Now, that we have looked at the structure
of the musculoskeletal system and we know
about how some of the components operate,
let us move on to applying the principles
of statics first. So, we are going to apply
the principles of mechanics in this course.
We will start off with principles of statics
applied to the human body .
So, we all know that the condition so, if
there are a bunch of forces acting on a body
then we know that if sigma of F equals 0,
then the part the particle or the body has
0 linear acceleration 
and for a rigid body if the sum of the moments
about any point on that ah any point is equal
to 0 then the body has 0 angular acceleration,
a particle does not you cannot apply a torque
about a particle. So, the body has 0 angular
acceleration angular acceleration does not
have any meaning for a particle, you have
ah you can talk about angular acceleration
angular velocity only for a rigid body right
okay.
So, in terms of components typically we use
a cartesian coordinate system. So, in terms
of components you would have 
sigma F x equal to 0, sigma F y equal to 0,
sigma F z equal to 0 and similarly for the
moments M x equal to 0, M y equal to 0, M
z equal to 0 this is for a standard cartesian
coordinate system .
And then we will also you use free body diagrams
as you should all be familiar with this concept,
you basically isolate a body and then represent
the effect of it is surroundings on it. So,
you isolate the body of interest 
and you represent the effects of it is surroundings
by means of forces and moments 
example if you have a beam sorry that is fixed
at one end okay.
Now, if I isolate this beam okay let us say
it has some ah weight. So, you could say that
the weight of the beam acts at it is centroid.
So, that is one effect of the external environment
on it and then because of the fixed support
the fixed support is equivalent.
So, let us as a 2 D equivalent F x F y being
applied to the beam to prevent translation
of the beam in both directions some moment
that is applied at the substitution of the
beam and that support if you had a pinned
beep which was then say supported on a roller
okay then you look at if I isolate the beam
now what does the roller do, the roller allows
motion along the x motion along the y so;
that means, there is a force at this. So,
let us call this point A there is a force
in the y direction which is being applied
by the support okay to prevent the movement
of that and then if you look at the pin joint
the pin essentially prevents x and y it will
allow rotation. So, it does not provide a
resisting moment okay.
So, this is how we draw free body diagrams
right we isolate and also in this case again
the weight of the beam is an x ah represent
all the forces and moments everything the
interaction of the beam with it is surroundings
in terms of forces and moments okay that is
what we do in free body diagrams and. So,
you show and then you use the principles of
statics ah in this case principles of statics,
but if it is a dynamics problem you would
use ah the principles of dynamics to basically
statics is basically just a special case of
dynamics where your accelerations are 0 linear
and angular accelerations are 0 you would
use those equations then to saw unknowns.
So, in when we draw a free body diagram if
we do not know the directions of the unknown
forces you either express it in terms of the
components own direction be your x and y or
whatever else that you take as a known direction
2 orthogonal ah components on the loading
of the ah um beam whatever unknown forces
the signs get determined based on the overall
equilibrium. So, you do not have to worry
about the signs of the ah forces or moments
you assume something and then if what you
get is negative it means the force is directed
or the moment is directed opposite to what
you assumed.
So, these are some basic ah principles that
you are all familiar with and we have seen
that we have looked at the various joints
in the skeletal system we have also looked
at the various ah muscles and how they are
go along ah and we also know that muscles
can only apply tension. So, muscles are like
cables that can only apply tension to the
body that they act on.
So, if you look this in the human body come
across 
you have what are internal forces and you
have external, examples of internal forces
would be forces due to muscles, the ligaments,
points at the joints, the joint forces, these
are all internal forces within the human body
and then the external forces the most common
one that we will encounter is gravity okay.
Then you could have manual or mechanical forces
that are applied external forces applied you
know it could be during different activities
exercise stretching etcetera therapy okay
these are all have devices forces applied
by external devices like assistive devices
.
So, if you see somebody wearing a braces that
are applied because of the interaction of
the body with the external device. In general
because they cannot be the internal forces
are your unknowns in general these forces
are unknowns because them because sometimes
they do put transducers inside they can actually
surgically insert ah to measure internal ah
forces etcetera, but in general we try to
estimate the internal forces through modeling
because they cannot they are not easily measurable
directly okay.
So, there are some things that we need to
know when we do this analysis build a model
or to do a mechanical analysis to know the
following we need to have some idea of the
proper locations of muscle attachments because
the muscles are the primary ah actuators in
the system when we are applying and in on
any part of the skeletal system we need to
know we also need to know the direction in
which the muscle is applying the force. So,
this is where some knowledge of anatomy comes
in you need to know what the muscle what is
going to be the muscle that is ah going to
cause ah this movement or keep it stable and
you need to know how it is going to act.
So, the line of action of the muscle forces
is also something we need to know, we need
to know these parameters, we need to know
the masses of the body segments 
and the locations of their c d s 
because again the weight is an external force
that you need to apply it and because of the
irregular shape you cannot always assume that
the mass is going to be at the ah centroid
of the body because most of these bones are
irregularly shaped. So, we need to know the
masses of the body segments and where their
c d s are located, we also need to know what
kind of a joint.
So, the type of joint that we are dealing
with so, that you know what is it like we
talked about the beam that is fixed versus
a pinned you know what motions are allowed
by the joint. So, that you know to apply the
appropriate reaction forces and moments at
the joint. So, you need to know the type of
joint that you are looking at and you need
to know the axes of rotation, it could be
more than one axes of rotation that you are
considering . So, where is the joint axes
because you again with the bones you have
2 irregularly shaped bodies that are moving
with respect to each other it is not your
mechanical hinge joint for instance where
there is no question where your axes of rotation
is.
So, ah skeletal system some of these axes
actually move as the segment the ah for the
posture that you are considering or for the
movement that you are considering what would
be the appropriate anatomical axes that you
need to consider at a particular configuration.
So, these this is information that you need
to know in order to do proceed with the mechanical
analysis. So, these are all parameters that
are, parameters are quantities that you would
know these are not unknowns you know these
are you may have they are unknown problem
okay, because the mass you know if you are
considering a particular ah segment that has
a specific mark mass for the person that you
are reactivity the person is doing right.
They call body segment parameters like the
masses and so, these are some things that
ah we need to know. So, these are typically
known as BSP and of course, when we go to
the dynamic problems we will also need to
know the moments of inertia of these segments.
So, these are called body segment parameters
and then we will talk about where we can obtain
this data ah .
So, typically the unknown joints and usually
we will make some assumptions to simplify
our analysis because if you look at the body
about any joint you have a variety of interactions
happening, you have multiple muscles that
act about that joint, then you have other
soft tissue, you know like you have ah ligaments
you have ah. So, we make certain assumptions
when we do our analysis in order to simplify
our analysis. So, like I said a model is only
an approximation of the actual system.
The more refined your model the more things
you include in the model the complexity increases
you have a chance of ah you have a better
chance of approximating the real situation
ah in a more accurate manner. Although that
is not always true because the more you know
if you may also have to make more approximations
as you increase the number of ah unknowns
in your model. So, ah first for some of the
things that we do in this course we will make
fairly ah will have fairly simple models and
ah these are some of the assumptions we will
make for we will stick to a planar 2 D analysis.
So, we will either look at will so, we will
say okay well we are restricting our analysis
to what is happening in a single plane and
for the statics problems we are basically
ignoring inertial effects. We assume that
the frictional forces at the joints are negligible,
we know the segmental, we know all the parameters
that we need to, we neglect the effect of
ligaments, tendons juice , the locations of
the muscle attachments are locations of we
know, the lines of action of muscle tension
and we know the anatomical axes. In most cases
also we will make the assumption that only
one muscle is acting for that particular case
that we are considered because if you go to
a 2 D analysis.
How many equations do you have, in the 2 d
analysis you will have basically 3 equations
and sigma of M about some point is perpendicular
to the plane. So, you have 3 scalar equations
and therefore, you can only solve for 3 unknowns
3 unknowns can be solved for solved for are
the muscle force 
and we will solve for the joint reaction forces
the joint reactions which will be some J x
and J y. So, these are typically because these
are the once you cannot direct the kind of
assumptions we make there because one of the
things that you know about muscles is the
reduction is proportional to length.
Velocity.
Velocity.
Um now we are looking at statics problems
we are looking at isometric forces in most
cases.
.
Ah that is at the if you look at you know
okay one muscle .
.
One muscle like this and one muscle like this
okay let us say they are the same length same
resting length suppose they say they are the
same which do you think will produce more
force A or B why do you say that.
Was much the.
The number of.
The cross sectional area right the cross sectional
area the muscle bellies cross sectional area
is something that tells you how much force
they muscle is capable of producing. So, a
muscle with the greater physiological cross
section area can produce more force. So, sometimes
when we use multiple muscle we will make an
assumption based on the cross sectional areas
of the muscle to say okay this muscle may
contribute you know something proportional
to it is cross sectional area.
So, we will ah.
Directly translate to the number of.
Sorry.
direct number for the.
Yeah it translate, but you cannot see what
can you measure okay, for a muscle the cross
sectional area can be measured you cannot
go to the sarcomere level 2 ah properties
that okay, relaxes does not change, but we
will come to that when we do the ah. So, in
a sense these are idealized problem know idealized
models for the body, that we will use, but
we will still be able to gain some insights
into what is happening and maybe a related
to some of the things that we see in our day
to day life that is sort of the purpose of
doing such an analysis . Okay before we go
to that .
So, we assume that anthropometric data, welcome
to what that is 
about the segment to be analyzed is available.
So, based on measurements taken on calibers
ah and statistical ah analysis of those what
we were talking about the mass of body segments,
mass of different bones location of their
CG moments of inertia about the CG, these
are all data that have been compiled for ah
various populations, but mainly caucasian
populations okay.
So, we will ah NASA for instance has a huge
database of this kind of anthropometric data.
So, this anthropometric data is very essential
for any kind of biomechanical analysis because
you need to know ah and a lot of a height
h you can say that the forearm is a certain
fraction of that height h okay. So, this is
so, there are tables available of this anthropometric
ah data which is what we will use for some
of this analysis.
So, this is where you get those body segment
parameters for this for this analysis and
we also make the assumption that you know
being mechanical and engineers we say muscles
function like cables they can only apply tension
okay, bones when we look at the analysis we
will treat them as either beams or rigid bodies
and the human joints we will correlate to
mechanical joints that we are familiar with
. So, muscles, ligaments etcetera would be
like cables and if you look at .
So, in the free body diagram if you had a
muscle or tendon or a ligament that would
be expressed in terms of a tension if I have
a body the action of the muscle on the body
would essentially be a tension and the only
unknown would be the magnitude of that tension
right because I will know this from the anatomical
data I know at what angle that muscle is acting
on that particular member.
The muscle will provide a tension pull.
Yes muscles can only.
Compress.
Muscles can only pull, muscles can only pull
then again if you know that something is so,
muscle is basically a flexible member like
a cable. Then if you have a 2 force member
again if a member is only subjected to 2 forces
and if it is massless you have a massless
2 force member what do you know about the
forces, they will be equal and opposite they
will be along the line of that diagram you
could assume that you can always assume a
direction, but it would be basically along
the member, then of course, rollers simple
support so, the equivalent would be if you
have bone on bone contact.
Mam.
Yes.
Already bring to this muscles to member also
the muscles.
So, we would ah the muscle would be that is
right so, you basically say that and the unknown
would be the magnitude of the force because
we are not really taking into account the
mass of the muscle when we do this analysis.
So, we say whatever tension is developed at
one end is the same tension that is developed
at the other end.
In some cases bone on bone contact may be
modelled as a roller so, you say that the
forces normal to the surfaces of contact let
me put it as forces along the common normal
in contact and so, again if you know the direction
of the force only the magnitude of the force
will be the unknown, then the hinge connections
that we model as actions now, we talked about
the knee, knee joint we talked about the elbow
which are akin to hinge joints.
There you will have 2 unknowns F x and F y
because the hinge prevents movement in 2 directions
okay, now you know that in the actual structure
with the condyloid joints you are like a pure
hinge, but it is the surrounding. So, you
have examples or the elbow or the knee and
basically the magnitude. So, you can either
think of it as 2 unknowns in terms of the
magnitude and direction of the force or 2
components so, you have 2 unknowns or magnitude
and direction of force yeah.
where is some hinge order hindrance some joints
will be there.
So, in some joints you could say that at that
instant so, you have something rolls that
at that particular instant okay. So, it is
like this I have a fairly flat surface and
the other joint is moving like that okay I
could also treat this as a contact similar
to a roller .
Then you have the ball and socket, joint like
your hip or your shoulder and in that basically
what is the situation you have F x, F y and
F z okay movement is prevented linear movement
is prevented. So, force resistive force prevents
a linear movement right the case of the ball
and socket it allows it does not support moments
in all 3 planes okay so, you have no resisting
moment.
Mam we are talking about only 2 D.
Will yeah this is just for completeness you
know this is how we ah map it to what we know
in mechanics.
Mam bone to bone contact is it ah really bone
to bone contact or there is some fluid or
soft tissue in between.
There will be yeah except in cases where there
is degeneration in the joint which is then
you know like after osteoarthritis or something
like that then if there is direct bone it
is very painful, direct bone to bone trying
that becomes very painful most of the joints
the movable joints are synovial joints which
have like we talked about the capsule and
they have synovial fluid and all that acts
to distribute the forces and when we talk
about a net force at that joint we are talking
about the resultant of that distributed force
because that is what we can measure we cannot
really measure the actual force distribution
across the joint so, you will have 3 unknowns
here 
F x, F y and F z.
So, if you look at joints which are more or
less fixed like the joints in your skull right
the fibrous joints where there is ah little
or basically no movement, then that is equivalent
to the fixed or welded or built in, similar
to your beam 
or the join between the tibia and the fibula
where there is no at the ah proximal end tibia
and fibula you there is practically no movement
there if you were to model something like
that and if you were interested in ah that
then you would use a and you would also have
3 moments.
So, I will mark it as with the double arrows,
but right hand roll we are talking about so,
at the moment is like this then M z is mark
like that. So, you have 6 unknowns here 3
forces, 3 moment so, this is basically just
a quick review of your statics you know how
you represent different joints how you represent
different kinds of members okay .
