Tensegrity structures are strong and resilient, with multiple paths for force transmission. There is no shear and no bending moments, and prestress can be adjusted to suit different circumstances. Tensegrities are transparent both in structure and design. Auxetic characteristics are useful for modeling biologic pumps. Advantages of tensegrity for robotics and prosthetics.
Context: Tom Flemons Archive
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Tensegrity structures are strong and resilient
New Approaches to Mechanizing Tensegrity Structures (2018) Tensegrity structures are extremely strong and resilient for their weight. No additional material components are needed to handle shear or torque forces because tensegrities only transmit tension and compression forces. Additionally, a tensegrity structure makes multiple paths available to dissipate forces and maintain integrity. The geometry of the tension net is a dispersion tree – as a force moves through a tensegrity it converges upon a hub where one or more compression members are constrained by multiple tension members. Thus forces have many available paths to follow, both through the tension network along the periphery of the structure and also cutting chordally through the structure by axially loading the compression components.
No shear and no bending moments; speed of force transmission depends on prestress
Tensegrity Levers (2015) Tensegrities achieve their stability through the prestressing of their components – the tension net is taut and the compression members are under pure compression – no shear and no bending moments. A minimal energy tensegrity system (and all tensegrities have to be seen as structures where all parts act systemically) contains just enough prestress to maintain its maximal possible volume. Any less and it is a deflated system – any more and the overall tension of the system rises. The higher the prestress the more rigid the body. A force acting on a tensegrity system whether endogenous or exogenous, propagates through the system at speeds and effect proportionately to its tension state. A viscoelastic system or a loosely coupled complex tensegrity like the 4-prism system (or a human body) has a certain amount of slack built in which dampens and absorbs some of the force as it propagates outward from the source. Because all tensegrities have multiple lines of tension radiating from each node, propagation trees are complex and non-linear because the network is reiterative.
Multiple paths of redundancy
Tensegrity Levers (2015) One of the reasons tensegrity systems are so strong and resilient is because force propagation is distributed efficiently through multiple paths of redundancy. It’s possible for a significant section of a tensegrity to be damaged and yet still be able to maintain structural integrity. This seems to be a property of all complex systems – the four lever/ three fulcrum model demonstrates similar integrity.
Tensegrities deflect and disperse loads rather than compound them
(Sept 11, 2015) The whole purpose of selecting a tensegrity structure for a purpose is to deflect and disperse loads rather than compound them. Traditional mechanical linkages spend a lot of effort constraining unwanted movement between compression elements, otherwise forces compound as they move through the structure and the weakest link is where it breaks. Tensegrity structures on the other hand do not have this problem because there are no shear forces or torque because the tensional and compressional elements have been differentiated out into separate components. Tensegrity structures possess multiple paths of redundancy and hence multiple ways to deflect loads to prevent localized failure.
Tensegrities do not rely on gravity to hold together
(July 8, 2016) [In a tensegrity structure] a continuous tensional net binds and constrains discontinuous compression members from ‘falling outward’. In traditional buildings things (solid components) want to fall down and are constrained by material methods (cement, nails etc.) from doing so. They rely on gravity to hold together – turn them upside down and they will fall apart. In a tensegrity things (solids) want to spring outward and are constrained by the tension system which bounds the. Tensegrities model shells or envelopes and the balance of the two forces is what holds them together. Fuller talked about the difference this way – tensegrities are integral independent of gravity – they are governed by force vectors which travel inward and outward not up and down.
Tensegrities are transparent both in structure and design
How Tensegrity Models Reality (2018) Tensegrities are transparent – both in structure and design. You can literally see through them, and through also to how the forces that hold them together are arranged. … A tensegrity is literally a map of the forces that goes into making it. All tensegrities have this property of being a diagram of their force vectors as well as being a structure – in this sense tensegrities are self referential. They point to the nature of structure in their structure and display fundamental geometrical properties which underlie the basis of all form.
Auxetic characteristics of tensegrities are useful for modeling biologic pumps
An auxetic structure expands in all directions when it is stretched in one direction; it shrinks in all directions when it is compressed in one direction. This is illustrated by Henry Segerman’s 2018 video of hinged 3D auxetic mechanisms.
(March 23, 2016) I get the auxetic nature of the expanded octahedron tensegrity and appreciate what a useful model it is for explaining biologic pumps. But I have to note that this tensegrity exhibits auxetic characteristics only when two struts are being pulled apart from each other. If the tensegrity is oriented so that it is resting on a triangle of tension members and a force downward is applied it acts like any other material and bulges in the middle.
Further discussion in Auxetic Tensegrity Structures.
Advantages of tensegrity for robotics and prosthetics
(April 12, 2015) I have been gravitating towards robotics and prosthetics. Reductive low resolution tensegrity models probably can provide some if not all of the requirements of mobile compliant structures using less energy, being more robust and more closely approximating nature’s solutions than traditional engineering and biokinetics.
(Sept 1, 2015) Tensegrity design principles can be usefully employed to build robots, exo-skeletons and even prosthetic limbs. They can yield significant advantages over traditional construction methods; they are light weight, extremely resilient and strong and yet their elasticity can be adjusted to suit different circumstances. It is possible to link discrete tensegrity units together to produce articulations. Forces are carried across the joint in a manner that seems more tensegral than not – i.e. forces dissipate into the structure rather than concentrate at the interface. The joint is not itself a tensegrity even if it involves a compression component revolving upon a tension member. At some level there is still a material connection which involves friction and wear and thus torque and shear. Also while it is possible to make a tensegrity with a high degree of prestress, any joint that joins together two discrete tensegrities has to deal with the issue of compliancy – precision and strength through a range of motion requires a high degree of control. We can’t hope to emulate the material and feedback systems the body possesses any time soon so any tensegrity system that tries to recreate articular movement with any degree of accuracy is going to have to be a hierarchical structure comprising of highly prestressed units connected through a comprehensive series of actuators which initiate and inhibit movement as required. As the actuators are pulling against the tensegrity units, the higher the prestress the more accurate the control.
(Oct 17, 2015) Borrowing from life to solve technical problems is biomimicry and I recognized that my models could simulate anatomy without necessarily looking like it. I think robotics and prosthetics will benefit from this approach and I call this Tensegrity Biomimicry to distinguish it from Biotensegrity concerns which are different but related.
(Dec 4, 2015) I presently see more applications in the fields of robotics and prosthetics but suspect that any advances in these fields will at some point fold back into clinical and diagnostic applications.
Systemic analysis of complex systems
(June 25, 2016) Why does the concept of tensegrity seem to attract so much interest in such a diverse range of fields? I think this is because there is a real dearth of metaphors that can adequately describe a paradigm shift from linear Aristotelian thinking (with cause and effect chains which proceed as a rigid linked series of axioms or syllogisms) to an ecological systemic way of thinking. This shift is taking place over decades and centuries and has varying influences in different arenas of study. Perhaps it was my eclectic education that steered me towards a deep interest in tensegrities in the late 70’s. I remember in university trying various ways to model the complex systems I was studying… Because I have always had a penchance for building stuff my modelling career began back then as I struggled to understand how to make sense of the world by making actually physical models. I was fascinated by tensegrites right from the start but for a long time their symbolic properties escaped me. They were simply cool structures and at some point I turned my obsession with them into a business and began to manufacture toys and other objects. I built some early vertebral tensegrities in the mid 80’s and sold a few to doctors and chiropractors but it was the toys that took off so that’s the direction I went.
I began to look closer at the anatomy and compare it to tensegrity structures. To encompass joints into tensegrity nomenclature requires some agile fiddling with definition and with structures. I began to see how you could build discrete tensegrities and link them through tensile slings in a form of universal joint. This linkage could be controlled with a separate set of tensile lines allowing for revolute joints like the knee to operate under restrictions of degrees of freedom and range of motion. By this point it slowly dawned on me that I was really building robots not biotensegral analogies of the body. I saw the advantages of building compliant robots this way but lost faith that this had much to do with actual anatomical structures. It required a couple of years of thinking before I came up with a solution that involved helical tensegrity masts representing fascial meshes that had the property of suspending stiff components (bones struts) inside their matrix. My second paper The Bones of Tensegrity spelled out how this might plausibly work.
I am trying and failing to come up with another modelling system that carries anywhere near the versatility and flexibility of tensegrity as an explanatory system for this new way to view complex systems. Cybernetics, Chaos and Complexity theory can all benefit from a bone deep understanding of how feedback loops, multiple inputs, turbulent flow create the need for an all encompassing description of non-linear behavior. Tensegrity is the sine qua non of systemic analysis of complex systems. It is as Bateson might say ‘the pattern that connects’ diverse fields.
A discovery that keeps expanding
(May 17, 2017) I have been exploring the realm of tensegrity science for about 40 years. I think it is one of those discoveries that keeps expanding and having applications in many different fields. I have applied it or found it useful in structural anatomy, sculpture, architecture, robotics, prosthetics, furniture and toy design, social organization theory, cosmology… it’s pretty endless actually. As such it can be a very rewarding endeavor to become acquainted with the basic principles and fun to actually build models.