The Need for Levers with Floating Fulcrums

Traditional fixed-fulcrum levers are inadequate for biomechanical modeling. In nature, levers form as needed, extend as needed, and have floating fulcrums. The fascial weave that wraps and passes over each joint can account for why our joints are so much stronger than third class levers should be.  The bones, muscles, ligaments, tendons and fascia form a networked array of floating interconnected levers operating without fixed fulcrums. So to sum up – vertebrate anatomy may be viewed as an articulating tensegrity structure with several layers – at the core are the bones acting as fulcrumless levers being augmented by fascial wraps that act as networked first class levers.

Context: Tom Flemons Archive

Traditional fixed-fulcrum levers are inadequate

(Feb 22, 2014) If we look closely at what a body achieves, is it possible to describe events operating in the body in a way that doesn’t invoke lever arms, fulcrums, moment arms, torque, and shear? Probably but it won’t be easy. Such a system would have the following characteristics:

  • There are no fixed points in space that define the origin point of a 1st, 2nd, or 3rd class lever; rather there are floating zones of low inertia that mediate the fluid transfer of forces that propagate throughout the entire body all at once all the time. In other words there are not origin points but transition spaces which forces move through.
  • Bones converging but not touching are held in suspension by a tensile net that is universally connected to every part of the body including the bones, muscles, and internal organs. This tensile net or fascia mediates local forces by global distribution outward and inward to the entire anatomical structure, so it is not possible to define isolated forces or predict force transmission using simple lever models. A force (lifting a weight) travels along a bone through a muscle around a joint, along another bone, through an extension of the same muscle train into the torso or through the pelvis. But the entire chain of events is mediated by a fascial network that interpenetrates and encompasses everything such that the forces become diffused and capillaried through the entire body. Within normal ranges of motion there is no torque that is unresolved and no shear forces to tear the body apart. It is only in high velocity impacts where the design parameters described by tensegrity fail, the body could be said to behave as a set of levers and fulcrums.
  • All material in the body is variously in tension or compression and it is not possible to delineate and label bones as solely compression elements or muscle spindles as solely tension members. In my paper The Bones of Tensegrity, I endeavoured to show how it is possible, for example, that fascia-wrapped muscles and ligaments can act as compression sleeves that surround joints and keep them floating and not touching. Similarly bones clearly are not always in compression and should not be treated as solid bodies. Rather they are  compliant tensegrity constructs themselves.

Tensegrity Levers (July 2015) Levin has clearly pointed out the flaws in the standard biomechanical model which assumes the body is full of levers pivoting around fixed fulcrums (joints) with individual muscles pulling across the joint from discrete bony attachments on either side. If the arm for example hinged at the elbow was just a simple third class lever, the mechanical advantage is considerably less than 1.0 and it’s hard to see how any significant weight could be held in the hand without tearing muscles or wearing down the joint due to excessive forces concentrated at the joint. Borelli, the father of biomechanics noted that the (assumed) levers in our body for the most part enable us to achieve a wide range of motion at the expense of a reduced mechanical advantage. 

Furthermore it’s axiomatic of a lever that there be a fixed fulcrum for it to operate against. We can secure a joint (e.g. elbow) and  (supposedly) isolate a specific muscle (bicep) to lift a weight, but most of the time our joints are fluid and unfixed in space, so how can they be acting as fulcrums for bone levers? This make it hard to accept the standard bio-mechanical explanation. Levin’s point is simple, no fulcrums means no levers. So he’s asking us to throw out 500 years of biomechanics and replace it with a better biotensegrity explanation. 

Which is fine I suppose, except biotensegrity doesn’t yet have a body of math attached to it that we can work with to predict and solve kinematic equations. (we’re getting there – the NASA TensegrityRobotics Toolkit software – NTRT is helping model complex tensegrity systems) lf people involved in clinical and scientific research are asked to throw out a bio-mechanical model which is outdated, there has to be something useful to replace it with. Besides, it is still difficult to understand how the body operates without invoking levers. Even if the fulcrum side of the equation is problematic, the way our limbs fold and extend certainly look a lot like levers. The way we rise up on our toes certainly seems to be a second class lever operating. And yet while muscles may insert via the periosteum across a distance and not at a single point, the mechanical advantage still seems inadequate to the task of lifting a significant weight any distance. 

So what is another way of looking at this? Over the years I’ve used the term floating fulcrums occasionally without giving it much thought. How can there be a lever operating without a fixed fulcrum that provides the resistance? The body is structurally a closed system – there is no fixed point that provides leverage to do work and any point in the body can contract to generate movement. And yet we are much stronger that we should be given what we know about simple machines. Rather than discard levers I want to suggest something different. I want to describe a type of lever that doesn’t require fixed fulcrums. If we could then also show a way that a tensegrity linkage could do the same work as a traditional lever or a mechanical linkage then we are describing equivalent structures that answer to the same kinematic equations.

In nature, levers form as needed

(Sept 11, 2015) In terms of evolutionary selection it’s likely that nature being parsimonious would choose the most efficient way (tensegral) to use material to build biologic structures. This seems to be clearly the case at the cell, tissue, organ level, but it is a jump in logical type to apply the same assumptions at a structural anatomic level. (i.e. it is not directly fractal) This suggests that it is incorrect to reason from smaller envelope structures which are not jointed (e.g. there is no liver joint) to articulated structures with endo-skeletons and linear appendages. The tensegrity system operant at the level of anatomy relies on the envelopes  i.e. the fascial connective tissue) wrapping at multiple levels the bones which are relatively incompressible. Bones are equivalent to the hydrostatic skeleton of invertebrates which provide pressure that the tensional matrix pulls against. Where two bones form a joint and hence a lever, the tensional integrity is continually dissolving and reforming as the joint’s range of motion changes, in order to augment the joint and facilitate a smooth transfer of forces across the joint.

This approach relieves us from arguing that there are no levers in structural anatomy which is clearly incorrect. Rather, levers can form contingently as needed (by stiffening one or more connected bones) with the surrounding soft tissue matrix stiffening in response and thus acting as provisional fulcrums.

To account for our strength, levers must extend as needed

(July 23, 2015) If the arm for example is a kind of third class lever with a floating fulcrum what does that imply? Well if it’s a third class lever (where the load is on one end, the floating fulcrum is on the other and the force applied is in the middle somewhere – the bicep insertion) then the mechanical advantage is less than one. This gives increased range of motion but isn’t very strong. From that observation (made by Borelli) two things follow – the materials our bodies are made from are extremely strong and can accept and cope with large forces and/or there is another system operating that augments the lever and lets us lift heavier loads than should be possible.

At which point I made a leap which I didn’t explain well enough. If levers that are interconnected in some way mutually support each other, is it possible that such a networked system can do additional work that a single lever cannot? A spiral tensegrity mast is a network system that can support weight and do work without a core. The way it is woven together could be seen perhaps as a series of first class levers (teeter totters) where the output at one end of any lever acts as a floating suspended fulcrum for an adjacent lever and so on. The network then acts as complex support system that maybe could be analyzed using engineering math. Some variables would need to be introduced to account for things like slop in the system, feedback loops, dissipative force vectors (the output of one bar is the fulcrum of the next bar which in turn affects adjacent bars and rapidly spreads (dissipates) the load to the entire structure. But it may be possible to write equations that could describes this process.

The next jump is to wonder if our fascia acts as such a system that augments the core skeletal system and this is pretty much the argument I made in my paper The Bones of Tensegrity. If so then there might be a way to see the articulating vertebrate anatomy as consisting of various kinds of 1st, 2nd, and 3rd class levers operating by means of floating fulcrums and  further augmented by a complex 3 dimensional network of first class levers embedded in a fascial matrix. This last part is hard to imagine and will take some effort on my part to spell out – essentially I note that if a facial matrix acts in ways similar to a braided rope (see Snelson’s paper Tensegrity, Weaving and the Binary World) then with enough layers of fascia wrapping muscles, joints and bones there exists the geometry hidden in this complex weave that allows the entire system to act as I describe.

So to sum up – vertebrate anatomy may be viewed as an articulating tensegrity structure with several layers – at the core are the bones acting as fulcrumless levers being augmented by fascial wraps that act as networked first class levers. It is the enveloping fascial matrix that makes it possible for the bones to act as levers without fixed fulcrums so everything depends on everything which is pretty much the definition of a tensegrity structure. The term ‘augmented fulcrumless lever system’ is the best description I’ve come up with so far…

Changing prestress allows joints to be alternately stiff or yielding

The Bones of Tensegrity (2012) The fascia is thus more than just another layer of compressive wrapping. When the equivalent of lateral bands triangulate the complex mesh of the fascia, a condition of pre-stress is formed which will cause the bones on opposite sides of a joint to separate and create a gap that is not completely supported by cartilage or joint capsules. The fascial sheath under lateral constriction and direct loading becomes more rigid and acts as an exterior compression stent or brace surrounding the joint. Release the compression force which supplies the pre-stress and the joint immediately becomes fluid and recovers its range of motion and degrees of freedom. This becomes a tensile solution to a compression problem. When any oblique wrappings contract and shorten they also somewhat exert this lateral banding force which shortens the tissue and carries the bones of the joint apart from each other. It may seem counterintuitive that tensile tissues can act in unison to create a compression structure but that is what the geometry indicates. Just as bone can carry a tensile load, so fascia can support a compression column. There exists more than enough beneficial geometry to keep the bones floating and suspended in the fascial net. As fascia has been shown to contract and relax in short intervals and as the contractions needed are small adjustments relative to the whole, this explanation can account for a joint that is alternatively stiff and yielding. It also explains how the compressive forces bearing down on a joint can be mediated so the cartilage is spared the constant loading involved in any activity.

Fascia manages forces tensegrally by means of a mesh that acts like a cluster of first class levers

(Aug 5, 2015) We discussed how what I’m now calling ‘contingent fulcrums’ are provisionally assembled as needed in the body, how segments can stiffen to extend the lever’s length and engage ever greater parts of the body as loads get larger. A small weight in the hand requires primarily a fulcrum maybe at the wrist to manage the forces but a further stiffening of the arm shifts the fulcrum further into the body – perhaps the elbow or shoulder if the weight increases. It would be a highly fluid affair that is managed by the fascia. Serge Gracovetsky notes in his lecture at the first fascia conference that e.g. in a dead lift the fascia is managing 70% of the load and the muscles the remaining 30%. He briefly mentions tensegrity as the mechanism that supports the body but doesn’t go into any detail. He also has no problem invoking levers in his argument.

I’m making the case that the fascia is managing forces tensegrally by means of a complex 3 dimensional mesh that acts like a cluster of 1st class levers linked in a cybernetic feedback system. The mesh doesn’t look like a tensegrity but I’m arguing that it acts like one. There are no struts but there is a hydrostatic equivalent of compression features that make up the equivalent of a tensegrity mast surrounding joint complexes and attached muscle systems.

Tensegrity cannot replace the joints of land based animals of any significant size

(Sept 1, 2015) Gross articulations found in revolute joints cannot be modelled as tensegrity structures. Tensegrities are prestressed structures that model envelopes not interiors. Whether the structure is filled with air or liquid, or modelled as such, the interiors are non-differentiated (at least in terms of structural relevance). Complex articulations are not part of the definition of tensegrities. A failure of structural integrity (a broken grass stem etc.) creates a (dis)joint that rapidly fatigues and disintegrates if flexed multiple times. That’s clearly not how animal joints work. There are constrained revolute joints found in exoskeletal creatures (i.e. jointed crab claws) which have only one degree of freedom and are rigidly bound by hard (read stiff) shells. In animals with an endo-skeleton, tensegrity stability constrains and directs the forces that pass through the joint by means of the fascial weaves that wrap it. A tensegrity mast based upon helical compression vectors can model how this support system works but cannot replace the joints of land based animals of any significant size.

Relax a tension member to elicit a lever action

All struts in all tensegrities are potential levers held in dynamic suspension by a network of tension

(June 16, 2016) Relaxing any one tension member in a six strut expanded octahedron will elicit a lever action.

(June 7, 2016) Struts that are suspended by tension members are each actually potential levers held in check by the network of forces held by all the other struts and tension members. This can be shown by cutting a tension member which causes a strut to spring outward from the structure exactly like a lever would if there are unequal forces on either side of a fulcrum.  The sketchup image [top left] shows the progression from classic levers to tensegrity levers. All struts in all tensegrities are potential levers held in dynamic suspension by a network of tension. We can now make the case for how our bodies can support forces at the extremities. We can lift weights because the attachment of the bicep (for example) is augmented by a fascial mesh that extends the attachment point down the arm and moves the mechanical advantage to greater than one.

There is no difference between Skelton and Snelson tensegrities in terms of levers – heterarchies and hierarchies really make my argument. Levers are acting at all fractal levels in heterarchical and hierarchical ways. I suggest we call them potential levers and contingent fulcrums. For a tensegrity to articulate or hinge across a joint, some portion of it becomes identified as the lever and the rest of the structure substitutes for the fulcrum. We can constitute levers of any length in the body depending on what is needed. If we need to reach for something the lever becomes an extension of the arm, shoulder, torso and opposite leg depending on how far we have to stretch and how much the object weighs. The rest of the body functions as the extended fulcrum for the purposes of any specific motion. Using this argument saves the science and math of 500 years of biomechanics and updates it with tensegrity principles.

A lever is not necessarily an open kinematic chain

(June 16, 2016) I showed how a lever is not necessarily an open kinematic chain (OKC) but can be linked in a circle to other levers and that at least one and maybe more fulcrums can be removed and the structure still does work (remember the movie I made showing this). The idea here is I’m reasoning by analogy that in a tensegrity system e.g. a helical mast is composed of dozens or hundreds of potential levers and that relaxing triangulation of a section of the mast creates a disjoint which can be controlled and modulated to create a larger lever (think long bones hinging the elbow or knee). I am speculating that because each tiny potential lever in a mast has an influence on its immediate neighbours the overall effect is to spread the attachment point along the length of the mast to change the mechanical advantage. So instead of the bicep muscle pulling across the elbow creating a third class lever with a mechanical advantage less than one, it is possible to see how that pull is spread further down the arm and thus improving the mechanical advantage. Because the attachment is spread myofascially via the periostrium to the entire length of the bone it may be possible to see how our tissues can support the forces acting on them (e.g. a heavy weight in the hand) by as Vytas might put it providing multiple tensegrity configurations as needed.

(Nov 22, 2016) I think that there is something wrong with the whole notion of kinematic chains when it comes to tensegrities. Chains imply serial connections between bodies – linear connections between solid bodies. In tensegrities we see bifurcating connections where forces divide and follow multiple paths so I suspect a whole new way to describe the kinetics of tensegrities is needed.