The effect of prestress on rigidity and force propagation. An extremely prestressed tensegrity is equivalent to a hard material like diamond; low prestress creates a compliant jelly-like structure. Use invariant-length materials to properly test compliancy versus rigidity. Highly-elastic tension members become stiff when prestress is high.
Context: Tom Flemons Archive
Prestress, rigidity and force propagation
Higher prestress: more rigid, with faster force propagation
Tensegrity Levers (2015) 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.
Viscoelastic or loosely coupled: dampen and absorb some of the propagating force
Tensegrity Levers (2015) 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.
The materials a tensegrity is made from absorb forces and dampen oscillations; a highly prestressed tensegrity would ring like a bell
(Feb 9, 2016) Now clearly in the body, bones can be put under tension (hang from a tree branch) and can flex in compression somewhat (femurs flex quite a bit when skiing moguls e.g.) Similarly struts can be tensioned in the manner you describe. Assuming no gravity, the only way a tensegrity can be stressed is from an outside force that introduces an imbalance in the system. As the imbalance is resolved tensional forces radiate throughout causing in turn oscillations in the compression components. Like waves in a pond all the forces eventually get averaged out and dissipate. How that happens is an interesting question. I think the materials the tensegrity is made from absorb the forces and dampen down the oscillations. It may be that they are translated into higher frequency vibrations by the molecular order in the material. If you built a tensegrity out of very hard compression struts – say crystal – and suspended them in the tension net at their nodal points (approx 25% in from the ends) and cranked up the tension system like a violin and then struck a strut with a mallet I’m pretty sure that it would ring like a bell. i.e. it would resonate.
An extremely presetressed tensegrity is equivalent to a hard material like diamond; low prestress creates a compliant jelly-like structure
(Feb 9, 2016) The implication is that a tensegrity system falls somewhere between two boundaries – an extremely prestressed tensegrity is equivalent to very hard materials – in diamonds for example tetrahedral bonds make for a very rigid material; or a very compliant jelly like structure where all the components have a lot of give in them.
So I would say, within limits you can model tensioners and compressioners (to coin a phrase) as springs if there is a reason to do so. An example might be modelling an extremely compliant structure like a soft rubber ball or a soft robot that has to squeeze through narrow spaces. At some point you defeat the exercise of keeping tension and compression separate and you end up with a ball of jello and shortly after that it’s a puddle on the floor…
Speed of information transmission in a tensegrity structure
(Nov 14, 2015 commenting on the Slinky Slow Motion video) Yes, I’ve seen this video before. Very cool! A wavefront propagates at a finite speed so in a tensegrity the information of a force applied to it propagates throughout the structure at a speed dependent on the shape and complexity of the structure including its stiffness.
No matter how high the prestress, there is always some give and deflection
(Feb 9, 2016, repeated from Definition of Tensegrity) 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.
Use invariant-length materials to properly test compliancy versus rigidity
(Nov 14, 2015 repeated from Modular Tensegrity Design ) When I am building a tensegrity using elastic cord and fixed length wooden struts, it is easy to add prestress to the structure by stretching the elastic cord as it is assembled. This works well for rapidly prototyping tensegrities using these materials but does not allow a real world test of compliancy versus rigidity using invariant length materials. With elastics I end up with a structure that is too compliant to be useful as a robot. (unless it is a small robot).
Highly-elastic tension members become stiff when prestress is high
(Aug 7, 2017) I have built models with a great deal of compliance i.e. elasticity built in. The more stress I build into a tensegrity the higher the strain or deflection of the resting length of the elastic. But there comes a point when the elasticity of the tension members allows for no greater stress in the system – the members have reached their maximum stretchiness. At which point they begin to behave as if made from very stiff members. If you build a tensegrity using steel cables there is for all intents and purposes no change in the resting length when put under stress. Resting length and stiffness are the same more or less for steel cables, spectra line or any tension member that does not have a modulus of elasticity. Interestingly though, no matter how stiff the materials (i.e. how little deflection) both tension and compression members are made from and no matter how much stress the entire structure is subject to (akin to over inflating a tire) a tensegrity will always have some degree of compliance built into the geometry. A six strut expanded octahedron tensegrity is always going to deflect a little when pushed no matter how high the tension.