Emulate Biological Systems by Modeling Force Vectors, not Anatomy

Tom models force vectors instead of exact anatomical features. Tensegrity in the body is not visible at a gross level.  The focus in tensegrity biomimicry is on creating tensegrity forms that are functional kinematic structures based on anatomic observations. Properties such as symmetry, chiral organization, point, edge and face bonding, and optimal actuation are more of interest than descriptors such as torsos, legs and arms. Crude ‘low res’ tensegrity models have to stray far from anatomy in order to be effective.

Context: Tom Flemons Archive

A model of force vectors

(Oct 17 2015) It dawned on me that how tensegrity operated in the body was considerably more subtle and nuanced than I could reasonably expect to model with dowels and elastics.  I realized I was probably modelling force vectors and not exact anatomical features with my models. i.e. what it took to build a self stabilized two or four-legged tensegrity model was pretty much what it must take to stabilize a body in space. Modelling anatomy as a tensegrity should give a rough approximation of what forces and vectors need to be accounted for.

The models are explorations

(Nov 6, 2015) What to do about all these files I have? I feel they need annotation so people understand where they fit in the spectrum of exploration. I don’t want people to misunderstand and assume these are given forms – they are not, they are explorations with a lot of false starts, It would be easy to criticize them (if you were for example a biomechanist or engineer or anatomist) if you misunderstood the attempt. And unfortunately because so few people have a deep enough understanding of tensegrity, they will almost certainly be misunderstood as attempts to ‘explain’ human anatomy etc. From the robotic side – engineers will probably not understand the criteria that are being tested because they don’t think in terms of nonlinear systems where local effects have global consequences. From a traditional approach appendages are attached to a torso/chassis and a lot of effort is spent dealing with torque, shear and additive forces that travel across multiple joints. The chassis is considered to be a fixed structure which lever arms are then attached to. Compliant (meaning flexible) joints and structure are considered problems which have to eliminated whereas in tensegrities they are the primary features that are to be managed quite differently.

Tensegrity in the body is not visible at a gross level

(April 12, 2015) The more I tried to adapt tensegrity to the body the more I realized that the models I made were misleading and incomplete. Tensegrity in the body is not actually visible at a gross level – it happens in the interstices between muscles and bones – in the chaotic wrapping of fascia that somehow transfers forces both tensional and compressive and is such a complex process that models don’t and can’t do it justice. Over the years I have built thousands of tensegrities and hundreds of them were iterative attempts to model anatomical structure. I have to keep a copy of everything I make so I can remember how I built it – this means I have large boxes of dusty floppy old models that I drag out now and then to remind myself how I was approaching the problem years ago. Some time ago, for example, I went and pulled out half a dozen different attempts I’ve made to model a foot and I found to my surprise some solutions I had forgotten about. Thankfully I had saved them…But all of these models are abstractions from the body. I’ve come to the conclusion that they are going to be more useful in a field like robotics or prosthetics, where simplified structures are normative given the limitation of materials and technologies as they now exist.

Tensegrity happens at a microscopic level whereby bones meet and are suspended by fascial bands – from our perspective we don’t see this level of connectivity and it looks a lot more like levers and fulcrums – muscles and bones. It is analogous to the way quantum mechanics and relativity subsumes classical physics – at the day to day level where we live quantum effects are not evident and Newtonian physics can provide useful if not exactly correct answers. Similarly classical engineering principles appear to provide sufficient explanatory power to how structures operate – except in the case of biology mistaken assumptions do matter – e.g. orthotics often make foot problems worse as do ‘correcting’ scoliosis in teenage girls by inserting support rods alongside the spine to straighten things out.

Tensegrity biomimicry

(Oct 24, 2014) I am presently preparing a paper based on tensegrity biomimicry which should be completed by December. This term is different than biotensegrity in that the focus is on creating tensegrity forms that are functional kinematic structures based on anatomic observations. Biotensegrity is more concerned with identifying the features of connective tissue that operate in the body tensegrally. I am interested in investigating anatomic structure for clues to building analogous tensegrity forms without being constrained by the need to closely conform to a mapping of anatomy. In other words I can identify, for example, that the pelvis in a quadruped or biped is a bilaterally symmetrical structure involved with transmitting forces from the torso through its structure to the legs and vice versa without being concerned about its other functions in biology which include cradling the viscera, or facilitating child birth. I hope to abstract out the essential geometry in any pelvis and to derive an optimal form that I can plug into a kinematic tensegrity system composed of a number of tensegrity elements. In the paper I plan to identify optimal component forms and to account for how I arrived at their structure. Properties such as symmetry, chiral organization, point, edge and face bonding, and optimal actuation are more of interest than descriptors such as torsos, legs and arms. Obvious applications include platforms for prosthetics and robotics, but also exoskeletons and wearable suits for hostile environments such as space or deep-sea diving.

Inspiration from anatomical forms, but not a model of biological structure

(Feb 23, 2014) I think it is very worthwhile to attempt a computer modelling of a tensegrity biped or quadruped. Perhaps the difficulty in finding alignment with various points of view here is to do as you suggest and not pretend that what is being modelled is an exact replica of biological structure. In fact I have been moving some distance from this goal over the course of my explorations. Instead I am asking a different question with a different goal in mind which sounds closer to what you propose: Is it possible to design a functioning self supporting robotic quadruped or biped that is tensegrity based and takes its inspiration from anatomical forms? This is different from the attempt to directly model biological form at high resolution, in that we do not at present have the requisite materials or actuators much less the control and feedback software systems to handle the undoubtably complex signal/response systems that are integral in biologic systems. (Vytas has pointed out that electro-activated polymers which contract under current and then return to their resting state when the power is turned off, may qualify in the future as useful actuators embedded in the tensegrity tension net.) I think the biotensegrity inquiry is quite likely splitting into different domains at this point. Whether they will come together again in the future is an open question.

In the clinical realm the concern is – does a biotensegrity description of biology give better powers of intervention and prescription? From alternatives to invasive surgery to correct anatomical injury, to better clinical practises in relieving pain and preventing degenerative disease, to the design and implementation of new prosthetic devices, this line of endeavour is biologically focused and doesn’t rely directly on functioning models of the processes in question.

(June 22, 2015) Instead of asking if Biotensegrity is true, a better question is, is it a useful description of bio mechanical forces? To answer that question, tensegrity must show a benefit – a better description should equal a better prescription. Can a diagnostic tool be developed around a tensegrity model of the body? Does it predict force transfers better than other models? Does it suggest a way forward into new therapies or new technologies? I think some of these computer tools that are being developed could be adapted to help answer those questions. My job is to build plausible enough models (complex enough to be useful but simple enough to be comprehensible) that can act as armatures to test the principal against.

(April 4, 2018) I have rewritten the paper ‘How Tensegrity Models Reality‘ and added new explanations. I rather like this paper as it talks about a topic I’m interested in – how metaphors influence our conceptual frameworks.

Tensegrity for prosthetics, exoskeletons, robotics

(Feb 23, 2014) Prosthetic devices, and exoskeletons based on tensegrity straddle the divide between biologic concerns and robotic ones. I use biology as the starting point but proceed without constraint from there. My first assumption is that biology is tensegrity based. My second is that Nature parsimoniously selects for optimum form and function and that tensegrity geometry qualifies as the sin qua non means to achieve least energy efficient ambulation and durability (among other things). My third assumption then follows from this – that it should be possible from close observation with a tensegrity perspective to understand somewhat how nature ‘does the trick’ and from there to abstract out key elements of design and attempt to replicate them in compliant structures which can be animated using actuator algorithms.

(Nov 6, 2015) I think I struggled for years with a not clearly defined goal – was I trying to model anatomy closely in a one to one correspondence or was it more abstractly modelling force vectors? Did the models have to look like anatomical structure or just provide tensegral equivalences that could support and distribute forces in the same way? That depended on whether I thought I was trying to build prosthetic devices and human looking robots. e.g. how important was it to build a tensegrity foot that fit within the envelope of a real foot? Also at the beginning after lots of talking with Steve [Levin] I began to see the possibility of filling in the gaps in his generalized theory with actual pragmatic based models that were specifically intended to emulate the body. Steve didn’t seem too keen on the details. He was happy to have a few models which better demonstrated his thesis (like the spiral mast) but he never critiqued the way I went about building the models or the logic I followed (as outlined in my paper The Geometry of Anatomy). So gradually I drifted away from the Biotensegrity realm and shifted my attention to robotic applications. In a way it was the same concerns. If we are intent on building a quadruped, then clearly jointed legs are needed and some kind of coupler that connects the front end and the back end must be considered which ends up being some kind of spine/scapula/pelvis contraption. Convergent evolution I suppose… But in another way focusing on robotics helped clarify a different goal. Given the state of material science and available actuation systems plus computational strategies it became clear that for the forseeable future these tensegrity robots were going to be considerably simpler that biological structures.

So it comes down to making good design choices that keeps as many options as possible on the table. Because tensegrities have feedback loops built into their very structure, a lot of the computational energy that it takes to organize and keep track of forces in a traditional robot can be handed over to the passive tensegrity modules. So for example  actions like foot fall or impacts from outside can be absorbed and forces transferred in a passive way without the need for a lot of extraneous control systems. At least that is my working theory… Not until we can simulate a reasonably complex enough quadruped in NTRT will we know if this a reasonable assumption.

Cannot build a tensegrity skeletal model using bones and bungee cords

(Dec 1, 2015. Tom responds to the question “Do you think it is possible to build a tensegrity skeletal model using bones and bungee cords instead of dowels and elastics?”) I am pretty sure this is not possible for a bunch of reasons. Muscle/tendon attachments to bones, which is all such a model would represent, is an inadequate model of tensegrity anatomy. The amount of prestress such a model would have to possess to self suspend (he wants it to stand up on its own) is beyond the ability of the available materials and attachment methods. Even my hobbit-sized dowel models, which are considerably lighter than a full replicate plastic skeleton, require higher prestress than I can manage with the materials and methods to even approximate self support. The only way tensegrity models anatomy is through a sophisticated systemic application of the principle at all levels of materials i.e. fascia modelled as woven tensegrity masts wrapping bones and muscles.

How Tensegrity Models Reality (Sept 2018) For example living structure may be usefully described as organized fractally in similar ways to cascades of nested tensegrities operating collectively at multiple scales from atoms, molecules, tissues, organs and bodies but even further into groups of individuals or even groups of species operating within complex systems of ecologies. It should be clear but often isn’t that this is a completely different and new metaphorical view of life that is far removed from reductionist biology or clockwork biomechanics. But it is still a metaphorical construction and shouldn’t be confused with the actual structure of the body at least at the level of structural anatomy. There are no struts and cables filling the body and bones cannot be reduced to simple compression members with muscles and ligaments acting as  the tension network. A model of the spine using stellated tetrahedrons can look on the surface to be a close approximation of the actual mechanism of the spine but a closer look reveals that there are no exact equivalences to struts and cables. In fact it looks as though the fascia which wraps every structure in the body in multilayered strands could be acting as a compression sleeve helping the spine achieve stability and flexibility. This can be modelled using tensegrity principles (see my paper Bones of Tensegrity) but it is a far cry of struts and cables.

Summary from 2015: modelling force vectors in the body – not exact anatomical structure

(Nov 15, 2015) For me, tensegrities were never just eccentric objects. Even as I was seeking practical uses for tensegrity I saw that somehow they conveyed in their structure hidden implications for diverse fields. In terms of engineering Fuller was right – tensegrities embody the coordinate system used by the universe at all scales. But also they perfectly represented fundamental ways to understand the synergetic operation of complex systems – they were ecological structures and by playing with them for 35 years, by building them, adjusting and fine tuning them, I have been given a haptic education and an intuitive understanding of object/events like super position, orbital rotation, symmetry, dispersion of forces, redundancy and feedback.

When I contacted Steve Levin in the late 90’s he was just beginning to finally get some traction among some of the disciplines that biotensegrity mattered to (e.g. biomechanics, movement therapies and body work). My immediate interest was of course to see if a consistent and plausible argument could be made for representing structural anatomy as tensegrity structures. It seemed to me that while the fractal nature of tensegrities was well understood by then, the leap from cell, tissue, organ systems to complete anatomical structures seemed a possible difference in kind rather than just degree. Livers for example don’t have joints so a modelling system that describes pneumatic and hydrostatic structures like tensegrity may be a good fit. But when it comes to articulating structures a new kind of description is needed. A joint in a tensegrity is a failure of the envelope – a disjoint as Jaap Van der Wal points out. Making tensegrites that articulate without going into failure is a major challenge.

For a number of years I really tried hard to find a good fit between basic tensegrity geometries and articulating bodies without being too atomistic or reductive. Of course a good model is one that is reductive enough to be wieldy but not so simple as to give useless outputs. I was trying to find one to one correlations with anatomy and specific tensegrity forms. But also I grew to realize that my models were at least a first order abstraction from actual bone and fascia, and I was really modelling force vectors in the body – not exact anatomical structure. From that came the realization that tensegrities actually were models of how mass accumulates and orders itself in a very similar manner that Wolff’s law operates in the body. In other words all structures could be modelled as tensegrities and doing so could reveal the hidden force vectors embedded in structures. I could model the neck of the femur for example as a tensegrity that illustrated the lines of tension operating within the bone. In a similar way I could model a chair or a table as a tensegrity and in doing so discover the minimum tension and compression elements and their arrangement to define a stable structure.

I moved from a biotensegrity position to what I’ve called Tensegrity Biomimicry. I can borrow from biology what is generally useful in creating ambulating entities and try to abstract out equivalent tensegrity structures based on function more than form. But a robot doesn’t need a digestive system and maybe a head is superfluous as well. However I suspect there will always be a market for human simulacra so the challenge is still there – to design a bipedal robot with a human profile.

In the last few months I’ve had some insights which I’m beginning to write about. One is the recognition that it may be possible to redefine lever and fulcrum linkages in tensegrity terms. I see levers clearly at play in the body, yet without fixed fulcrums classical mechanics does not appear to apply to human anatomy. Levin and others (Gracovetsky) have made it clear that using accepted bio-mechanical formulations, the tissues in the body should not be able to withstand the forces on them ≠ and yet they manage just fine. How tensegrity works at the scale of anatomical structure is no small matter but to date most attempts have remained general and abstract. I think that every compression member in a tensegrity acts like a lever which revolves around a fulcrum that is not fixed and indeed dispersed and created by the surrounding structure. Levers can extend past joints – when a pitcher unwinds for a fast ball his entire body crossing many joints becomes an extended lever that revolves around an ever changing set of fulcrum arcs. In this expanded sense levers and fulcrums are both contingent and provisional.

A second insight was to realize that describing tensegrities in terms of tension and compression elements is limiting and not a complete description. For one thing it does not account for the chiral rotations built into their fundamental structure. Except for tensegrity prisms which are in a sense monads because their handedness is absolute, most tensegrities contain within them clockwise and counterclockwise rotations which additively cancel each other out. In a six strut expanded octahedron tensegrity there are eight triangular facets formed by the ends of any three struts spiralling around each other. Four have a clockwise rotation, four rotate counterclockwise. Tensegrities are dynamically stable partly because these rotations absorb energy by acting like springs which oscillate in and out to restore balance. This led me to investigating the nature of centripetal forces whereby a continuous force acting upon an object compels it alter its motion and changes its accelleration. Gravity is a centripetal force that describes the relationship between discrete bits of matter and causes them to fall into elliptical orbits around each other. Newton’s three laws of motion describe this very well. It occurred to me that the tensional envelope that bounds a tensegrity acts like a centripetal force field exactly like gravity. Objects in orbit around larger orbits tend to find stable configurations which can last for a very long time presuming other forces like friction are absent or minimal. I wondered if tensegrities could be looked at (at least metaphorically) through the lens of orbital mechanics. [This text is continued on the orbital mechanics page]

Summary from 2017: Crude ‘low res’ tensegrity models have to stray far from anatomy in order to be effective

(Sept 11, 2017) The problem is quite complex partly because I deliberately had constrained myself to modelling human anatomy as exactly as possible. This in turn was a result of the claims biotensegrity was making and continues to make that structural human anatomy can best be described as a tensegrity system. My thinking has changed considerably over the past 18 years (I started working with Steve Levin in 1999) and even going back to 1985 when I built a working model of a tensegrity based spine. Initially I took the claim at face value and really attempted to shoe horn anatomy into the shape of tensegrity forms. This I now believe is the wrong way to go about things. It reverses the scientific process and requires the ‘facts’ to fit the theory rather than the other way around. It may be that tensegrity is the best explanation for how structural anatomy operates but at this point evoking tensegrity as an all encompassing explanatory principle is little more than a metaphor. How the body actually works structurally happens at a scale and complexity that is far too subtle to be modelled even approximately by crude ‘low res’ tensegrity models.

Trying to model the anatomy of the spine

(Sept 11, 2017 continued) For example when I looked in detail at the shape of individual vertebrae and how they relate to each other I slowly realized there were no equivalent tension elements (ligaments, muscles) that corresponded to the wiring diagram of a set of stacked stellated tetrahedrons arranged as a tensegrity mast. Further, the only vertebrae that could be even said to have the same or similar geometry to a stellated tetrahedron are thoracic – cervical and lumbar vertebrae don’t fit the model. I eventually refined my thinking in my paper ‘The Bones of Tensegrity‘ to attempt to grapple with this problem and concluded that fascial ‘sleeves’ in the body that wrap everything including joints may bear a resemblance to helical tensegrity masts and thus could support the compression loads that travel through the body.

Trying to model the anatomy of the pelvis

(Sept 11, 2017 continued) To further complicate matters, I think I have identified geometric properties of the pelvis (that can be modelled as class 2 and class 3 tensegrities – both halves of the pelvis resemble tetrahedral elements that are hinged at the pubis and sacrum and the space between them forms an octahedral cavity which in combination describes an all space filling truss system known as a octet truss). But again it’s quite a stretch to then attempt to model the pelvic system as a low res tensegrity model. I’ve done my best to show how it might work but to actually build a working model that bifurcates and distributes forces from the torso into the legs is a daunting task.

Reasons for choosing a 4 fold prism for modeling the foot

(Sept 11, 2017 continued) So where does that leave us? Well, I think it is possible to make do with low res crude models that might have a real advantage over traditional robotic constructions which attach and hang lever arms off of a solid chassis (torso). It may be possible to make do with crude models that emulate some of the functions of the body. If and only if, the goal is to build simulacra of bipeds or quadrupeds that would fit inside the footprint of the actual shape of a working body (for purposes ranging from prosthetics to androids that resemble us or four legged creatures) then we have to accept some limitations and short cuts that stray far from actual anatomy. The foot is a case in point. I have chosen the core of the foot to be a chiral 4 fold tensegrity prism and then attempted to add on features that serve the function of tarsal and metatarsal bones. I could have started with another basic form such as an expanded octahedron tensegrity or a 3 fold prism but I chose the 4 prism for several reasons. First it is chiral, that is there are two versions available – a right handed and a left handed rotation. This seemed to fit well with the chiral nature of our extremities. Second a 4 fold prism allows a wider attachment face to connect it to a leg. If a joint is to have a smooth range of motion and controllable degrees of freedom then a square polygonal face allows for the possibility of a revolute hinge to operate more easily because it can mate with a second square face from the descending leg (which would then also be modelled as a helical 4 fold tensegrity mast. Third, a 4 fold prism allowed me to account for the way the talus (which is the bone the tibula/fibula interconnect with) distributes forces to the calcaneus (heel) and the rest of the tarsal bone forward of the leg. Pronation at foot fall requires choosing the correct chiral form to get the proper rotation to occur.(see attached image for my best guess at this).

But then I run into problems because there is no easy way to model the rest of the tarsals, metatarsals and phalanges as a tensegrity. At some point the foot model devolves into a linear series of connected long bones or struts that have little relationship to a tensegrity structure. Which brings me (finally) to the model Dorothea presented to you. This was one of many attempts to model more of the foot as an actual tensegrity. Here the rest of the tarsals are represented as a section of a 4 fold helical mast somehow stuck onto the base prism and then again a bunch of struts are lined up and stuck on underneath to represent the metatarsals (toes). Still not very satisfactory because while I can fake it in a demo model – in a real working model the toes would be radically unsupported and need a lot of cross linked tension lines to restrain the degrees of freedom. I suppose this is all possible but I wasn’t satisfied that this was the best alternative. Following the inner logic of tensegrity construction demands that the forces a model has to bear must be tensegral, that is, there must be no forces carried across compression members. For the purposes of expediency this may prove to be too difficult to achieve and will require hybrid forms that accept that the long bones of the foot are wired together as lever arms under compression. I am hoping that PmPm [PushMePullMe] may help resolve these types of questions – can the model as it exists actually support not only itself but the weight of the body bearing down in a gravity field? What is required in terms of additional tensioned support lines?