# tensegrity

• Stability Tensegrity prisms The three-rod tensegrity structure (3-way prism) has the property that, for a given (common) length of compression member “rod” (there are
three total) and a given (common) length of tension cable “tendon” (six total) connecting the rod ends together, there is a particular value for the (common) length of the tendon connecting the rod tops with the neighboring rod bottoms that
causes the structure to hold a stable shape.

• Concept Tensegrity structures are based on the combination of a few simple design patterns: • members loaded in either pure compression or pure tension, which means that the
structure will only fail if the cables yield or the rods buckle.

• The formula for its unique self-stress state is given by,[31] Here, the first three negative values correspond to the inner components in compression, while the rest correspond
to the cables in tension.

• As long as the angle between any two cables is smaller than 180°, the position of the rod is well defined.

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

• A three-rod tensegrity structure (shown above in a spinning drawing of a T3-Prism) builds on this simpler structure: the ends of each green rod look like the top and bottom
of the Skylon.

• As Ingber explains: The tension-bearing members in these structures – whether Fuller’s domes or Snelson’s sculptures – map out the shortest paths between adjacent members
(and are therefore, by definition, arranged geodesically).

• Furthermore, geometric patterns found throughout nature (the helix of DNA, the geodesic dome of a volvox, Buckminsterfullerene, and more) may also be understood based on applying
the principles of tensegrity to the spontaneous self-assembly of compounds, proteins,[16] and even organs.

• However both sets of coordinates lie along a continuous family of positions ranging from the cuboctahedron to the octahedron (as limit cases), which are linked by a helical
contractive/expansive transformation.

• Levin claims that the human spine, is also a tensegrity structure although there is no support for this theory from a structural perspective.

• The tensegrity structure provides structural compliance absorbing landing impact forces and motion is applied by changing cable lengths, 2014.

• [21] Many traditional structures, such as skin-on-frame kayaks and shōji, use tension and compression elements in a similar fashion.

• This can produce exceptionally strong and rigid structures for their mass and for the cross section of the components.

• Tensional forces naturally transmit themselves over the shortest distance between two points, so the members of a tensegrity structure are precisely positioned to best withstand
stress.

• This view is supported by how the tension-compression interactions of tensegrity minimize material needed to maintain stability and achieve structural resiliency, although
the comparison with inert materials within a biological framework has no widely accepted premise within physiological science.

• This enables the material properties and cross-sectional geometry of each member to be optimized to the particular load it carries.

• A multiple-mast, cable-stay structure based on the principles of tensegrity, it is currently the world’s largest tensegrity bridge.

• The roof uses an inclined surface held in check by a system of cables holding up its circumference.

• [4][5] Applications Tensegrities saw increased application in architecture beginning in the 1960s, when Maciej Gintowt and Maciej Krasiński designed Spodek arena complex (in
Katowice, Poland), as one of the first major structures to employ the principle of tensegrity.

• Because of these patterns, no structural member experiences a bending moment and there are no shear stresses within the system.

• While three cables are the minimum required for stability, additional cables can be attached to each node for aesthetic purposes or to build in additional stability.

• • mechanical stability, which allows the members to remain in tension/compression as stress on the structure increases.

• • Dissipate, an hourglass tower art sculpture including tensegrity structure, constructed at AfrikaBurn, 2015, a Burning Man regional event

• In 1949, Fuller developed a tensegrity-icosahedron based on the technology, and he and his students quickly developed further structures and applied the technology to building
domes.

• The other three cables are simply keeping it vertical.

• [17] Therefore, natural selection pressures would likely favor biological systems organized in a tensegrity manner.

• Its self-equilibrium state is given when the base triangles are in parallel planes separated by an angle of twist of π/6.

• For example, Snelson’s Needle Tower uses a repeated pattern built using nodes that are connected to 5 cables each.

Works Cited

[‘1. Gómez-Jáuregui 2010, p. 28. Fig. 2.1
2. ^ Fuller & Marks 1960, Fig. 270
3. ^ Fuller & Marks 1960, Fig. 268.
4. ^ Lalvani 1996, p. 47
5. Gómez-Jáuregui 2010, p. 19.
6. ^ Swanson, RL (2013). “Biotensegrity: a unifying theory of biological
architecture with applications to osteopathic practice, education, and research-a review and analysis”. The Journal of the American Osteopathic Association. 113 (1): 34–52. doi:10.7556/jaoa.2013.113.1.34. PMID 23329804.
7. ^ Hartley, Eleanor (19
February – 21 March 2009), “Ken Snelson and the Aesthetics of Structure”, Kenneth Snelson: Selected Work: 1948–2009 (exhibition catalogue), Marlborough Gallery
8. ^ Korkmaz, Bel Hadj Ali & Smith 2011
9. ^ Korkmaz, Bel Hadj Ali & Smith 2012
10. ^
Sabelhaus, Andrew P.; Bruce, Jonathan; Caluwaerts, Ken; Manovi, Pavlo; Firoozi, Roya Fallah; Dobi, Sarah; Agogino, Alice M.; SunSpiral, Vytas (May 2015). “System design and locomotion of SUPERball, an untethered tensegrity robot”. 2015 IEEE International
Conference on Robotics and Automation (ICRA). Seattle, WA, USA: IEEE. pp. 2867–2873. doi:10.1109/ICRA.2015.7139590. hdl:2060/20160001750. ISBN 978-1-4799-6923-4. S2CID 8548412.
11. ^ Lessard, Steven; Castro, Dennis; Asper, William; Chopra, Shaurya
Deep; Baltaxe-Admony, Leya Breanna; Teodorescu, Mircea; SunSpiral, Vytas; Agogino, Adrian (October 2016). “A bio-inspired tensegrity manipulator with multi-DOF, structurally compliant joints”. 2016 IEEE/RSJ International Conference on Intelligent
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Tensegrity-Based Inchworm-Like Robot for Crawling in Pipes With Varying Diameters”. IEEE Robotics and Automation Letters. 7 (4): 11553–11560. doi:10.1109/LRA.2022.3203585. ISSN 2377-3766. S2CID 252030788.
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J.; Floreano, D. (2017), “Bio-inspired Tensegrity Soft Modular Robots”, Biomimetic and Biohybrid Systems, Cham: Springer International Publishing, pp. 497–508, arXiv:1703.10139, doi:10.1007/978-3-319-63537-8_42, ISBN 978-3-319-63536-1, S2CID 822747
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Hall, Loura (2 April 2015). “Super Ball Bot”. NASA. Retrieved 18 June 2020.
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17. ^ Souza et al. 2009.
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375–88. doi:10.1142/S0219519402000472. ISSN 0219-5194.
19. ^ Jump up to:a b Ingber, Donald E. (January 1998). “The Architecture of Life” (PDF). Scientific American. 278 (1): 48–57. Bibcode:1998SciAm.278a..48I. doi:10.1038/scientificamerican0198-48.
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Natalie K.; Gordon, Richard (2016). “The organelle of differentiation in embryos: The cell state splitter”. Theoretical Biology and Medical Modelling. 13: 11. doi:10.1186/s12976-016-0037-2. PMC 4785624. PMID 26965444.
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28. ^ In Snelson’s article for Lalvani, 1996, I believe.[full citation needed]
29. ^ David Georges Emmerich, Structures
Tendues et Autotendantes, Paris: Ecole d’Architecture de Paris la Villette, 1988, pp. 30–31.
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31. ^ See photo of Fuller’s work at this exhibition in his 1961 article on tensegrity for the Portfolio and
Art News Annual (No. 4).
32. ^ Lalvani 1996, p. 47.
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37. ^ Kenner 1976, pp. 11–19, §2.
Spherical tensegrities.
38. ^ “Tensegrity Figuren”. Universität Regensburg. Archived from the original on 26 May 2013. Retrieved 2 April 2013.
39. ^ Coxeter, H.S.M. (1973) [1948]. “3.7 Coordinates for the vertices of the regular and quasi-regular
solids”. Regular Polytopes (3rd ed.). New York: Dover. pp. 51–52.
40. ^ Archived at Ghostarchive and the Wayback Machine: Fuller, R. Buckminster (22 October 2010), Vector Equilibrium, retrieved 22 February 2019
41. ^ Verheyen, H.F. (1989). “The
complete set of Jitterbug transformers and the analysis of their motion”. Computers & Mathematics with Applications. 17, 1–3 (1–3): 203–250. doi:10.1016/0898-1221(89)90160-0.
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Photo credit:
https://www.flickr.com/photos/oraziopuccio/8562144481/’]