In the pelvis model, ilium and sacrum are modeled as a section of an octet truss. A leg model has tensegrity prisms linked to create a controllable hinge with no hyperextension. The entire foot is modeled as a distorted section of a 4 fold helical tensegrity mast. An arm model demonstrates how a tensegrity ‘sleeve’ (based upon a spiral tensegrity woven mast) could wrap around two rigid bars representing the long bones in an arm to approximate a right angled joint like the elbow.
Context: Tom Flemons Archive and Modular Tensegrity Design
Tweaking the models
(Oct 16, 2015, repeated from page Modular Tensegrity Design) Designing and building tensegrities at this stage is still an art more than a science. The basic construction proceeds from a catalog of modular shapes but rapidly morphs into something unique. For example building my leg, the tensegrity prisms are altered in length and proportion on the fly. How they are hooked up to each other affects their overall proportions. Balancing all of the tension components is really done by feel and observation, a tweak here and a tweak there to get the thing looking right. In other words, an approach that allows one to approximate things quickly may be more helpful than a numerical precise methodology. This is especially true when building an asymmetrical chiral form like the foot. As I build one I don’t know what length the struts should be or what amount of tension I need to apply. What I am aiming for is four struts which contact the ground evenly and their opposite ends forming a perfect rhombus parallel to the ground at some distance from it. (which I can then more easily attach a lower leg prism to). This is not as easy as it may appear.
Torso models
Youtube video (Sept 4, 2012) This is a tensegrity representation of the torso demonstrating basic movement patterns including gait, rotation, flexion and extension and also expansion and contraction. While this iteration is elementary, all the components are present that someday will be present in an autonomous robotic biped.
Tom provides additional information about this model on his web page Biotensegrity Models: This model puts together the torso with the pelvis and femurs. The QuickTime video illustrates a human range of motion including flexion, extension, lateral bending, rotation and walking. This model represents the minimum tensegrity structure necessary to create an anatomical form analogous to a human being. Tom’s reference sheet discusses torso modeling and the range of motion of this model.
Click on this image to see the model rotating 
A simpler torso model
Tom provides information about this simpler torso model on his web page Biotensegrity Models: A simplified schematic model of the torso made in wood. A useful diagnostic tool that allows simple distortions in symmetry to represent fundamental dysfunctions in human anatomy and suggest possible therapeutic interventions.
Images of other torso models
Pelvis and spine models
Tom provides information about two pelvis models on his web page Biotensegrity Models: Tom’s reference sheets give details about the single tensioned pelvis model and the double tensioned pelvis model. He models the spine using tetrahedral and spiral vertebral masts.
A closer look at the pelvis suggests that ilium and the sacrum together can be usefully modeled as a section of an octet truss. (more…)
(Feb 22, 2014) My pelvis model is based upon direct observation of the shape of the ilia, (they are clearly tetrahedral) and their relationship to each other and the sacrum which together form an octahedral space and thus collectively is an octet truss. The dihedral angles in octet trusses are greater than 90 degrees (109.47) and thus forces are directed more efficiently through such a structure. Additionally tetrahedral geometry can have chirality so the forces spiral through the pelvis and thus up into the spine and down through the femurs into the legs. I model the ilia and sacrum as modified 3 bar tensegrity prisms coupled through three somewhat compliant joints, the pubis and the sacroiliac joints. When forces travel up from the legs through the acetabulum into the pelvis they are sent into a spiral pattern that describes a figure eight mobius movement as seen in the transversal plane which generates a sinous helical sine wave up the spine. At least that is the theory, and I would be very interested in seeing a computer modelling of this.
(Oct 9, 2015) The pelvis model [in the following video] uses three modified 6 strut tensegrities arranged as a tensegrity linkage that emulates the complex movement of a pelvis.
An earlier pelvis model is demonstrated and discussed at 26:35 in the following video. Tom explains that this is an abstract model, shows how it can move, and at 27:25 simulates injury by shortening a tension member.
Youtube video: Tom Flemons in conversation with Steve Levin. ©2005 Steve Levin
Other images of pelvis models:
Leg/foot models
See Tom’s reference sheet for the tensegrity leg/foot.
Youtube video (Sept 4, 2012) This bio-mechanical representation of the leg and foot employs articulating tensegrity joints. No compression components (i.e. bones) pass forces across a joint directly – All forces are mediated by a web of tension equivalent to the fascia that wraps and contains the muscles, ligaments and tendons and their attachments to the bones.
Tom provides additional information about this model on his web page Biotensegrity Models: The representation of the leg and foot combines several different tensegrity elements. The pelvic connection is indicated by an expanded octahedral structure. The knee joint is suggested by a modified octahedral tensegrity structure that transfers weight from the femur and torso above through a connecting joint that allows limited flexibility in one axis. An attempt has been made to model the forces transferred from the tibia to the talus and the calcaneus using a four strut rotational tensegrity (this model can demonstrate pronation to some extent). Additional struts are then added to suggest the tarsals and metatarsals. The photos illustrate the essential stability of the structure combined with flexion joints, and medial and lateral arches. The resulting form is stable and self-supporting yet none of the compression elements are in direct weight bearing contact. Tom’s reference sheet discusses the gait exhibited by this model.
Tom designed many different knee models. The tensegrity leg/foot above uses one of his early knee designs. A similar knee is demonstrated at 10:30 in the following video.
Youtube video: Tom Flemons in conversation with Steve Levin. ©2005 Steve Levin
A more complex design for a tensegrity knee
A 2015 leg model
(Oct 9, 2015) The leg/foot model strays far from anatomy to demonstrate that it is possible to link discrete tensegrity prisms in such a way as to create a leg that hinges in a controllable way with no hyperextension. Four fold prisms are employed because they create parallel tension lines at their poles suitable for attaching other prisms such that the hinge operates relatively freely.
(March 5, 2016) The foot by is a 4-fold tensegrity prism with extra elastic members and some dowels added to represent the tarsals and metatarsals. It is not easy to describe the process by which I chose this form or how I modified it. Briefly, because feet are chiral i.e. right or left footed I chose a tensegrity prism which is also chiral to represent it. There was some attempt to match geometry to anatomy and the attempt was to create a prosthesis that was the same size and approximate shape as a foot. If this isn’t necessary, there are many ways to model the role of a foot as a different tensegrity. The key seems to be to abstract out the important features (stability, resilience, controlled flexibility, ability to store and release energy etc.) of a foot and then design from there. I’ve done the same for the body. I don’t pretend I’ve ended up with a model of anatomy, rather it’s a way to model forces and their vectors in anatomical structures. There are no doubt several ways to do this depending on what geometry I choose. I don’t model individual bones or muscles- rather I see fascial wrapped tensegrity braids that can be represented as tensegrity masts. These can stand in for the long bones and their musculature.
(March 9, 2016) Also tensegrity forms do not equate with biological forms. My leg/knee/foot model acts a bit like our bodies (function) but the form is only slightly similar and in some cases not at all. My most recent leg/foot for example doesn’t have a femur, tibia or fibula – rather I used elongated 4 fold tensegrity prisms and joined them with a complex revolute joint which is also composed of two more 4 fold tensegrity prisms. In this sense I would say that tensegrities can be analogous to biology but are not homologous.
(Nov 22, 2016) I have some new ideas for joints that came from our talk and when and if my energy holds plan to begin to build a new knee joint based upon the crosslinked T-prism model I built.
(July 17, 2017) As you probably can guess, the tarsal/ metatarsal aspect of the foot is really not tensegral… at the time I designed that particular model I was more concerned with Biotensegrity and being faithful to human anatomy so I made some short cuts. There are clearly a number of ways to proceed. For example we could design a foot that looked and worked more like an elephant’s. Such a foot would probably be built as a complex double layered prism with five fold or six fold symmetry. In terms of robotic applications there is no particular reason to design a bipedal foot that looks or acts like a human foot. But if we are creating a close analogy to humans i.e. an android then my approach in this model makes more sense.
When it comes to designing joints however, something like my knee joint is going to be necessary. The key component to a tensegrity joint is a high level of compliance mediated by high pretension. And ultimately a tensegrity joint requires compression members rotating around a tension member. This is not how typical mechanical joint work… it is far too sloppy but if we can find a way to make it work then the advantages of Tensegrity design can be maintained and utilized.
My sketch up files include a detailed representation of the pelvis based on two Tensegrity tetrahedrons rotating around three joints – the pubis and the sacroilliac joints (a class two tensegrity system). The spine is represented as a series of stacked stellated tetrahedrons and the connection to the pelvis seems plausible in the sense that reciprocating the pelvis creates a scoliotic motion in the spine similar to what happens in the human body when it is in motion. The connection of the pelvis to the femur is more problematic. The answer is probably a universal joint that is highly constrained by a number of actuator lines. I believe I began to approach this problem in the sketch up file that Mohamed worked on several weeks ago – Ts-biped… 
When I get some time I will try to build a more representative bipedal foot in sketchup similar to the image I sent two days ago. The problem as I see it is, there are aspects of human anatomy which are difficult to model as a tensegrity at a gross simplistic level and the foot is a good example of this.
(Aug 29, 2017) Simulating the knee joint may be difficult because 3 four fold prisms are interlinked such that the joint can only operate with one degree of freedom and will not hyperextend. One prism substitutes for the femur and the bottom one substitutes for the tib fib. The middle prism creates two axes that cause the two outside prisms to rotate in the same plane just like a knee does. Because they are linked in such a way that the tension sling is partially trapped the joint cannot pass 180 degrees. Thus tension members cannot pass through each other in simulation for this to work.
This may be a few iterations away as I’m sure it will be difficult but this is where the software could become very useful for designing real world robots or prosthetics. As it is now, I have to guess the lengths of all the struts to create a structure that conforms to the purpose I’m trying to achieve. For example if the goal is to build a functioning human-like foot then the perimeter of the structure has to fit within a shoe. So far I’ve only tried to approximate a foot and of course it’s considerably larger given the materials I have to work with. But with pmpm [PushMePullMe] it is now possible to figure this out before hand in the computer. That would be terrific!
(Sept 11, 2017) Finally I have decided to try and model the entire foot as a distorted section of a 4 fold helical tensegrity mast – in fact I tried this approach years ago and managed to build one model that suggested it was possible. Strut congestion and the crudeness of the model stopped me in my tracks but I’m going to try and do this again with finer struts and a different way of construction. Again perhaps a combination of PmPm and Tomohiro Tachi’s work might be able to form find an analogous foot structure and save me a lot of trial and error work. Essentially to model a complex non-symmetrical form like a foot requires altering the lengths of all the struts to create convex and concave sections and also possibly altering the tensioning of individual lines.
Arm models
Youtube video (Sept 4, 2012) This version of a tensegrity arm demonstrates pronation of the forearm utilizing a basic tensegrity ‘elbow’. The two fingered ‘gripper’ is controlled by two actuator lines which are engaged when the arm extends and continues to operate during pronation. The gripper is built from ‘tensegrity joints’ – all forces are pin loaded with no shear or torque and are mediated by the tension system. This model is controlled by human manipulation but could of course be actuated by computer algorithms.
Video of a tensegrity arm with saddle sling elbow
(Oct 9, 2015) The arm model [in the following video] demonstrates how a tensegrity ‘sleeve’ (based upon a spiral tensegrity woven mast) could wrap around two rigid bars representing the long bones in an arm to approximate a right angled joint like the elbow. (Aug 29, 2015) This woven tensegrity braid bends when actuated. Without the dowels the bend is gradual and sinuous. With dowels inside, the angle is acute and sharp.
(Jan 26, 2018; commenting on discussion of shoulder-joint modeling in the IEEE Spectrum article Tensegrity Robot Could Be Creeping Through Your Ducts Right Now) As for how his double tetrahedron resembles a shoulder joint – well it’s very intriguing but I’d have to build one to see how it might work. I would want to make a version that didn’t use fixed tetrahedrons. I’ve purposely kept my designs as pure tensegrities because I believe there are useful things to be discovered by avoiding the temptation to make hybrids like this duct robot. There are trade offs – a pure tensegrity is highly compliant which makes precise movements hard to control but it is much, much more resilient and able to recover from collision insults. A hybrid like Jeff’s duct robot or the revolute joint in the youtube has promise but the temptation is to substitute a tension based section into a traditional biomechanical system. In some circumstances this makes sense. Jeff’s duct robot works well and the inherent rigidity of fixed tetrahedral components is a good match for the function it has to serve.
I’m really afraid that almost everybody is making the same basic mistake and trying to do two things with the tensegrity argument – preserve the classical geometry of a pure tensegrity model with discrete islanded compression members and a tensional net and then shoe horn the description of whatever they are focused on – vertebral bodies, compliant robots, kinematic systems into an ever broadening category of tensegrity systems. I get approached about 10 times a month and have for years by people all over the place who want to use my models to argue for their pet theory, thesis, book, class, system of everything etc. It wears me down – I usually just give them permission but now and then I write back and try to provide a little nuance and criticism. We are pattern seeking animals and confirmation bias infects just about everything we do. Almost nobody asks for my opinion as to whether their approach oversteps the boundary between metaphor and reality. And almost always it does.
