So, so far we have looked at the statics of
the ah upper extremities, then we look at
the statics of the spinal column. ah We looked
at various tasks like bending, lifting, etcetera
with respect to the spinal column and we analyzed
the loads on the body. Now, we move on down
to the lower extremities.
So, the spine connects to the pelvis and then
from there on to the legs and to the ground.
So, the lower extremities play a very important
role. You know they are weight bearing structures,
but also highly mobile. So, there is a lot
of ah muscular action that is necessary to
provide this combination of stability as well
as ah mobility, ok. So, we will look at some
of ah the major ah bones and muscles in the
lower extremities and then we will go on to
do some analysis static analysis of the ah
lower extremities.
So, as you all know should be familiar by
know the thigh bone is your femur and the
hip the hip joint is the joint 
between the head of the femur and the socket
is what is called the acetabulum of the pelvis.
This is a ball and socket joint, and actually
at the head of the femur you have a very nice
ball covered biarticular cartilage. It is
a very mobile ah again it is a synovial joint
, ah very mobile and its shaped, so it is
a 3 degree of freedom ball and socket joint
. So, the socket is the acetabulum and the
ball is the femoral head .
So, you have, so this is the structure of
the pelvis you have the anterior and the posterior
view. You can say this is the sacrum ah the
last analysis that we did was at the top of
the sacrum, you know where the fifth lumbar
vertebrae, vertebrae sets. So, we were looking
at loads at this level here, ok. Now, we move,
ah now you look at the sacrum, the sacrum
actually consists of multiple bones which
are all fused together in adults like the
ilium, ischium and the ah pubis, ok. They
are all fused together ah in adults and that
is your hip bone, ok.
So, this, about the hip joint the movements
it is a 3 degree of freedom joint so the movements
that are possible are you have in the sagittal
plane flexion extension. In the frontal plane
what do you have? Abduction, adduction and
in the transverse plane you have internal
external rotation. So, all 3 motions are available
at the hip. And the extent of the movements
as always is constrained by the other structures
like the ligaments, the ah bony structure
of the hip, and the muscles surrounding the
hip joint. So, they control how much of the
motion is available.
So, let us look at some major muscles at the
hip. So, you can you can see here this is
a nice picture ah showing the hip joint here
with the ball and the socket. This view is
the posterior view, this is the anterior view
and muscles that two major muscles in the
posterior side one is your gluteus maximus
which is a hip extensor, ok and the gluteus
medius is a major hip abductor. So, the pelvis
is stabilized in the frontal plane mainly
by the gluteus medius the hip, abductor.
We will see this when we do the analysis ah
ah shortly ah and you will find that the gluteus
medius is majorly responsible for stability
in the frontal plane, ok keeping the ah body
erect.
So, more muscles you have these muscles the
and the lliacus which are hip flexors, ok.
They are flexor muscles of the hip and then
the tensor fasciae latae also also a hip abductor,
but more of a minor hip abductor. As you can
see its cross sectional area is considerably
lower than that of the ah gluteus medius.
There is also gluteus minimus ah that is hidden
in this, but so those 3 are the hip adductors
then you have these muscles here which are
the adductors of the hip. So, they would be
the antagonist when the hip is being abducted,
ok. By now, you should be familiar with this
terminology that you know you are not wondering
what I am talking about when I ah say this,
ok.
So, you have the other hip extensors are your
hamstring muscles. So, this is the ah, ok
sorry before let us here you can see the ah
hamstring muscles. So, this is the posterior
view if you look at the pelvic and thigh muscles.
The hamstrings consists of the biceps femoris,
the semimembranosus and the semitendinosus.
So, these muscles together form the hamstrings.
So, when we talk about the hamstrings we are
talking about this group of muscles and these
are hip extensors, they are also the this
is what kind of a muscle these are biarticular
muscles, ok. So, ah actually the biceps ah
femoris is a biarticular muscle. So, these
are also knee flexes. The hip extensors and
knee flexes. You can see here only when you
cut this is the gluteus medius, when you cut
it you can see the gluteus minimus which is
also a hip abductor, both are hip abductors
and gluteus maximus you can see when its cut
this is a hip extensor and then you have the
adductor group of muscles, ok.
So, if you look at the anterior view then
in the anterior view you have at the hip you
have the iliacus and the ah psoas which are
hip flexors, and then you have the quadriceps
femoris. So, this is the 4 headed muscle.
So, it is called because all 4 come together
to ah to a tendon at the knee. So, in the
front of your thigh are the quadriceps which
consists of these 4 muscles you have the ah
rectus femoris, rectus femoris, you have the
ah vastus medialis, the vastus intermedius,
and the vastus can you guess; lateralis. So,
these 4 muscles they are responsible for knee
extension. So, these are the knee extensions
These are also a very important group of muscles,
because you have this mobile ah you know two
link system if you just take the thigh and
the ah shank connected by the knee joint and
for it to be able to bear weight and not you
know collapse, ok. These muscles are very
important because that is what keeps it that
is what straightens out your leg, ok. So,
I mean if if I can you know simulate say if
this is my thigh and this is my ah this thing
when you are bearing weight the tendency will
be to collapse. So, but for the action of
the knee extensors, ok the ah this stability
during walking or any standing activity would
be compromised. So, the knee extensors are
very important group of muscles, ok.
So, and then you have all these stuff it is
called the quadriceps because these 4 muscles
come together into this tendon which is called
the quadriceps tendon or the patellar tendon.
And then you have the sesamoid bone you remember
the patella your kneecap ok, your kneecap
is your is a sesamoid bone. So, it is embedded
in the tendon and that tendon is called the
quadriceps tendon or the patellar tendon,
ok.
And the other side of this tendon, because
the insertion of this is on the tibia ok,
the quadriceps muscle in order to be able
to straighten the leg, inserts into the tibia,
ok. So, the portion of the tendon that 
is below the patella which connects to the
tibia, ok that is called the patellar ligament
it is basically the tendon that comes down
this some people still refer to it as the
patellar tendon on either side of the patella,
but because we refer to structures that connect
bone to bone as ligaments the correct name
would be the patellar ligament for that, ok.
So, these are some of the major muscles you
need to remember when we are doing analysis
of the lower limbs. Hip flexors, hip extensors,
knee flexors, knee extensors, right.
.
And the abductors, ok abduction, adduction,
yeah.
So, we will move on to; now, during walking,
ok one of the critical periods is when you
are supporting your entire body weight on
one leg. So, you have alternating faces when
you are walking, you have alternating phases
where you are supporting your body weight
with both legs and then part of the time you
are supporting it with only one leg. Now,
we will look at a quasistatic analysis because
we are freezing, now walking is actually a
dynamic activity, but we are just going to
freeze at a particular instant when one leg
is off the ground and all the weight is being
supported by the other leg, and then look
at you know what is the influence at the hip
of this kind of a ah of this phase of the
gate. So, this is called single stance, when
all the body weight is on one leg. So, in
this case this is the right leg you have ah.
So, we want to analyze what is happening at
the hip joint in this single stance. So, when
I am looking at the frontal plane. So, I am
doing this analysis in the frontal plane,
ok I am looking at what is happening at the
hip and you can see that the muscle of interest.
So, if I look at the hip joint, ok this is
the, so there will be some joint force at
the hip and the hip abductors will be the
muscles that I am going to be looking at,
ok. That is my that is the muscle that is
acting to kind of prevent the pelvis from
going down. See because when this is lifted
off the ground, ok you have an articulation
here at the hip, this you have this body weight
acting like this, ok and you have the this
hanging leg also and the tendency would be
to do that what prevents that it is got to
be the hip abductors here, ok. So, that is
the muscle that we would be ah looking at
as acting to prevent the tilt. So, let us
say I have F m act, ok.
Then before I do that when I look at the whole
body, ok in single stance for my body to be
ah in static equilibrium, ok the entire body
weight has to pass through the foot, right.
So, my ground reaction acts opposite to that
and this would be equal to simply the the
weight of the body, ok. So, if I draw the
free body diagram of this leg which is on
the ground then I would have the ground reaction
is there anything else I am missing the weight
of the leg itself.
of the leg is coming included in the weight
of the .
So, you have that is the ground reaction,
ok. So, I have the weight of the leg. So,
the assumptions now, would be I am doing an
analysis in the frontal plane. I am assuming
I am clubbing all the hip abductors together
and saying its acting as this muscle force
and let us say I know the angle of that as
some theta and let us say theta equal to 70
degrees.
.
So, if you look at the speeds that are involved,
ok here first of all what what are you considering
as rotating here.
When the legs will be flexing, so there will
be some .
When it is you are talking very low speeds
first of all, ok that you have to consider
inertial forces in cases where the masses
are very high or the and it is. ah
Omega is .
Omega is high, right. So, here we are considering
a quasi static case which means we are saying
omega 0, I am freezing it at a particular
instance and the speed is very low. So, omega
square will be very low, ok. So, I do not
need to consider any inertial forces, ok.
Plus if I look at the entire leg in a if you
are considering rotation about the hip that
omega is going to be negligible, ok. So, you
it is a static analysis we are doing.
So, let us say we have the muscle may give
you some dimensions for this. So, let us say
the weight of the leg is 0.16 W, ok then and
you have these dimensions I say this is acting
theta equal to 70. So, I need say this distance,
let me call it a, then this to this b, c,
ok and the distance between this and this.
So, my ah diagram is not very ah is not the
scale, but let me give you these values a
equal to 7 centimeters, because I do not think
I have the inclination properly it should
be more like this, ok. So, if you look at
this then then these numbers will make sense.
So, I have W leg, I have R equal to W, then
I have F m and J, ok.
So, and then and if this is the line of action
of the body weight then a equal to 7 centimeters,
ah from here to the line of action of the
body weight which is b, b equal to 17.8 centimeters.
This distance c is 10.2, I already have b.
So, I do not have a yeah d is essentially
b. So, c is 10.2 centimeters.
.
Sorry this is a. Now, I can write my equations
as usual and I can find F m and J Can you
find them? What do you mean y is there, only
one I can take it as J x and J y. So, I can
instead of writing just J I can write it as
J, ok I have taken J like that. So, I can
write it as I can split it into the components,
I do not know the angle at which, so those
are the two unknowns the magnitude of J and
the angle at which it acts are the two unknowns
I can either express it in that form or I
can express it as two unknown components J
x and J y.
.
Sorry.
.
Sorry angle.
.
Which angle do you want? The angle of the
muscle, 70 degrees.
.
Yes, you; so I am giving you these dimensions
instead I could either give you the angle
or I could give you these momentums a b c.
.
Which one?
Either the inclination of the of that one
.
This one?
Yeah or hide from that the joint to the bottom.
What would you need that for? For F m.
other component of F m for talk you will not
be able to calculate.
Ok, ok ah let me see what ah hm yeah if I
give you this you can find that, right. So,
say this is the angle that the neck of the
femur, that part is called the neck of the
femur this part, ok. That let us say we know
the angle that makes to the horizontal or
the whole ah inclination I can give you the
inclination of the leg, ok from which you
can find. Let us say we give the inclination
of the leg, ok ah let us say this angle is
say beta, let us say beta equal to an 80,
80 degrees so the leg is inclined at that
angle, ok. It is nearly vertical, ok.
Say if you do this analysis I mean since I
picked beta out of the air, but ah see if
you can give me the values because the values
that I have may not match, I can I find F
m is approximately 1.6 times W, ok if I solve
and I get the joint reaction J the magnitude
of that is 2.4 W you get this by doing, ok.
So, fairly high loads at the hip when you
are in single stance.
I could also do the same analysis by using
the free body diagram of the upper body and
the left leg. So, I am interested in this
interface. So, instead of separating out this
part you know I look at the free body diagram
of that, ok. Then there is no ground reaction
because its suspended, ok it is in the air
and so there is no ground reaction you have
the weight of the body minus the weight of
one leg that is what will be. And the reason
say if this is the midline you put it slightly
to that side of the midline because you removed.
So, if the the right leg removed your cg is
going to be closer to the ah more on the left
side of the midline, ok. So, this is the weight
minus the weight of the leg that would be
acting there and it would essentially be a
3 force system. So, you have this is wrong,
so now, this is way.
So, if I look at this I have F m acting on
the pelvis, ok acting on the upper body then
I have the joint. So, how can I then find
the ah angle of the joint force? So, again
this is there are only 3 forces acting now,
I have F m, J and W minus W leg, they form
a 3 force system. So, saying the 3 forces
are concurrent is equivalent to sigma m equal
to 0, right. So, I am using one equation like
that. So, if I have I know the direction of
F m, I know in what direction it and I know
the direction of W. So, that point of inter
section and my joint wherever I pick my joint
if I join those two that gives me the line
of action of that gives me the line of action
of F J, ok J would act such that it would
also pass through that point.
So, now the direction I know the angle at
which this acts, ok. So, I have F m, I have
W minus and I know that F J has to ah or J
has to act like this so I can determine the
angle at which it acts and then using the
components I can find J x and J y and hence
the magnitude of J, ok. So, direction of J
is determined and then the only thing left
to do is find the magnitude of J, ok. So,
this is using the upper the other portion
of the body as the free body, ok because the
ground reaction does not come into play so
it becomes a 3 force system.
Now, you know that sometimes people who have
trouble walking, ok use a cane, right you
have seen how a person may use a cane while
they are walking. Typically happens when a
person is aging or you know they have had
some injury or ah and it is usually caused
by weak hip abductors they have trouble balancing.
So, balance is a big reason why a person may
want to use a cane, right.
So, what happens is when you have let us let
us look at single stance when you are using
a cane. How does that change things? Let us
say the cane in this case takes up one-sixth
of the body weight, ok let us see. So, the
person presses you know puts about one-sixth
of their body weight on the cane and they
are holding the cane say about ah this distance
is ah 35.5 centimeters about a foot away from
the midline of the body, ok. So, they are
using a cane, let let us look at the same
single stance when you are using the cane.
Now, what happens to the inclination? Ok,
now, you are earlier in single stands your
body weight had to pass through the foot,
ok. Now, your foot is somewhat away from the
midline of the body, ok. So, and first we
need to compute the reaction here, ok. So,
what if this distance is ah we want to compute
what would be this distance L. Now, what is
the value of this reaction?.
5 W.
5 W by 6, the remainder of the body weight,
ok. Where is it going to act? If you take
moments about the midline then what is L?
6.1.
6.1 centimeters; because I have if I have
some moments 5 W L sorry, 5 W by 6 into L
equals W by 6 into 35.5, so I have L equal
to 6.1 centimeters, ok. So, now, my foot is
away from the midline so that also changes
the inclination of my leg. Earlier it was
80 degrees, now it might be something else,
ok. So, it is probably let us say 85.
And if I now do the analysis, so if I look
at I will give you some distances. So, this
is 6 point, ok I called this a, right. So,
a equals 6.98 centimeter now, ok then W leg
acts at a distance b equal to 6.65 centimeters
and again I should draw this more exaggerated,
this distance from where the foot is due this,
this distance c equal to 11.7 centimeter.
Earlier it was 17.8, now it is 11.7. Earlier
it was at the midline, now that is been shifted
by 6.1, ok. So, the main difference is that
the, right foot is no longer at the midline
and then the reaction on the foot earlier
it was the entire body weight, now it is only
five-sixth of the body weight.
So, if you do the analysis now, ok you will
find for this case F m equals 6 time 0.61
times the body weight and J, so I have J and
F m. And let us assume that it may not ah
it may not be true, but we kept we could assume
that theta still remains 70, ok. We can make
an assumption that theta the angle at which
m F m acts with respect to the horizontal
is still 70 degrees in which case I get J
to be equal to 1.26 W. Yes.
we the, should not we calculate the case where
the, for the leg which is near to the stake
like for the critical analysis.
That leg this off, so we we will come to that.
So, that leg is off the ground now.
That means, like we are ah doing the analysis
for the leg which is fine, not the one which
is like damaged or this.
So, you you are making the assumption that
you are going to use the stick on the side
that there is a problem.
.
In the case of weak hip abductors it is the
opposite. So, if you have weak hip abductor
muscles you use the cane on the side opposite
the bad side, ok because the aim is to reduce
the or if you have a painful hip then you
use the cane in on the side opposite to the
painful hip. In other cases where you know
where you do not want to bear the full weight
and so you use the cane on that side that
is a different case. Here we are talking about
at the hip joint when if you have weak hip
abductors or if you have a painful hip, you
will get the benefit of using a cane only
if you are using the cane on the side opposite
the bad hip, ok. Because that is what helps
to reduce the; so even though the cane is
only taking one-sixth of the body weight it
makes a significant difference in the muscle
force that is required to stabilize the body
in the abductor muscle force and correspondingly
the joint forces are also reduced. Because
anytime you have the muscles around a joint
contracting your joint contact forces are
going to increase, in the net joint reaction
force is going to be ah more.
So, the idea is that you use the to compensate
for weak hip abductors or a painful hip you
use the cane on the opposite side. So, this
is sort of counterintuitive to what we normally
think, ok. We all always think if there is
a problem I am going to use a cane on that
side, but in the case of this because in while
walking you need the the maximum effort or
the maximum ah loading at the hip joint happens
in single stance, ok and so that is when you
require this ah assistance, you need to reduce
the loads and that therefore, you use.
So, this moment arm of help you know of the
ground reaction force is what has changed,
right and that has played a big role in reducing
the moment that has to be counteracted by
the hip abductors. So, that is what you are
doing with this ah. Same thing if if you ah
the reverse of it in instead of using a cane,
ok if I am carrying a load on one side then
this is going to be the case where when I
am on single stance on the opposite leg that
is when the loads will be the most on my hip.
So, what do we tend to do normally? You will
tend to lean more towards the side you are
trying to reduce the moment arm, ok that has
to be of the external force that has to be
counteracted by the hip muscles, ok; so that
is the ah effect of the.
So, using a cane you use a cane on the side
opposite the affected side so for injured
side.
Ma'am, in the previous slide.
Yeah.
when position c equals to 11.7 centimeter
previously it was the momentum for the leg
, instead of the leg. Just before this.
Just before this, ok. Let me see.
Here c is the W .
Sorry, sorry, sorry, ok, ok.
.
Hm?
.
Here also. Now, here I have b is 17.8, right.
I have switched b and c in the other one,
ok. So, this should be b.
