the art of tensegrity

M U LT I - S C I E N C E P U B L I S H I N G C O . LT D .

5 Wates Way, Brentwood, Essex CM15 9TB, United Kingdom

Reprinted from

INTERNATIONAL JOURNAL OF

SPACE STRUCTURESVolume 27 · Number 2 & 3 · 2012

The Art of Tensegrity

by

K. Snelson

International Journal of Space Structures Vol. 27 No. 2&3 2012 71

When Professor Motro invited me to contributesomething for a special tensegrity issue of the JournalI was not sure what I would be able to write that mightinterest architects and engineers. As an artist I workdirectly from small scale models, quite different fromthe way other professions analyze tensegrity structuresmathematically. My large works are required only tostand up by themselves and survive out of doors whichthey have done extremely well. “Easy Landing” onBaltimore Maryland’s Inner Harbor (Fig. 1) and “FreeRide Home” at Storm King Art Center have stoodwithout need of repair for more than thirty-five years.Many more of my sculptures can be seen at:www.kennethsnelson.net

Because so many papers have been written abouttensegrity’s performance and its proposed uses what Ican add is the history of early discoveries; to relatesome of what I learned for the first time over a half-a-century ago.

I want to be clear that I am writing aboutendoskeletal floating-compression structures nothybrids that include bicycle wheels, spider webs andWWI aircraft construction. A Google “tensegrity”search turns up nearly a half-million entries, many ofwhich have nothing to do with discontinuouscompression, continuous tension, structures.

The Art of TensegrityKenneth Snelson

(Submitted on 25/10/2011, Reception of revised paper 19/03/2012, Accepted on 15/04/2012)

The tensegrity story is likely to begin with thequestion who discovered what and when. In 1996,Volume 11 Nos. 1 & 2 of this Journal, the differentviews of Buckminster Fuller, David George Emmerichand Kenneth Snelson were thoroughly debated. I toldof Mr. Fuller’s 1959 New York Museum of ModernArt exhibition when he finally credited me fordiscovering the tensegrity principle.

That local public acknowledgment offered me thefreedom to go back to where I had begun and toexplore whatever might still be left to discover abouttensegrity. Mr. Fuller had always concentrated onspheres based on the geometry of his geodesic dome.His audiences saw models and pictures of the spheresas well as his “mast” adapted from my original X-Piece. Though my 1948 plywood and monofilsculpture (Fig 2) had given birth to “tensegrity”, Mr.Fuller chose not to describe it in his lectures or in hiswriting. Most remarkably, none of his students inschools where he taught had discovered it on their

Figure 1. EasyLanding Figure 2. WoodX-Column1948

*Corresponding author e-mail: [email protected]

own. As a result the tensegrity X-module wasunknown to anyone but Bucky and me.

So, in the Fall of 1959 I began constructing studymodels to explore ways of extending theconventional kite frame, the proto-tensegritystructure — a two-strut figure held together by a girthof string. It is generally disallowed as tensegritybecause its sticks touch one another. While this is afair distinction, the kite frame is a sturdy, prestressed,triangulated, endoskeletal structure whoseparallelogram shape is endlessly adjustable. It is alsoa space-filling structure that can be repeatedindefinitely by adding kite-frames module aftermodule in all directions.

My studio was a small sixth-floor-walk-upapartment in a tenement-building on York Avenue inupper Manhattan. In those years I had many days offree time since I worked as a free-lance documentarymovie cameraman which usually meant having a jobonly a few days a month.

My first experiments were with 1/4” dowel sticksand fishing line. Using these simple materials broughtme back to my boyhood happily alone for hoursconstructing balsa and tissue model airplanes. I soonadvanced from dowels to aluminum tubes and bead-chain. Bead-counting made it easy to measure tensionlines, at least to the accuracy of a single bead. (Fig. 4)I quickly learned many things about basic tensegritystructures and how they work.

I moved ahead that Winter with such concentrationthat by the middle of March, 1960, six months after Ibegan, I was ready to apply for a patent for a collectionof previously unknown rudimentary ideas. It wasimportant this time around to have a proper record ofwhat I had invented. I found an expensive patent

attorney and a draftsman, the least expensive one Icould find, and by March 1960 my patent was appliedfor. It was not until five years later that U.S. 3169611,“Discontinuous Compression, Continuous TensionStructures”, was issued.

The descriptive first paragraph tells of myoptimism and what I hoped was true about thesuperior performance of floating compressionstructures. In fifteen pages, including thirty-fourfigures/drawings, it describes the several ways toexpand the X-module. It also describes five different,previously unknown, towers including the three-waytower. (Fig. 5) (I appreciate it greatly wheneverengineers acknowledge in their papers where thisarchetype three-strut column originated.) I included adouble-shell dome as well as a faux Eiffel Towerembellished by the draftsman with a tiny humanfigure to indicate its gargantuan size.

Considering the many technologies from societiesof the past such as ropes-and-pulleys, hot airballoons, weaponry, weaving, goldsmithing, origamiand the vast knowledge of materials and chemicalsthat came from the alchemists, is it not remarkablethat there never has been a tensegrity craft? Even ifonly for the delight of children? I can think of noexplanation for this except that it never had thatfamous mother known as “necessity”. But suddenly,today, on the internet, there is a wealth ofinformation. YouTube has many “How To Make aTensegrity” videos. There are websites devoted totensegrity and even a specialized Tensegrity Wiki.Tensegrity-as-a-craft is here at last.

72 International Journal of Space Structures Vol. 27 No. 2&3 2012


Figure 3. Kites variations

Figure 4. BeadChainTower

Kenneth Snelson

But what about patenting in this case, what did Iachieve? After going through the legal processseveral times I see patenting in a different light fromthe way most people think of it — as a possible roadto becoming a millionaire. I am speaking of privateinventors not corporations like IBM, Pfizer orGeneral Motors with hundreds or thousands ofpatents to protect their commercial interests. Yearsbefore the internet came along it was necessary to goto the patent office in Washington and pour overstacks of patents to find out if your idea was unique.It was expensive to have a law firm do it so I had thefun of searching all by myself. And I did find it fun.All the U.S. patents ever done and many foreignpatents are arranged there according to aclassification system that keeps changing andgrowing. It tries to place ideas in their appropriatecategory. Some things turn up in odd places such asartificial limbs being classified as “toys”.

I went there several times and spent hours lookingand hoping that the brilliant idea I had brought withme had not already been invented by someone else.Searching took me through hundreds of wonderfuland wacky ideas. As a continuous record, patent filesrepresent a history of inventions that is neitherselective nor interpretive as written history is, wherean author chooses to include some examples andleave out others The nonsense of the time is recordedalong with the profound discoveries. Almost anythingcan be patented if it can be shown to be new anduseful and it is evident that there has always been thebroadest interpretation of what is useful: an airplanemade of riveted steel plates with flapping wings?

A patent in the U.S. allows the inventor seventeenyears of protection for his idea; or, as patenting is often

called, “an invitation to litigation”. He must describeand illustrate his invention and state his claims. Theclaims, the patent’s legal teeth, allow only what is newand different from existing patents or commoninformation familiar to “those skilled in the art”. Fromthe moment the inventor applies for a patent itbecomes available for the public to read. I decidedfinally that one of the main values of patenting is forthe history of the nation, to document inventors’ ideasand discoveries for future generations.

Despite imagining early-on that tensegrity wouldturn into gold, my patents — all five of them — are forthe purpose of publication. Architects, Engineers,scientists and those in other professions have journalsand conferences where they can present papers. Artistshave art magazines with unintelligible articles writtenby art critics. So I have applied for patents which giveevidence that my ideas were new and original and tofully explain the subject, even though the text is oftenin stilted legalese. They will continue to be availablefree for as long as the nation survives. (And one dayeven my Atom Model will be paid attention to.)

After applying for the tensegrity patent I began tothink of planar structures. The X-module itselfbecomes a plane by repeating modules in x and ydirections.(Fig. 6) I first made planes out of three-wayand four-way modules which were easy and obviousonce I knew how to connect things together. (Fig. 7)

The most remarkable example I had in mind thoughwas an economical structure that amounted totransforming woven fabric into a tensegrity plane. Itwas during this experiment in fact that I began toidentify weaving with tensegrity. For a trial model Iused small thin-wall aluminum tubes with holes drilledfor connecting monofil tension lines. (Fig. 8a) It was


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Figure 5. DCCT Towers

the sparest system imaginable. To make a larger pieceI found a local factory to stamp out steel inserts withholes in the center for connecting bicycle spokes thatwould act as adjustable tension wires. (Fig. 8b) Inthose years New York still had many machineindustries of all kinds that were soon to disappearalong with the rest of U.S. manufacturing.

My planar weave piece was tricky to build becausethe prestressing had to be symmetrical to prevent theplane from warping. Completed finally, it was but askeleton, six feet square, weighing only twelvepounds. (Fig. 8c) I finished it on a warm and clearSunday morning in April 1960 and decided to takepictures of it on the roof of the building where I oftenphotographed things because my studio was filled upwith models. I carried the lightweight structure up theflight of stairs and through the steel fire-door to theroof where I set it down by its edge. I took one shot but

the only way to get a picture without the neighboringbuildings in the background was to place it on theparapet which was about two feet wide — and shoot itagainst the sky. I set it down, again on its edge, andstepped back to look through the view finder.



Figure 6. X-Planar Tower

Figure 7. Triangle & Square Planar

(a) Planar Weave

(b) Parts for planar piece

(c) Planar Roof York Avenue

Figure 8.

Kenneth Snelson

Suddenly I felt a strong gust of wind and in an instantI was watching my elegant work tilt backward towardYork Avenue. I rushed to grab a wire. Too late. Then,in what seemed like an unreal dream, I saw not onlythe structure but my brand new Canon Reflex crash tothe sidewalk six stories below. Because it was Sundaymorning only a few pedestrians were nearby andthankfully no one had been hit by the tubes, wires andcamera that all lay scattered on the sidewalk. A womankindly helped me gather up the pieces as I mumbledsome sort of confusing explanation. As people oftensay “It takes a helluva lot to surprise New Yorkers.” Inthat sad experience I had learned a great deal moreabout the hazards of gambling than about the practicaluse of a woven tensegrity plane. I knew at least that thestructure was not unbreakable.

At the end of 1960 I moved to a large loft on SpringStreet in SOHO (Fig 9) and began building biggermodels. The tallest was a tower twenty feet high which Iassembled, once again with the free use of the roof. Wordwas getting out about my structures. A friend, RichardBender, who taught architecture at Cooper Union,brought his class for a studio visit in order to introducethe new “tensegrity” to his young future architects.

Another friend came by with a friend of his, a writerwho worked at Fortune Magazine. He wrote a nicearticle for next month’s issue with lush colorphotographs. It was titled “Sculptures to Build With”and it said that “These ingenious frameworks of wireand tubes may become the architectural framework ofthe space age... A space station framed according toSnelson’s system could be attractive to rocketeers whomust count every gram they boost into orbit.” Evenback then! But I could see how easy it was for Buckyto get his outlandish claims published aboutsensational tensegrity. And the title reflected perfectlyhow ambivalent my own thinking was at that time. Noone could be more passionate about anything in the

world than I was about my captivating structures, yetgiven my odd position, not being an engineer butschooled in art I was sitting squarely between chairs.

Then, by surprise, I received a commission to makeart, to build two sculptures for the 1964 New YorkWorld’s Fair at the Electric Power and Light Pavilion.Fortune magazine’s “Sculptures to Build With”, hadbeen noticed and in this case the question, “Sculptures”vs. “to build with”, was pre-decided. They wantedsculptures, not buildings which I would have had no ideahow to begin in any case. I was excited since it was myfirst opportunity to construct big works that would beseen in public. One was a seventy-foot high three-way,straight, tower, far bigger and more massive thananything I had done so far, plus it was going to beilluminated by a twelve-billion! candle-power shaft oflight pointed straight up through the tower’s central axis.I was to be part of the “Brightest Show On Earth” asadvertised by the PR people. The second sculpture, wasa complex translation of X-modules thirty-five feetwide, that would stand over the entrance to the Pavilion.

Here was a completely new experience. I madeexact scale-models and had my arcuate-lip cable-adjusting hubs made by sand-casting. I found apolishing plant and an anodizer to finish the aluminumtubes. In the studio I cut and fixed ends on thehundreds of carefully measured stainless aircraftcables. Then came the trial assemblies. I put theentrance sculpture together in the loft and then thetower, lying on its side. (Fig 10). Finally, a few weeksbefore the opening date, everything was shipped to theFair grounds for a remarkably smooth installation. It


Figure 9. Spring St. Loft 1960 Figure 10. World FairTower Loft

had taken all of ten months. And I was getting paid!The commission covering fabrication and everythingtotaled $20,000. Quite a lot of money! (Fig 10a)

A month earlier a reporter from the New YorkTimes, Gay Talese, came to the loft to interview the“artist at work” and amazingly, two days later, thearticle with a photograph of me appeared on the frontpage. Talese said “an artist named Kenneth Snelsonshares his dark, dusty, loft with what appears to be agigantic grasshopper. Upon closer inspection,however, it is a modern structural design...”

With the pride of a famous son, I mailed the Timesclipping to my mother in our hometown of Pendleton,Oregon. She immediately passed the article on to thetown’s newspaper, the East Oregonian, whichannounced that native Pendleton artist KennethSnelson had created a gigantic grasshopper for theNew York World’s fair.

A Fair’s carnival-environment with so much to seewas not the greatest location for an artist hoping thatvisitors would take a moment to admire and tocontemplate truth and beauty. When the lights wereturned off a year-and-a-half later and everything wastaken apart I was a little sad it was all over but 1964had been a valuable learning experience.

A few days after the closing, a man phoned me athome to say he had just purchased my two sculptures. Iwas taken by surprise since I had not thought muchabout where they would find a home after the Fair camedown. I told my new collector that I would be glad tocome there and help him take the sculptures apart. “Noproblem,” he said. “we’ve cut the wires so they’realready apart. I deal in scrap and I wonder if you happento remember the alloy of the aluminum tubes?”

While the Fair was going on an engineer, Nick —whose last name escapes me — worked on thepavilion and also taught at the University of North

Carolina, told me that one of his students was lookingfor a thesis subject and if I liked the idea he couldmeasure the stresses on a structure. I would have toadd aluminum inserts on a few cables in order to attachthe strain gauge foils. Nick said the student would nodoubt come up with some valuable information. Itsounded worthwhile so I made a three-way columnstructure and added the small aluminum plates. After afew weeks went by Nick phoned and confessed thathis student had not come up with anything definitiveabout tensegrity’s efficiency but that my tower had“performed quite well”. I think it was at this time thatI began to have doubts. Just how well would mystructure hold up in comparison to an equal-sizealuminum step ladder? The only reward from Nick’stesting-adventure was a funny photo a friend took ofme perched on the tower with its strain gauge plates inplace. (Fig. 11)

In those years I began to think a lot about the spatialproperties of tensegrity structures, especially as theyrelate to other matters in geometry’s huge house ofmirrors; thoughts that lead to what properly educatedpeople in any specialized field might look down uponas metaphysics.

Yet an impulse to make thought-associations—toconnect together what may seem like unconnectedideas—is what enables every inventor everywhere toinvent new things.



Figure 10 a. Tower of Light 1964

Figure 11. Ken On Tower

Kenneth Snelson

I recognized that everything about tensegrity is binaryjust as opposing tension and compression forces arebinary. The primary example of binariness can be seen inthe kite frame itself where the two crossed sticks createtwo axes, one clockwise and one counterclockwise. (Fig. 12a) If you slide two fingers toward the intersectionalong the two struts your hand will tend to rotate eitherin a right-screw direction or a left-screw directiondepending on which of the two axes you start with.

In the six-strut tensegrity, four of its eight face-triangles are clockwise helixes and the other four arecounterclockwise, alternating over the figure likeadjacent squares on a chessboard. (Fig. 12b) Thisprinciple of alternating rotating directions is found inall tensegrity structures and it is fundamental to howthey work.

It is also how fabric-weaving works. There are twofundamental types of weaving: the standard two-wayplain weave and the three-way triangle/hexagon weaveused mostly in basketry. In each of these weave formsthe adjacent polygons rotate right and left, alternately,just as in tensegrity figures. (Fig. 13)

The basic weave cells of two, three, four, five and sixcrossings can be translated into basic tensegrity cells.(Fig. 14) The tensegrity helical phenomenon and itssimilarity to weaving suggested that it might to bepossible weave rods of some kind in three dimensions.I tried it using thin dowel sticks and happily found that

it works. These weave structures, or woven space-frames, are composed of polyhedra whose edges,instead of coming to a point at the vertex, bypass oneanother in a helical rotation. (15) They are “weave-polyhedra”. I discovered three basic woven 3D patterns:One is composed of weave-octahedra alternating inspace with weave-cuboctahedra. (Fig 15a) A secondtype is composed of weave-tetrahedra alternating withweave-truncated-tetrahedra. (Fig 15b) A third 3D weaveis rectilinear, analogous to six-strut tensegrity figuresrepeated in space. Because the cubical weave is nottriangulated it is a wobbly space-frame. I constructedexamples of each type in 1964. I took pictures and setthe prototypes aside. (Fig 16)

My woven space frames traveled with me for nearlyforty years as I moved my studio from place to place. In2002 when the internet made it easier to do searches Ilooked all over the web for 3D weaving and I wassurprised to find no such thing. Since I had neverpublished a picture or a description of three-dimensionalweaving I decided to apply for a patent to record that itwas a new idea. US Patent number 6,739,937 “SpaceFrame Structure Made by 3-D Weaving of RodMembers” was approved two years later.

I have described weaving as the “mother oftensegrity” although it is fair to ask which is thechicken and which the egg.

Another example of binary forces associatedelegantly with tensegrity geometry concerns the northand south polarity of magnets which I found by trying tovisualize what it would look like to transform the helical,static, motion of the six-strut tensegrity’s eight face-triangles into propellors or circles representingclockwise and counterclockwise rotation. In a seriessteps—too many to describe here—I discovered thatround magnets with poles on opposite faces like headsand tails of coin will snap together edge-to-edge incertain numbers to form closed “circlespheres”. (Fig. 17)When one of the magnets is made to revolve by hand theothers around the sphere follow, rotating as a single gear-train.


(a) Crossed Sticks

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Figure 12. Figure 13. Square & Hex Weave Mar27

This subject, magnets-on-spheres, which camedirectly out of tensegrity, took me along the path to mylong-running open-ended artwork I call “Portrait of anAtom”1.

I discovered also that certain Platonic andArchimedean polyhedra can be constructed out ofpolygon-shaped magnets with alternating north andsouth faces. (Fig. 18)



Figure 15. Four Twist Figures

(a) (b)

Figure 14. Tensegr. & Weave Cells

Figures 15a & 15b. Octa and Tetra Weave

1My atom model is fully described and illustrated at my websites — www.snelsonatom.com and www.kennethsnelson.net; also in twoatom patents: US Patent 3276148 and US Patent 4099339.

Kenneth Snelson

All of these ideas came from my following thethread of the 1948 X-Piece which would seem like afar cry from speculations about the atom’s electronicarchitecture. These side-adventures are cousins to theirprototype, the kite-frame with its built-in prestressing,its cross-over intersection, its binary helical axes andits ability to repeat in space, cell after cell, adinfinitum.

I have come to believe that this reversing oralternating principle in its many manifestations isthe prime means used wherever nature requiresseparate parts to be connected together to form anew whole.

ART AND TENSEGRITY, QUESTIONAND ANSWERSince the 1960s many engineers and architects havecontributed to the tensegrity culture by analyzing howsuch structures perform and by inventing ways toapply tensegrity for practical use. And many peopleconsider tensegrity to belong properly to the study ofengineering. In regard to my work they earnestly askthat well-worn question, “but, is it art?”. Mr. Fullerhimself was the first to assert that tensegrity should notbe used as art yet the only visible tensegrity structureattributed to him is a “sculpture” that hangs in theEngineering Centers building at the University ofWisconsin.

My first solo exhibition was in 1966. When theshow opened the “is it art?” question was resolved in aday because the reviews about my sculptures at NewYork’s Dwan Gallery were laudatory. By the luck ofperfect timing the pendulum had swung at thatmoment in the direction of geometric painting andsculpture; and the movement was soon given a newname, “Minimalism”. Because the art-world movesahead in a way like Haute Couture, fickle in the sameway, the celebration of Minimalisim lasted less thanthree years, to be replaced by something new calledEarth Art which was soon replaced by Conceptualismwhich was soon replaced... I watched the art scenemove forward like a ping-pong ball bouncing on atable with ever reduced importance at each bounce.


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Figure 17. Seven Magnet Spheres

Octahedron Cuboctahedron Rhombicuboctahedron Icosidodecahedron Rhombicosidodecahedron

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Figure 18. Magnet Polyhedra

Figure 16. Ken with Weave Space Frames

Now, half-a-century since my first exhibition, art hasgone through many fashion changes and now seems tohave spread out into a wider support of many styles,largely because there are thousands more artists thanthere were in the 1960s.

This paper’s narrative is about the beginning oftensegrity, my primary schooling. I look forward towriting more about it. Some wise person observed that“Youth creates the melody, the middle years add theharmony. In old-age, grace-notes.”

REFERENCESKenneth Snelson is represented by Marlborough Gallery, NY.

Snelson, K 1965, Continuous Tension, DiscontinuousCompression Structures US Patent 3169611

Snelson, K 1966, Model For Atomic Forms, US Patent 3276148Snelson, K 1978, Model For Atomic Forms, US Patent

4099339Snelson, K 1997, Magnetic Geometric Building System, US

Patent 6017220Snelson, K 2004, Space Frame Structure Made By 3-D

Weaving of Rod Members, US Patent 6739937www.kennethsnelson.netwww.snelsonatom.com



the art of tensegrity

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