Thank you very very big. But the reasonable amount on mechanics in fact I'm going to ask you Can I borrow a dollar from a dollar do you have a dollar bill you don't have any money on here I realize I'm not having a lot of the money. That he gives net value. This is how he responded in the. Well if you are going to go after after the first minute or if you're going to fall asleep which sometimes happens the ten minutes I would like to take the falling away this is really all I'm going to tell you which all of us know it's a dollar bill that's really floppy if you go up to a vending machine and wanting certain wanted to be stiff you could you call it slightly in the transfers direction and it becomes very stiff in the longitudinal along its long axis and that's really all I'm going to tell you today if you don't believe this is true or if you don't believe this is relevant to feed infants hopefully try to convince you that it has some relevance at least thank you for that. Sometimes you have to give money back to a fund. This is likely. No interest. This is a slightly more controlled demonstration of the same phenomenon and the question here about feet and fins is in the context of propulsion and if you use an app and beds to put propel yourself doesn't matter Waterland effectively what you need to do is push in order to move forward you're up and it needs to be stiff enough so that it doesn't completely give away and bend under these forces one way to make stiff things is by just making them really fact which is bending stiffness of objects goes like cube of its thickness so if I double its thickness I get an eight fold increase and it's bending literati that would be great but then you're investing more into tissue into mass so the question we're thinking about is how do you make light weight. Family structures that can be stiff and we think the common principle in feet and fins is curvature in the transfers direction that leads to stiffness heat this is a articulated Tim pansy foot you can mop the bones of the chimpanzee foot to the human foot one is to one but it's really a rescale human foot and in the middle of its foot has great flexibility so flat relatively flat chimpanzee foot unlike a human foot is quite floppy and these are the considerations I'm going to tell you about that's the qualitative phenomenon everything else I'm going to tell you about is how do we work out its relevance its relative contribution in the context of feet fins and why these these don't look like each other so how is this principle itself manifested in these different objects so let me first A college various people involved in this. First that a social experiment. You're welcome to scan this with your fortnight see more people using their phone or talks that will give you a link to P.D.F. of all the papers are things that I live in to it. This work was done by a whole host of people but foremost I wish to time these two coconspirators. Shares is an upright a mathematician a drone and my Haitian is an experimental software to physicists and Okinawa and Japan and the three of us were also various dollars were given to us by the human from the science program to pursue crazy ideas of the same. I and there's a whole host of people and I will point them out as we go along a lot of what I'm going to talk about today on feet is in the review and that pre-print so Comments welcome please do to look at it so without further ado I'm going to give you really a story of two artists This is an overview of how I'm going to progress through the talk I'll first tell you a little about what do we know about stiffness in the human food what makes it stiff I will then walk you through how the transfers out how does the dollar bill work when you call it that's really what and walk you through and use that to interpret some of the fossil fuel in a paleontologist experiment is an experiment in the sense it's already it's an event that's happened with probability one we cannot control the experiment we can only interpret existing samples and this. Approach of thinking about mechanics and geometry gives you a window into how things evolved. And once I finish with this hopefully everything about things will be obvious and I'll tell you a little of both. So first why do we care about the foot at least the human foot we care about in the context of human evolution and this is a picture I have adopted from Dan Lieberman and I would like to walk you through it this is a time when millions of years. The solid lines show some sort of moan are fairly well believed inheritance that is about when chimpanzees and us we think split. The There are other branches here are not showing on the human lineages there are many other branches some of which were and did not lead to humans lead to other animals which we don't think said wife today there is no known survival today of huge interest is Australopithecus which is around three and a half to four and half million years ago and it's of huge interest because by then we have reasonable evidence that this animal was probably walking climbing and perhaps print now how do you make such inferences you start drawing inferences by making comparisons of anatomy would take this thing animals that's a very common tool for how to make inferences about an extinct animal Homo erectus this is Java man a kind of boy if you if you are paying attention the press. Humans are treated as a model for Homo erectus and we think a lot of specialization of humans does the genus Homo has to do with not just walking ability but ability to sustain drowning for very long distances so if you were to ask me How do I characterize a human said. To other primates or perhaps every other animal we are specialists in two things we have big butt and we sweat a lot we have big butts because we we are really good at depth runners for long distances and these are very important muscles involved in turning. And we sweat a lot because when you run you put you generate a lot of heat getting rid of the heat is in fact a big way by which we think early humans used to hunt so you run. After other runners but they can't spend as much some point they overheat so why heat stroke and die and you can walk up to it and take it home and this is called persistence hunting and very effective way of hunting but the story of walking which is again one of propulsion overgrown by people walking for long distances is much older than human insects. Let me give you one of the examples of how we know walking. There was this track of footprints about seventy five feet long I think seventy seven feet I think in length at night only futile footprints very very nicely preserved we think in very volcanic ash. And this footprint consists of the one I'm showing you is from litle B D consists of an adult and a juvenile walking side by side. The footprints and remarkable in that they appear to correlate with someone having walked with the style that I would use strike the heel go to the front push off with the front of my foot strike the next key so there are deeper imprints associated with the heel and the four foot which is not typical of chimps for example but very typical of humans and. These footprints are found in the same strata where lots of other samples of us tell a particular So the belief is telepathic is made this footprint. Afferent this is a little strange I have more props that don't involve money. So that's a human foot. So if you pay attention to the human foot or pay attention to your own foot it has a fairly pronounced arts in the lawn and direction and one hundred year old story of what makes the foot stiff is that the longitudinal art is a big part of making it stiff and the effort has a very weak longitudinal not best there's some debate about it in fact quite a lot of debate about it. But it's not clear it has a long as pronounced as humans but it apparently was capable of supporting its body weight on it for food like we do when we push off how could that be is one of the debates we would like to address. Foot stiffness away from the evolution side lots of other functionality there's lot of interest for many of the reasons lots of things going on in the Slate So let me start walking from a peer so that's video of a runner running on a force treadmill what I'm showing here is the work tickle force as the person is running and that's fraction of body weight that the foot experiences and when they're pushing off the foot experiencing more than two times the body weight but you don't you do if you pay a lot of attention and use him a day on it you see some amount of defamation of the foot but the defamation is very minute on the other hand here is a experiment where someone is asked to simply support the weight on the ball of the food that's a healthy food that's a dying person with diabetes and that's about how far they could lift diabetes becomes important in the sense that people with diabetes many of them will lose the art in the foot in the foot becomes flattened and when you lose the arch it becomes a soft relatively flexible which is also reminiscent of. A cousin of the chimpanzee the bonobo this is a very beautiful photograph taken by a collaborator out as the bonobos walking the middle of the foot bends and again the bonobo has a relatively flat foot that's a chimpanzee walking compared to a human example some of the interest in this again goes back to comparative biomechanics and thinking in the in the context of evolution because chimpanzees whether they walk by previous quarter P.T.V. consume a lot more energy than humans do. Humans consume about seventy five percent less energy per unit bodyweight per distance they cover relative to A by people are quite typical chimpanzee is this due to the foot is completely open of course there could be many other factors going on but one of the big differences people think is to do with the food here is an this is not from the same experiment but from a different experiment of flats. That person when they push off with their foot this is showing you the normal traction and on the ground average over the entire contact period of the foot you see these huge pressure points in the middle of the foot that you do not see in healthy so they are just have something to do it's different so the shape has something to do with its behavior what does it have to do with behavior is a question the hundred year old story has been the longitudinal arts and I'm going to tell you a little today about the chances that but let's first understand what the what. Approach we want to take to understand it relating form to function Ultimately I would like to begin to apply it to fossils of first I'm going to insert the idea of what type of forces you even find. So this is another representation of human evolution but Clock know how to Zante this is today millions of years ago chimpanzees often treated as a model for the last common ancestor between humans and chimpanzees these are all feet from fossils identified as genus homo and one of the rays there identify the genus homo say the foot looks a lot like humans you can do this far more quantitatively and they look a lot like humans this is one of a key fossil base in which a lot about there for instance is known it's one born so your foot has raise it a foot has five race spawning to five digits that corresponds to the fourth born that's the fourth matter Thompson and for us it was very lucky the fourth major task and you see why this is a mysterious animal all that's been found is the foot that's why it's called the tele foot we don't even know what there's nothing else that's been found beautifully out a very good way and skulls are a very good way to identify species and nothing of that was found for this animal and dates to around the same period after it says. So paying attention to the longitudinal arch world the way we think the longitudinal art works is like a bow and the string. Because at the base of the longitudinal art a bunch of tough tissues called the plantar fasciitis enlarging of audiences invariably few of us have been to the doctor and the doctor says you have plantar fasciitis and they give you ibuprofen or something like that to reduce the inflammation what they mean is this tissue is become inflamed if you look at the foot sideways a caricature is I take all the bones in the foot when the two feet account for a little over twenty five percent of the bones in the body two hands and two feet a concert more than half the bones in your body these are complicated structures doing somewhat simple things sometimes. I lump all the degrees of freedom of the foot bending into one joint here then you can think of this is a ball with a string and in order to bend the ball I have to stretch the string and that's the role that the the longitudinal arch play so the higher the arch the more the stretch in the string and therefore a high art help to stiffen the foot one very classic experiment comes from the 1980's due to. Xander some of you who are by mechanism want to. Make a little Xander and experiment they did was take good our feet and do a three point bending test on it and when they're doing the bending test they start systematically cutting various tissue so that is the healthy food the red dotted line of shown or laid is a foot to the plantar fasciitis cutaway these are cutting away various other ligaments but when you cut the plant a fashion you lose about twenty five percent of the stiffness but I define stiffness of the means difference of the scope and this observation that it behaves like a bonus thing is much older Martin and one thousand nine hundred two writes about this so they're in and Martin's paper. Review so it makes me think that the view of how the foot functions in the art is related to stiffness it's probably much older than that. So that's one thing that the student Arts does but there's something even cooler that the longitudinal Arts does and it's well I should I should make one side comment before I jump to it it's the same sort of experiment that these same authors few years later two years later carried out in monkey feet the used feet of running monkeys the feet are relatively flat and here for example removing the planter fashion reduce its stiffness by about forty percent so having a longitudinal art helps the plant a fresh air cond it works in a roughly same way but the second cool way in with the long student large works is something called the windlass mechanism to remember this is the food the longitudinal arts of the plant to fashion but the plantar fasciitis started to heed and end up a touching to your toes so when it does that if I flex my tool I increase the tension in the plantar fasciitis which would actually unload the foot a little bit so when you want to actually push off with your foot and your toe flexes there's a passive mechanism in there which unloads the foot and effectively makes the foot different so it's like taking a spring and having a paddle force component so these are all the various brings in the foot due to the launch to lower the transfers the plantar fascia and flexing the toe is like offloading the body waited and this was in fifty four wrote about this and the windlass mechanism and it's a reference to a mechanism for lifting water out of this so it seems that we know a lot about how the arch relates to foot stiffness so. And it and I would argue most of the debates in the field surround Well does the longitudinal arts height for example predict foot function turns out not there are a lot of people who are flat footed in the sense you cannot measure and longitudinal arts different from other flatfooted people but who can walk quite fine and push off with the ball of the foot. There are people for whom there are surgical reconstructions done to actually reconstruct the longitudinal arch and in the end they still cannot support body weight in the So it's a very very on the one hand seems very well understood on the other hand there's a lot of things that are not panning out the way it should if you just pay attention to the two D. picture and that's where I'm going to make a case let's look at the other asked in the wood So first a little geometry Why do we have the other part remember we have a longitudinal lot but if I look at the lateral side of the foot not the central but the lateral side there is no longer so you have a longer two large and one side of the foot and not the other which means you end up automatically forming or transfers out in the other direction it's a half dome the chances are it's not that we're the first to say hey there is a chance of no fact he talks a lot about the transfers art and the transfer as art is always treated as a germ a tick artifact of having a longitudinal art in just one side of the foot and therefore even in fossils for example people try to infer the chances are to know whether there is a longer Toodle art to know whether the animal could have walked like a human but I'm going to argue this Dominic artifact is no mere act of. To remind you the end of my talk is this color dollar bill it gets stiff and it's coveted in the transfers direction that dominates stiffness in human feet is my claim which it does not imply many feet this is a discrete realisation of the same print. Three Metra tassels the method ourselves are these long bones. With flexible jointed the base end of one ligament the rubber band running transversely at the very distant end of the foot now if I curl the structure then it becomes a very stiff structure. Ten fold but there's no way to compare these two directly they are completely different structures they're not the same material but the point is curvature difference that in continuum and discrete Russians and we're going to first understand continuum structures a little bit more when the feet have said told you a lot of bones. Typically when I want to mathematically understand something something with three or four or more degrees of freedom is much harder to understand under the number of degrees of freedom get to infinity so in in continuum structures are often Marty easier to understand let's see if we can understand what is the mechanical principle behind this curvature induced Ignace we going to use simulations and physical experiments with shells by Shell I mean things with a chip and compare it to fairly. I won't call it straightforward but pen and paper calculations so this work. The simulations were done in console and what we simulated was shallow thin shell equations so that we assume the shell is very thin we assume it is very shallow and David's working with be carried out experiments with shells I I won't go into it in detail here but this is I think these experiments of my age Bundy design belong in a textbook in terms of the quality of the experiments and you see soon see why I say quality of experience. What you see here is a log log graph of stiffness which is defined as applying a knife it's load clamping one and looking at the displacement of that edge and the ratio stiffness as a function of curvature this is dimensional one hundred meters and you can put me to. The doctor simulations experiments and I'm showing you here variation with those many parameters I can vary the length of the material all of the about changing the stiffness roughly increasing curvature difference in lot of spread but looks like systematic spread so we would like to understand is this thread can we collapse it to do some underlying master equation that would be the principle we are after. So for that incomes serious and thinking about shells is a lot happening here so bear with me and walk with me slowly reminded this is the experiment right so there's a camp and one and there's a shell and I load it and to remind you the simulations assume shallow shells when that experiment is practically a half cylinder and it's a flat fat blob of P.T. a mess so the experiments of course I'm not trying to mimic these idealist cities. When I displace the tip there's a reaction force in the ratio tells me what the stiffness is the first thing one could say is hey this is the classic I beam those of you who've done strength of materials in Engineering Mechanics what curling it in the transfers that action does is move the neutral plane. Up gives a larger lever arm and so it becomes a stiffer structure. Well that's not the full story so what I'm showing here is a deformed shell. And I'm plotting see the stress in the X. X. direction so it's one of the principles stresses. And one of the components. If this was an I.B.M. then the stress of where the neutral plane intersects with the material should be zero because the neutral plane is the plane that doesn't stretch are compress and what you see is that's a very good approximation in the bulk of the shell but towards the tip there is a clear departure from that simple beam it is not he does not behave like a linear elastic be. Another way to see it is if I look at all the defamation if I just had a classic beam and deform it there would be defamation. Everywhere but this shell most of the defamation is concentrated at the tip I think and return my dollars very soon to my funder and he's gone but if you took a dollar bill and try to apply a load on it's the thank you. What you see is just the tip tends to play and bend a lot of the defamation is concentrated in the tip so understanding this principle is really to ask why use curvature crossing phenomena around the change in costings to play a part one very simple picture let me use the arms and demonstrate if I have curvature and let's pretend my arms are made to feel tissue on the dollar. Each strip of material wants to displace normal to its surface. But because of curvature if they want to displace Normally they have to play a part so in order to bend I have to stretch it so small a very thin sheet may feel very soft and bending but it's very stiff instruction So another way to more systematically do this is think about looking at the dollar below or headed for I want to displace it normally because of the radius of curvature I stretch and therefore the total strain and or G. is a sum of a stretching strain an agenda bending strain and now let's assume this bending and stretching based on the medical experiments Let's hypothesize that it happens in some boundary in the small and so the energy here Keynes with small N. for stretching but the bending strain and because all the bending is localized here scales with one zero or cube so the ratio when I have bending and stretching I could a the bend everywhere and stretch very little or stretch everywhere and bend very little neither is the optimum the optimum is to roughly equally partition my energy between these two modes so balancing the energy partition into these two more gives rise gives rise to a link scale which goes like square root of R T What are is the radius of curvature or square root of P. by curvature that links K. compared to the total length tells me something about how curvature of the structure to. To see this more systematically If I have very low curvature cracked almost flat shell then the stiffness of the shell is approximately the same as the stiffness of a flat plate that identical in all regards but for codes so dimensionless stiffness which is the ratio of the shell to a flat plate would be one but without high curvature then the stiffness the dimension the stiffness would be some function of this dimensionless ratio feelings so here I see was that smaller squared so L. by L. squared is the dimensionless curvature that matters and what I will show you but I'm not going to walk you through the calculation here is you can more systematically find out that that exponent has to be three house in its dependence for high curvature so there's a look of a plate like behavior and a high curvature Kota dependent stiffening behavior that a theory of shallow shields predicts and if you know take I showed you all this experimental data variation and thickness and if you plot all of those in a dimension this graph this is the normalized stiffness and that's the normal curvature it's the same data. They collapse onto an underlying mastic of the massacre of has one asymptote around one that the flat plate behavior and another are simply syntactic behavior that looks like tree house. That does a log log graph and the slope here is approximately three halves and these two are some toads meet at around ten in the in the dimension that's covered so we can do a lot about now asking if you want to be you want to translate my claim about human feet one way of asking the question is are human feet in the regime or are they in the flatter Gene just because you have curved transfers curvature doesn't make it cover to be induced It depends on which regime you're in. That takes a little bit more work and the work it takes is well I can do this and I thought experiment I cannot take the. Human foot and find its exact flat analog which in northern rays pathological in stiffness I could if I have a large of cadaver sample where I can find these feet and we haven't done that experiment no one else has done that experiment either but we're going to use a slightly modified way of using already existing data and the way we're going to do this I know that monkeys can stand the monkeys here monkeys are flat feet so I would like to use the monkey as the flack plate model but there's a small catch monkey feet are different in size than human feet so what I'm going to do is take human feet data and normalize it by some elastic plate which is identical in dimension to the human feet but flap and normalize the monkey feet data by some plate but same materials as this plate but of the monkey four dimensions and that gives me a ratio of the normal a stiffness of the human to monkey feet and I'm going to say monkey feet of flood so by definition I'm going to call the normally stiffness of monkey feet as one so if I have data for human feet and monkey feet and few length parameters of human feet and monkey feet I can estimate what I expect the dimensionless difference to be. These cadaver experiments are done with a few samples one two three five samples at most There's a lot of anatomical variability and we can use a classic approach in statistics of bootstrapping to say what distributions of lengths exist in human feet monkey feet to generate distributions for the dimension the stiffness for human feet. So. That gives me stiffness independently but I also want curvature How do I get courage to get curvature so remember this is the human foot that's the chancers art one I could just put a parabola to the transfers out that's that's not a hand drawn parabola and Power Point that is a database parabolic fit second or to fit two to the transfer so that it's a fairly good fit and that I can use to compute the mean curvature over the width of the foot that would give me one coveted estimate. But that's not the only curvature estimate it turns out because human feet have these distil in. And laying flat on the ground but an art in the middle of the foot the bones themselves have a twisted judgment so this is a cartoon version the presentation of it so if I pay attention to individual bones they have a tartan about their long axis this is again thanks to the anthropologist well known forever one of the biggest ways of discriminating a human foot born from some of the bone is if you have the fourth or the fifth Magic Castle you simply look at and say hey does it look like a twisted judgment or if it does it's probably. So but this is simply the tosh and could be approximated as essentially curvature integrated over that rate so if I know the torsion angle and divided by the wood that also gives me average coverage. Of the Interior art but so. I'm arbitrarily picking this you could fit it to the interior I do not pick the interior because if I pay attention to which part of the bone is actually articulating with a nearby bone not all of it is for sure towards the top you have articulation towards the interior you have these spiny bony projections because there's a this is not a big cavity it's filled with actuators there's lot of soft tissue attaching there this is easier indicated to measure. And this is a sanity check I can use a caution based curvature parameters are a part of a low base curvature parameter and do the Monte Carlo Well first observation human feet the more the distribution at least is above ten there already gives an indication that human feet the the dimensionless curvature is in the regime where it is in the stiffening regime for my shells. That should not hopefully a super skeptical you should be because. Can I do this can I do that what am I going to use that shifts the mortar round a little bit it doesn't shift a huge amount but what we would like to do is we have a separate estimate of the dimensionless difference between use the curvature and the Shelley questions to also predicted dimensionless thickness independently and would like to compare the two distributions and that's exactly what we did so remember these are the dimensional data collapsed the blue band is the dimensionless stiffness of human feet as. Found from the mesh could have an assurance the white box is the dimension of the stiffness due to the curvature predicted independently and that showing you the middle fiftieth percentile is a band and that the middle fifty eight percent of curvature so logarithmic axis so when you see these long tails remember that the it's a logarithmic axis so we're not too far off to me this gives some confidence that there may be merit to this weird. Thinking not just qualitatively but as a quantitative predictor of stiffness there are a few additional datapoint this towers that have appeared there are no stars earlier the stars are experiments with shells but not curved in the transfers direction but curved in the longer Toodle direction along with no plan to fashion the thing so there's no curvature dependent effects if I have just landed didn't cover it I need planters committed that's that's a sanity check it should not be surprising. OK. But how do we then go about building more confidence or really the question is how do you go both finding what are the limits of a theory like this how do you break the theory well one of the predictions is bending becomes couple to stretching. That the effect of transfers curvature so if you can take human feet and mess with the stretching coveted sort of stretching stiffness we must be able to mess with the bending stiffness can we do that is the natural next question we followed. And this was work done by an undergraduate at that point in the lab was a graduate student and you pen and a Ph D. student in the lab the core ideas when you load it bending induces playing. It's tempting to say that you can actually observe this if you load your foot there's a slight bit of play should be very wary of this experiment because there's a bunch of soft tissue under her foot I could just be squishing that and that's some wall concert volume that leads to stretching so you need a slightly more systematic way of knowing if this phenomenon really exists of course we can cook up fairly simple models of the tree matter to us and foot with some radius of curvature take all stiffness other than the transfer stiffness and lump it into toughness brings at the joint and have a separate spring associated with this that this is also really a sanity check it shows that really the contributions are additive so there is some stiffness that is due to the plant a fashion. Blah blah and some stiffness due to the transfers stretching stiffness and these are additive and the experiment we're going to do is an almost obvious experiment which is the I can't reduce the stiffness I would like to take the tissue away and collapse of stiffness The alternative is I can apply a paddle spring on the outside take a lastic tape and wind it around for you know the stiffness of the lastic tape I know how much I increase the stiffness by and that's what we did with a few other controls and the controls of the falling remember I told you there's a windlass effect in the windless mechanism is if I flex the toad brain in the middle of the foot so the windlass other than being a cool phenomenon serves as a probe of foot stiffness measuring foot stiffness in life people is nontrivial people have really really stiff foot you need about one body weight to displace the foot by a few millimeters and if you are playing when people are already supporting half a body weight in the foot in your play another additional body weight. You could have issues from simple pain people tipping over and never coming back to participate in experiments. So how do you measure it will we use the windlass as a probe where you see and only designed this rig where I can set the two angle externally with or without tape and I measure the incremental change in the middle of the road if the foot is already a stiffer structure then the windlass will not be able to deform it as much so that reduction in defamation of the middle of the foot when I bend your toes gives me a controlled way of finding what is the percentage increase of stiffness of your own foot so you serve as your own control. But we want to control various other things like the mean load in the foot where the load is being applied and so on so early ploy that visual feedback to subjects which actually doesn't look very different from this this is a screen capture where the person is standing on to force plates and we ask them to keep the center of pressure around the ball of the foot and the vertical load magnitude to about half body weight plus or minus five percent that's the constraint we impose. While they're standing on the sap one foot standing on this apparatus the other foot standing on a dummy which is locked into place so this is on a sliding device and it sliding because if I change the height of the foot the length of the foot a lot of teams if I don't have a no friction sliding device I'm an essential in measuring noise due to friction to friction was a big problem in this experiment and we can do this with and without tape but we can also do thumb slightly more nuanced control which is a play loosely attached tape in case there is some psychological effect of sticky things and if. We did this and let me show you what we find Let's first look at one representative experiment so when you flex the foot the foot go the midfoot goes up. Here I'm plotting the change in height of the mid foot as a function of the toe angle do not pay attention to any of the great data points because that. At point the experimenter Ali is physically flexing the toll so that when he's flexing the toe people are not necessarily maintaining constant load on their foot because he's pushing against them so we don't give some time for people to equilibrate and we let them equilibrate at the start of the experiment and if the average slope that tells me something about stiffness of these two without paper loosely apply tape and that is when I apply tightly played tape tape is a horrible material rubbers a great material if you're interested in materials science is horrible material if you want to control the stiffness but that what can you see a logical tape are there primarily latex. So what a lead does here is measure the perimeter of the foot and tries to maintain consistency between when he applies the tape but this is a big source of noise in these experiments. What this shows is that relative increase of stiffness relative to the control to zero means I'm like the control higher and higher means I have less and less a change in me too tight if I apply tape barring one subject everybody else different I do not know what what's going on there but that's that's what we find you find a lot of spread but the trend is very clearly consistent I don't need statistics to say that it's significantly different from. From from the control when I don't have a tape data clustered around the country the foot is a living. It has muscles and people do change muscle activity and we think that has a lot to do with this spread of data we see but we are able to increase stiffness on average by about fifty percent Remember fifty percent increase in foot stiffness is a big deal for cut the planter fashion you lose twenty five percent of the fruits difference what we can elicit is a fifty percent increase in France difference and that is a big deal also because the tape stiffness due to the tape based on just anatomically the can I. Directly measure stiffness in the transfers direction but we can estimate based on what we know about those ligaments and typical size of those ligaments the tape was roughly sixty percent of the time first if so we increase the transfer stiffness by about sixty percent and got a stiffness increase of about fifty percent remember the stiffness had additive terms. So I'm holding this approximately constant for increase this by X. I get a total increase here of X. that already tells me that the transfers are dependent stiffness is mostly dominating for stiffness so this is still consistent with the other measurements we made so now I feel at least confident enough in our understanding of the transfers out that I was now willing to go look at fossil samples to know where do these fossil samples lie where does the curvature in the transfer success for the fossil samples right relative to humans so these are the samples I am going to look at I want to make I already told you about these two. That is a very cool sample it was found in a lady two thousand and fifteen was when it was first reported. First people targets ritual burial there is some debate going on about it. We don't know its aid because it was found in caves we think it was the animal had a habit of ritual burial which means you cannot use the sign strata to date it but it looks Homo like everywhere that regard in the longitudinal axis it looks very flat you can't see that here so the authors actually conclude although it has a human like foot it's probably a soft foot because it doesn't have a longitudinal art but it does have a fairly pronounced trance or such that the chances are you and I can directly estimate the curvature of that fitting parabolas So where where do these different feet like so to remind you this is what I told you about and maybe the other foot you see these authors remember the single bone and that bone happened to be the fourth major tussle so they could look at Parchin of it and here is data off the fourth mattress and caution for chimpanzees gardeners humans and I for instance the Lucy related and it falls within humans so they actually conclude this is probably a human like foot although it's from utterances and many other references features are not quite. That but Tenley know the protos even more complicated you Mark various landmarks calculate lots of dimensional of the ratios of lengths of all the bones you have you do the same thing thing with many other animals primates and use principle competent analysis and pluck this foot it's more for metrics on the principle component axis fugues zoom in that these two icons stars are humans clusters of gorillas so in the principal component analysis humans and gorillas are pretty close to each other although the centroid one could argue is separated and they argue that but only falls within gorilla not human so it was probably a good deal and like flexible that's a current. Understanding of these feet if I calculate the dimensionless stiffness the dimension is curvature and then is just a visual aid of where the two asymptotes meet humans are there gorillas are here chimpanzees and the running monkey feet I mean there's a lot of axis so that you don't even see the median here it's a very flat foot. All the three genus homo including the lady fall within the within typical human variation within the middle fifty percent of what's even cooler to me is but only falls within the middle of the percentile of the human although the principle competent claim was that for an accident says isn't is clearly outside the middle fiftieth percentile of human and clearly outside of good in which is to me somewhat more consistent with the light only footprints remember the fourteen the two foot set of footprints they look almost human not quite and they've been experiments of getting people to walk on very well kind of cash and looking at how the imprint forms the imprints in the forefoot are not as deep as human but clearly deeper than any of that private so to me these data are at least consistent with the fossil data we have enough threats is consistent with the lady being a genus homo but only when we can only call this a hypothesis until there are more forces and I'm generally enthusiastic This is the closest you can get to a controlled experiment in evolution where I can hypothesize something about the species before more fossils are found there's a lot of digging going and going around in the battell area so hopefully they will find something to falsify or show us right so you know where I'm going with fishnets now but let me say a little bit more about why I care about fish fins and where in my head fins and feet are closely related everything I told you about feet in a century of plate of fishes but it's in an aquatic environment. If you pay attention to the evolutionary history of animals of course a lot of tetrapods pedestal animals came from aquatic animals that didn't quite look like this but we think they looked a lot like these much keepers of African long fishes that's a walking fish and it's using its fins to support its body weight so its fins not surprisingly can serve some similar function to feat in terms of being able to propel it but fins also work aquatic and what we were curious to know is how the first level question before I can start seeing anything so grand is. How this is structured like a fin actually becomes different of to push water than what us happy. This work was done by a whole set of people led by strace. The whole. Two Co He was an undergraduate at Brown and he started working at trade some problems include mechanics and then spent time with my husband be at Okinawa where he started the Fischman work and he's now a pity student in my group so the when I say we collaborate in many aspects. So we started paying attention to the pectoral fin and leading the experiment had the choice of what to study he said he likes my taste good so he went and bought mackerel and so we have we analysed. Instead of me walking you through the entire thing I'm going to show you a video made by shares to demonstrate how things work and I find this video very appealing this work was published sometime last year. I'll be silent while we watch the video. It's one minute long. So that's the point it's not that you need physical cover to what he needs. Bending direction needs to be misaligned fundraiser a little different from Feet Under body weight loads I can compare to much completely ignore bending of these bones themselves put themselves bend appreciably and they don't have one band of ligaments at the distant land and sit down a membrane everywhere to the map to slightly different so for today Finn for example I'll tell you a little about this but today Finn when I bend I end up stretching a membrane that's on the other side which I'm going to mimic by Linnaeus spring so the bending equation because of this bending stretching competition again has just one small and it's the it's a bending and stretching competition leads to a length scale and in this case the length scale depends on the membrane stiffness K. the bending rigidity of the individual and the degree of misalignment of each ray but it also depends on whether self is approximately equal meaning it's equally easy to bend in all directions or if you just WRONG them and isotropy in in its bending rigidity that's Garma that's a bending digital parameter. But all of that is to say hey there's one link scale in the problem and the link scale is because of bending stretching competition. And little bit more attention to detail well I could get this bending sitting competition using curvature like I've been demonstrating the dollar bill but in a composite structure I can do the same thing in a flat structure but having lay individual rays that have an isotropic bending and Miss aligning them systematically so. MacHall stuck it between two flat plate the pectoral fin did a C.T. scan and calculated the principal bending moments of the cross sections of different rays along along the car direction and what you see is a systematic misalignment of the bending direction of each rate but that alone do. To imagine I have a very very soft membrane just because I have bending stretching coupling if the membrane is very soft eatery simply going to overpower the membrane the presence of the membrane doesn't matter or for how very very stiff membrane again it makes no difference because very stiff membrane just forced my race to bend together and it to behave like a flat structure so if you want to be a fish who does many things and not just push maximally in the water you typically want to have a balance between the membrane stiffness and the bending stiffness you can take the statement and can convert it to a more systematic design criteria so this is my statement that there are two US imparted behaviors of stiffness as a function of this dimensionless parameter which is kept as the bending stretching a night I can because it has it always goes to some asymptotic and normalize everything and pretend that this behavior isn't into pollution between two US into Arctic limits the point is depending on the degree of isotropy of each race that into pollution happens a different values of this dimension this parameter and what you want to be a. Versatile fin meaning able to model its stiffness by modulating curvature is to live in this regime and this regime is defined by how much and isotropy each race so if you pay more attention to the fin itself what you want to compare is against one plus government of the one third and do this calculation not for today fin but for an end and what we want to then compare in terms of numbers turns out to be is twenty what created the one for one third and that's in the eye of the beholder I argue twenty is much greater than one. So I will in my talk with this and leave you with the following message which is what I started with that cover to induce the stiffness but coveted itself in a composite structure can be manifested non-trivial case where externally it could look. But internally could behave like a structure. But different manifestations of coated induce differences I think is what is common between feet and things of course these don't look like feet these don't look like things why they don't visit is a topic of huge interest to us and we're now beginning to look at walking fish to know what are the tradeoffs they suffer. From using things like structures to walk on girl. Thank you and leave you with your. Yes. All. Right. So I can lease attaches but I have a foot so I can. Sew the Achilles attaches to the heap and the pontiff touches the heel so in some grass in some grand sense you can think of these the springs in series with a stressed strained relief or a stress relief and in between my model thinking about the foot had no uncle in it so the foot itself there's enough evidence even in vivo the days bones don't move too much relative to each other but your question of can I do something with the Achilles to change foot stiffness. There's no reason that I can think of that it can because it attaches to this very stiff born and does not actually feed over to the plantar fasciitis. There is there's more subtlety because a cough is not one muscle it's a big muscle group and there are muscles that actually sent tendons all the way in here people haven't paid attention to it one of them called posture to be Alice goes into touches and has a big transfers transversely oriented tendon we think that is part of how we model it stiffness so broadly the cuff muscle group can and that's that from diabetes in fact there's a lot of data if you have paralysis of that muscle the arts just collapse. All the. Control of the so. So part of that is the posture to be honest the the foot has deg antic muscles it is not entirely clear. It is clear that I can do things to the muscles to tensed change various measures of stiffness but it is not clear. And I think it's not clear how because computing us we are only now beginning to think about the foot in the third axis with that that's a that's I think a very relevant question to proceed. So I went to the very pertinent question. The Continuum model is not meant to mimic the foot In fact I mean wholly agree with you the foot isn't anything but continue and anything but homogenous highly and isotropic highly in homogenous active departure from our model in every possible way the goal of the model is to identify the geometry principle of how curvature fix difference that only gives is that one geometry parameter the dimensionless curvature parameter. How does manifested in the foot is the question that in the center asking the fish fin model for example was explicitly a composite structure because they could no longer be what we were interested in paying attention to the details of the design of the can itself are the three pronged foot model is again a discrete model of the whole structure mostly we've been thinking about models as guiding an experiment as opposed to trying to match an experiment so the three pronged foot model now tells me I need to pay attention to the transfer ligament which I could control to some degree in the human subject with elastic tape there's a version of that experiment under construction we are trying to use controlled Springs or do it in cadavers where I can selectively cut that tissue alone so that those are all ways in which the composite models inform our thinking. Even if the material is isotropic the courage to depend and so that's where the emphasis on the exponent but I agree with you can you I can do select very clever and isotropic design to violate a lot of things I'm doing. Here and that's why the functional courage of a flat structure can look out. So I think a lot of what I'm brushing under the rug right now is. What does this why does a fin not look like a foot if I put a shirt I want some surface so that the future doesn't just float right past I would like to trap the fluid. But it does a very very different manifestation I think it does a lot to do with the impedance if I can use the word impedance off my environment and there is an impedance matching problem to be taken care of and it is not obvious to me about how the different structural design lead to impedance matching and we were having a conversation with Greg earlier on face relationship of bending in fins in water. And how a purely viscous load would lead to facing purely mechanically versus what face relationship I want and bending the different parts of my fin in order to generate maximum propulsion or minimum propulsion in some cases for want to hold station I don't want to interact with my fluid so I think those differences are the ones that matter. So we this summer if you're I will send you a video taping a bunch of my Goby fish in Okinawa in my lab walking in clay because they live in these sludgy environments and they are trying to design some clever we can do some amount of P.A.B.. But. You. Are. A Christian. To that's a very good question I mean we have jokingly commented internally that a curved foot on a flat ground is a flap we're going to get on but they can get a little bit more seriously can the does the foot mimic a flat structure of my ground is appropriately cover conforms to my foot I'm not talked enough about this that's a good that's a good. Yeah so the insides of complicated because you you don't you don't stick to inserting a foot to foot can actually come off of it and flatten it is not obvious about how the Internet itself would work there are some attempts at imaging it and so on. Your question about the transfers out few climbers there have been a couple of climbers in it when I've given this talk and say of course what we do is put in the distance direction pretty hard because we're interested in being able to support nodes in the foot and not having to rely on a muscles some amount of that thinking is already dead by trial and error and I don't think we're going to be the first to say hey a play a tape in the chances that actually I think a lot of people have been doing this under the. Design one of the biggest considerations is the fabric of the shoe you can't have a brutally soft fabric if you want to confine the foot this is language the true design is use I don't know how that translates mechanically but it sounds a superficially like some of the things we see so you are I agree with you that in service not not clear how it looks. Good growing the way. OK so. Absolutely so the tape up location experiment is a first Tara confrontation with the boundary conditions second confrontation the boundary condition is sure there was if I did not control through the contact point. Then the foot is trying to play the talk the bone is trying to play this fairly complicated interactions and the measurements become undeniable so I needed to control multiple degrees of friction One is the sliding thing and the ball when I flex the skin wants to stir it and in fact have to use two plastic sheets of baby powder in between to have a fairly low friction interface so friction does affect quantitatively how the stiffness works this absolutely no doubt about it in the shell experiment on the simulations if I use a frictionless knife edge. Clamp on both ends and displace on a pin condition and displace each of those quantitatively leads to different stiffness is the three house power log does not change that does not depend on any of these where the asymptotes interacts with shift that's the consequence of the bonding.