Tensegrity geometry is a language I’ve used to interpret and represent anatomic form as a dynamic interplay of forces

in four dimensions (bodies moving through time). What I've found out is intriguing– movement and degrees of

freedom in the models seem roughly analogous to human movement and freedom. In addition, changes to one part of

the model (e.g. local increased tension) are reflected throughout the structure; this is similar to the observation that

pain in the body often occurs at a distance from the source of insult. This is suggestive but it isn’t proof. Beginning to

work out the details of the theory is what this paper attempts to address.

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Tensegrity is...

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Tensegrities are all about tension and compression.

Every structure, whether an artifact created by intelligence or a

living form evolved by natural selection, is a balance between these two and only these two forces. Engineer and

architect Mario Salvadori points out in his book Why Buildings Stand Up, that shear is equivalent to tension and

compression forces acting at right angles and is not a separate force.(1)

Tensegrities are special case structures where the play of these two forces is visible in the design.

But tensegrity is also certainly one of the most powerful memes in the modern era. I think this is because of the elegance and power tensegrities have to describe and illustrate the behaviour of whole systems as fractals.

Tensegrity is a potent metaphor for envisioning existence in syncretic and non–atomistic ways. It has come to be imbued with multiple meanings at many levels of intercourse…

 

Carlos Castaneda appropriated the term as… “The name given to the modern version of the magical passes: positions

and movements of body and breath that were dreamt and stalked by men and women seers who lived in Mexico in

ancient times…”(2)

It turns out that Castaneda admired R. Buckminster Fuller who coined the term; he then borrowed and copyrighted the word for his own purposes.

The Canadian theoretician Stafford Beer, the founder of Management Cybernetics also admired Fuller and used

tensegrity as a social metaphor to describe complex decision-making relationships in groups. He coined the term

Syntegrity as tensegrity had already been copyrighted…

The Wikipedia weighs in with, “Tensegrity is a portmanteau of tensional integrity. It refers to the integrity of structures as being based in a synergy between balanced tension and compression components.”(2) Synergy refers to the

observation made first by R. Buckminster Fuller that in any system the whole is always greater than the sum of its

parts. The behavior of tensegrities is a visual demonstration of this.

How does Fuller define it? From Synergetics 700.011:

“The word tensegrity is an invention: it is a contraction of

tensional integrity. Tensegrity describes a structural relationship principle in which structural shape is guaranteed by

the finitely closed, comprehensively continuous, tensional behaviors of the system and not by the discontinuous and

exclusively local compressional member behaviors.”(3)

Easy for him to say… Fuller went on to design the largest 

enclosed domes ever built utilizing tensegrity principles.

The sculptor Kenneth Snelson who made the first tensegrity structures in 1948 called them something different. In an

interview he said, “Tensegrity, the word, has become so confusing through multiple uses that it calls any definition

into question. This is the reason I've long advocated Floating Compression… "It" describes a closed structural system

composed of a set of three or more elongate compression struts within a network of tension tendons, the combined

parts mutually supportive in such a way that the struts do not touch one another, but press outwardly against nodal

points in the tension network to form a firm, triangulated, prestressed, tension and compression unit. Why triangulated? The reason is that it's possible to build such a structure whose network is non-triangulated. Such structures are flaccid and decidedly not firm.”(4)

In the art world Snelson is well known and his floating compression sculptures are found in galleries, private collections, and museums around the world.

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A tensegrity requires at minimum three conditions to fit either Kenneth Snelson's or Buckminster Fuller's definition.

1.) A continuous connective tensioned network supports discontinuous compression struts. Snelson insists that struts

must be free floating in a web of tension and not touching.

A geodesic dome, which Fuller considers to be tensegrities,

has multiple compression struts meeting at central hubs but they are discontinuously connected, that is, they do not

transfer compressive loads. In these domes it is the tension forces that travel along the outer edges of the struts that are

continuous. Similarly, if anatomical structures operate as tensegrities, then in most orientations the bones do not pass a

direct load across the joint– rather the tension members; ligaments, tendons, and fascia transfer loads and the bones

float in this tension matrix.

2.) All tensegrities are prestressed under tension; they are self–supporting and independent of gravity. But the weight

of the structure also adds to the prestress. As you increase the weight load the tensegrity tightens and gets smaller. The

heavier the structure is, the greater the tension, and the less the range of motion. This presents real design problems

when trying to model living systems that have and use joints with multiple degrees of freedom. My models for

example can emulate biologic movement because I use elastic tension nets that are taut enough to maintain the shape

of the model yet have enough residual elasticity to move through a wide range of positions. When the size and weight

of a model increases, so does the prestress. It is always surprising to discover how high the tension levels climb when

building large tensegrity structures. In some of Snelson’s largest sculptures (50’–100’) the tensile cables carry

thousands of pounds of force. To make human scale tensegrity models that articulate and are prestressed is not a trivial

challenge.

3) Tensegrities are self–contained non–redundant whole systems. All components are dynamically linked such that

forces are translated instantly everywhere; a change in one part is reflected throughout. These features distinguish

tensegrities from all other tension structures, e.g. a radio mast or a sailboat’s mast is fixed at the base and needs that

fixed point to keep it upright. The boat does not need the mast for it’s integrity but the reverse is not true. Every part in

a tensegrity is reliant on the entire structure for its continued existence. In terms of living forms, a discontinuity in a

structure marks the boundary or interface between separate tensegrities. Also, molecules within cells within tissues

within organs within bodies, and bodies within environments are all synergistically linked tensegrities in a hierarchical

cascade from the smallest wholes to the largest.

At the macro scale of human anatomy, I see tensegrity as a diagrammatic way to model in four dimensions forces

acting on complex shapes in terms of stress vectors. I suggest that this analytic technique can explain the structure of

individual bones as well as aggregates that make up the body. Tensegrity in this sense is an applied principle– a map

of the nature of structure. If tensegrity is seen not so much a building system as it is a description of the most efficient

way that all form is organized, in terms of most economical use of energy and material, then we would expect

parsimonious nature to utilize this principle universally. The task is to determine exactly how this might have been

achieved at each scale of the continuum.

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Biotensegrity

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In the last 25 years tensegrity has come to be associated with various inquiries into the nature of living structure.

Donald E. Ingber MD PhD, Professor of Pathology at the Harvard Medical School, has done cellular research that has

been widely reported in major scientific journals as well in Scientific American, The Architecture of Life, January 1998.

He has found conclusive evidence that tensegrity provides the best explanation for the cytoskeleton of the cell,

its movement and behavior.

Stephen Levin M.D., an orthopedic surgeon who coined the term biotensegrity has applied the principle to macro scale anatomy in papers and numerous lectures around the world for over 25 years. His vision of biomechanical biotensegrity is radical and comprehensive. (biotensegrity.com). Others such as Tom Myers, well known writer and teacher of Structural Integration (http://www.anatomytrains.us/), and George Roth a writer and

chiropractor from Toronto (http://www.matrixinstitute.net/) both use the term in helping explain their practice and

methodology but the usage is general and mostly metaphoric. There are many others writing on this subject, but not

everyone understands tensegrity in the same way.

And some clearly understand less…

In a paper for an osteopathic journal, an American osteopath used tensegrity to model cranial sacral work but labeled a

picture of a train trestle bridge an example of tensegrity. The trestle bridge is an open braced framework– a truss that

conveys forces to the ground through the compression members– this disqualifies it as a tensegrity. A physiotherapist

interested in the concept thought that a spider’s web was a tensegrity structure. But a spider’s web is arranged the

same as a trampoline– a flexible tension membrane suspended from an exterior framework which is independent of the

membrane. The branch doesn’t rely on the web for support but the web needs the branch. Individual tensegrities are

integral– all parts are connected in a non–hierarchical relationship. A body worker who uses tensegrity as a metaphor

compares it to a mast in a sailboat. But a ship’s mast acts as a lever arm whose fulcrum is the deck of the boat (which

doesn’t rely on the mast for its integrity) and is prevented from tilting by tension shrouds. Tensegrities have no lever

arms or fulcrums in the classical sense. Forces are transferred globally across the entire structure. A well–known teacher of yoga teachers, who talks about tensegrity in her instruction, thought she lives in a tensegrity house because it had triangular roof sections. She no doubt has a stable roof but it isn’t a tensegrity. Each of these clinicians has used

tensegrity as an analogy based upon tension structures or stability through triangulation to describe their work but no

one is using the term correctly. All tensegrity structures are tensile but not all tensile structures are tensegrities. As we

are bound together with connective tissue that acts in tension, it is legitimate to ask what kind of tensile form we are.

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Geometry of Tensegrity

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The yoga teacher was partly right; it is about triangles. The only way to fully stabilize and constrain any structure is by

triangulating surfaces or cavities in compression and/or tension in all three dimensions. This fact may not be obvious

at first as many artifacts conceal their triangulation within their form such as the square walls and roofs of buildings.

Tensegrity structures on the other hand show the forces acting upon them by differentiating out tension and

compression vectors into separate components. Most are based upon iterations of regular geometric forms known as

the five Platonic Solids. Complete triangulation and full stability occurs in only three of these, the tetrahedron,

octahedron and icosahedron and these are the best candidates for modeling anatomy. Without triangular bracing, the

cube and the dodecahedron are inherently unstable. All five convex regular polyhedrons demonstrate faces, edges and

angles that are congruent, that is, all faces are equilateral, all angles are the same and all the edges are identical.