Definition of Tensegrity

A tensegrity is a self-supporting structure of isolated compression elements suspended in a tensioned network. A pure tensegrity has no compressiblity or stretchability in its components, but real life structures always have some give and deflection. In a pure tensegrity the struts are not in contact; Skelton’s expanded typology allows contacting struts.

Context: Tom Flemons Archive 

Tom’s email text is preceded by the date. Text from a publication is preceded by a link to the publication.

(May 17, 2017) My intent is to make all of my work open source and easily accessible to others who may want to continue where I leave off.

Isolated compression elements suspended in a tensioned network

New Approaches to Mechanizing Tensegrity Structures (2018) A tensegrity (tensional integrity) is an endoskeletal structure that maintains dynamic stability by isolating compression elements within a tensional matrix. Tensegrities mediate all static and dynamic forces through the prestressed tension system, and can act as dynamically tuned resonating structures. A force exerted upon a tensegrity structure is almost instantly dispersed and spread throughout the entire form. One of the chief strengths of tensegrities is their robustness; if a tensegrity suffers local damage, the structure as a whole can continue to function in a slightly degraded manner.    More discussion of tensegrity properties in  Advantages of Tensegrity. These advantages are not fully realized in hybrid structures that combine tensegral and non-tensegral elements.

Tensegrity structures are self-supporting:  tents and spiderwebs are not tensegrities

New Approaches to Mechanizing Tensegrity Structures (2018) A tensegrity is a self-supporting tensile system that is not dependent on external supports or an external gravity field. Thus it cannot include lever arms or fixed fulcrums. All tensegrities are tension structures but not all tension structures are tensegrities. It is true that a circus tent holds its shape by balancing the compressive forces in the poles with the tension forces carried by the tent fabric and rope cables, but it is not a tensegrity because the whole structure relies on pinning the cables and the poles to the ground. Similarly, a spider web relies on the support of a tree branch; a struggling fly transmits forces throughout the web, alerting the spider, but ultimately the forces are dissipated and resolved by the branch. Many manmade structures employ a tension network to maintain stability – for example sailing rigs, suspension bridges, and radio and TV masts – but these are not tensegrities because they rely on a separate structure for grounding and stability.

A pure tensegrity has no compressiblity or stretchability in its components, but real life structures always have some give and deflection

(Feb 9, 2016) A ‘pure tensegrity’ assumes zero compressibility and zero stretchability in its components but we know that isn’t 100% possible – there’s always a bit of give even if it’s invisibly small. It is also impossible to tighten a line so tight that it cannot deflect a little if a force is applied. Think of hanging from a rope stretched between two trees. You would have to tighten the rope infinitely tight to prevent a deflection towards the ground by a weight hanging from it. Similarly in a tensegrity – (say 6 struts) no matter how rigid the materials are and how much prestress is added to the system there will always be some deflection – that is to say elasticity in the model. It may not be much but it’s there.   Related discussion in Adjusting Prestress and Allowing High Prestress.

In a pure tensegrity struts are not in contact; Skelton’s typology allows contacting struts

New Approaches to Mechanizing Tensegrity Structures (2018) Anthony Pugh (1976) gives a detailed taxonomy of tensegrity forms. In a pure tensegrity, struts are not in direct contact with each other but Skelton and de Oliveira (2009) propose an expanded typology of tensegrities that allows two or more struts to be in point-to-point contact. A class 2 tensegrity has two struts in contact at their nodal ends, a class 3 tensegrity has three struts intersecting and so on. In practice, strut and line congestion at the nodal ends mean that few useful designs involve more than two struts touching, and such contact should never transmits torque or shear forces across the node.

Reaction to Skelton’s typology

(April 28, 2016) I generally don’t have a problem with Skelton’s nomenclature because I see no benefit in holding to some idealized definition of tensegrity when applying it to the body. For example the myriad microtubules in the cell must cross each other in random and chaotic patterns and some undoubtedly come into contact with each other thus disqualifying them as a type 1 tensegrity. Somewhat similarly, the compression elements in the body as a whole are in part the various bones, some of which meet at a hub like the shoulder for example. Loads may not be carried through the compression elements directly and the clavicle, humerus, and scapula may not come into direct contact but there may be some benefit to ascribing a class system to some types tensegrity structures.

In my work with robotics I’m faced with making trade offs – increasing stability sometimes requires more than one axially loaded strut at a node (e.g. in my foot models I use a 4-fold T-prism with 4 additional  struts added to stiffen the structure making it a class 2 tensegrity), and as long as there is no direct compression load passing through the node I still consider it a tensegrity. There’s precedence for this point of view going back to Anthony Pugh’s book  (Introduction to Tensegrity – 1976). In it he notes that circuit diagram tensegrities involve the possibility of strut ends coming into contact with each other but as they don’t pass compressive loads across their common node they should still be considered tensegrities.

Snelson’s dislike of Skelton’s system is the objection of an artist – it’s an aesthetic position from someone who never saw a functional use for tensegrities beyond their artistic appeal. An engineering perspective is more expedient and pragmatic. I do think Skelton goes too far when he describes certain arrangements of solids as tensegrity systems – this muddies the waters because some of his examples show no sign of homeostatic adjustment to external loads via a tension net acting on freely moving compression elements and thus I wouldn’t consider them tensegral.