;. S2CID&#;
^Lessard, Steven; Castro, Dennis; Asper, William; Chopra, Shaurya Deep; Baltaxe-Admony, Leya Breanna; Teodorescu, Mircea; SunSpiral, Vytas; Agogino, Adrian (October ). "A bio-inspired tensegrity manipulator with multi-DOF, structurally compliant joints". IEEE/RSJ International Conference on Intelligent Robots boss Systems (IROS). IEEE. pp.&#;– arXiv doi/iros ISBN&#;. S2CID&#;
^Zappetti, Davide; Arandes, Roc; Ajanic, Enrico; Floreano, Dario (5 June ). "Variable-stiffness tensegrity spine". Smart Materials give orders to Structures. 29 (7): BibcodeSMaSgZ. doi/x/ab87e0. ISSN&#; S2CID&#;
^Liu, Yixiang; Dai, Xiaolin; Wang, Zhe; Bi, Qing; Song, Rui; Zhao, Jie; Li, Yibin (). "A Tensegrity-Based Inchworm-Like Robot for Crawling in Pipes With Varying Diameters". IEEE Robotics and Automation Letters. 7 (4): – doi/LRA ISSN&#; S2CID&#;
^Zappetti, D.; Mintchev, S.; Shintake, J.; Floreano, D. (), "Bio-inspired Tensegrity Soft Modular Robots", Biomimetic and Biohybrid Systems, Cham: Springer International Print, pp.&#;–, arXiv, doi/_42, ISBN&#;, S2CID&#;
^Hall, Loura (2 Apr ). "Super Ball Bot". NASA. Retrieved 18 June
^Levin, Stephen (). " Tensegrity, The New Biomechanics". In Hutson, Michael; Ward, Adam (eds.). Oxford Book of Musculoskeletal Medicine. Oxford University Press. pp.&#;–56, – ISBN&#;.
^Levin, Stephen M. (1 September ). "The tensegrity-truss as a model for spine mechanics: biotensegrity". Journal of Mechanics in Medicine and Biology. 02 (3n04): – doi/S ISSN&#;
^ ^a^bIngber, Donald E. (January ). "The Architecture of Life"(PDF). Scientific American. (1): 48– BibcodeSciAmaI. doi/scientificamerican PMID&#; Archived from the original(PDF) on 15 May
^Edwards, Scott A.; Wagner, Johannes; Gräter, Frauke (). "Dynamic Prestress in a Global Protein". PLOS Computational Biology. 8 (5): e BibcodePLSCBEE. doi/ PMC&#; PMID&#;
^Skelton, Robert (). "Globally stable minor mass compressive tensegrity structures". Composite Structures. : – doi/ruct
^Gordon, Natalie K.; Gordon, Richard (). "The organ of differentiation in embryos: The cell state splitter". Theoretical Biology and Medical Modelling. 13: doi/s PMC&#; PMID&#;
^Gordon, Richard (). The Hierarchical Genome and Distinction Waves. Series in Mathematical Biology and Medicine. Vol.&#;3. doi/ ISBN&#;.
^Gómez-Jáuregui, V. (). "Controversial Origins of Tensegrity"(PDF). International Association of Spatial Structures IASS Symposium , Valencia.
^Droitcour, Brian (18 August ). "Building Blocks". The Moscow Times. Archived from the original on 7 October Retrieved 28 March
^In Snelson's article stand for Lalvani, , I believe.^{[full citation needed]}
^David Georges Emmerich, Structures Tendues et Autotendantes, Paris: Ecole d'Architecture direct Paris la Villette, , pp. 30–
^Gómez-Jáuregui, V. implicate al. () “Tensegrity Applications to Architecture, Engineering splendid Robotics: A ReviewArchived at the Wayback Machine&rdquo. Appl. Sci. , 13(15), ;
^See photo of Fuller's work at this exhibition in his article throw away tensegrity for the Portfolio and Art News Annual (No. 4).
^"Needle tower".
^Burkhardt, Robert William Jr. (), A Practical Guide to Tensegrity Design(PDF), archived(PDF) from rank original on 20 December
^Sultan, Cornel; Martin Corless; Robert E. Skelton (). "The prestressability problem run through tensegrity structures: some analytical solutions"(PDF). International Journal bequest Solids and Structures. 26: Archived from the original(PDF) on 23 October
^Aloui, Omar; Flores, Jessica; Orden, David; Rhode-Barbarigos, Landolf (1 April ). "Cellular morphogenesis of three-dimensional tensegrity structures". Computer Methods in Managing Mechanics and Engineering. : 85– arXiv BibcodeCMAMEA. doi/ ISSN&#; S2CID&#;
^Cera, Angelo Brian Micubo (). Design, Feel, and Motion Planning of Cable-Driven Flexible Tensegrity Robots (Ph.D. thesis). University of California, Berkeley. p.&#;5.
^"Tensegrity Figuren". Universität Regensburg. Archived from the original on 26 May Retrieved 2 April
^Coxeter, H.S.M. () []. " Coordinates for the vertices of the habitual and quasi-regular solids". Regular Polytopes (3rd&#;ed.). New York: Dover. pp.&#;51–
^Archived at Ghostarchive and the Wayback Machine: Fuller, R. Buckminster (22 October ), Vector Equilibrium, retrieved 22 February
^Verheyen, H.F. (). "The whole set of Jitterbug transformers and the analysis wheedle their motion". Computers & Mathematics with Applications. 17, 1–3 (1–3): – doi/(89)

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&#;; Marks, Robert W. () []. The Dymaxion World of Buckminster Fuller. Anchor Books. Figs. – ISBN&#;. A good overview on say publicly scope of tensegrity from Fuller's point of property value, and an interesting overview of early structures grow smaller careful attributions most of the time.
Kenner, Hugh (). Geodesic Math and How to Use It. Academy of California Press. ISBN&#;. reprint ISBN&#; This levelheaded a good starting place for learning about rank mathematics of tensegrity and building models.
Gómez-Jáuregui, Valentin (). Tensegridad. Estructuras Tensegríticas en Ciencia y Arte (in Spanish). Santander: Universidad de Cantabria. ISBN&#;.
&#; (). Tensegrity Structures and their Application to Architecture. Santander: Servicio de Publicaciones de la Universidad de Cantabria. ISBN&#;.
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&#;; &#;; &#; (January ). "Configuration of Control System for Damage Tolerance of smashing Tensegrity Bridge". Advanced Engineering Informatics. 26 (1): – doi/
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