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.