bio mechanics.pptx

BIO-MECHANICS,
APPLIED ANATOMY &
KINESESIOLOGY
DR.P.Muthukrishnan,.M.P.T,(Ortho)

INTRODUCTION
• Define the terms biomechanics, statics, dynamics,
kinematics, and kinetics, and explain the ways in which they
are related.
• Describe the scope of scientific inquiry addressed by
biomechanists.
• Distinguish between qualitative and quantitative
approaches for analyzing human movement.
• Explain how to formulate questions for qualitative analysis
of human movement.

Cont,
• The term biomechanics combines the prefix bio, meaning "life,"
with the field of mechanics, which is the study of the actions of
forces.The international community of scientists adopted the
term biomechanics during the early 1970s to describe the
science involving the study of the mechanical aspects of living
organisms.
• Within the fields of kinesiology and exercise science, the living
organism most commonly of interest is the human body.The
forces studied include both the internal forces produced by
muscles and the external forces that act on the body.

• anatomy, physiology, mathematics, physics, and
engineering provide background knowledge for
biomechanists.

BIOMECHANICAL APPLICATIONTO
JOINT STRUCTURE AND FUNCTION

INTRODUCTION
• Humans have the capacity to produce a nearly infinite variety
of postures and movements that require the structures of the
human body to both generate and respond to forces that
produce and control movement at the body’s joints.
• Although it is impossible to capture all the kinesiologic
elements that contribute to human musculoskeletal function at
a given point in time, a knowledge of at least some of the
physical principles that govern the body’s response to active
and passive stresses on its segments

FOUNDATIONAL KINE- SIOLOGIC PRINCIPLES

KINEMATICS AND INTRODUCTIONTO
KINETICS
• Kinetics is focused on
understanding the cause of
different types of motions of
an object such as rotational
motion in which the object
experiences force or torque.
• Kinematics explains the
terms such as acceleration,
velocity, and position of
objects.

Descriptions of Motion
• Kinematics includes the set of concepts that allows
us to describe the motion (or displacement) of a
segment without regard to the forces that cause
that movement.
• The human skeleton is, quite literally, a system of
segments or levers. Although bones are not truly
rigid, we will assume that bones behave as rigid
levers.

THEREARE FIVE KINEMATICVARIABLESTHAT FULLY
DESCRIBE MOTION OR DISPLACEMENTOF A
SEGMENT
• (1) the type of displacement (motion),
• (2) the location in space of the displacement,
• (3) the direction of displacement of the segment,
• (4) the magnitude of the displacement, and
• (5) the rate of displacement or rate of change of dis-
placement (velocity or acceleration).

TYPES OF DISPLACEMENT
• Translatory and rotatory motions are
the two basic types of movement that
can be attributed to any rigid seg-
ment.
• Additional types of movement are
achieved by combinations of these
two.

TRANSLATORY MOTION (LINEAR
DISPLACEMENT)
• It’s the movement of a
segment in a straight line. In true
translatory motion, each point
on the segment moves through
the same distance, at the same
time, in parallel paths.

Rotatory Motion
• Rotatory motion (angular
displacement) is movement of a
segment around a fixed axis (center
of rotation [CoR]) in a curved path.
In true rotatory motion, each point
on the segment moves through the
same angle, at the same time, at a
constant distance from the CoR.

General Motion
• When nonsegmented objects are moved,
combinations of rotation and translation (general
motion) are common and can be very evident.

LOCATION OF DISPLACEMENT IN SPACE
• The rotatory or translatory
displacement of a segment is
commonly located in space by
using the three-dimensional
Cartesian coordinate system,

• The origin of the x-axis, y-axis, and z-axis of the
coordinate system is traditionally located at the
center of mass (CoM) of the human body, assuming
that the body is in anatomic position
• the x-axis runs side to side in the body and is labeled
in the body as the coronal axis; the y-axis runs up
and down in the body and is labeled in the body as
the vertical axis; the z-axis runs front to back in the
body and is labeled in the body as the
anteroposterior (A-P) axis

• Rotation of a body segment is described not only as
occurring around one of three possible axes but also
as moving in or parallel to one of three possible
cardinal planes.

Direction of Displacement
• Even if displacement of a segment is
confined to a single axis, the rotatory
or translatory motion of a segment
around or along that axis can occur in
two different directions.
• For rotatory motions, the direction of
movement of a segment around an
axis can be described as occurring in a
clockwise or counterclockwise
direction

• Flexion and extension are motions of a segment
occurring around the same axis and in the same
plane (uniaxial or uniplanar) but in opposite
directions. Flexion and extension generally occur in
the sagittal plane x axis (passes from side to side)

• Abduction and adduction of a segment occur around the
same axis and in the same plane but in opposite directions.
Abduction/adduction and lateral flexion generally occur in
the frontal plane around an A-P axis,

• Medial (or internal) rotation and lateral (or external)
rotation are opposite motions of a segment that generally
occur around a vertical (or longitudinal) axis in the
transverse plane.

Magnitude of Displacement
• The magnitude of rotatory motion (or angular dis-
placement) of a segment can be given either in
degrees (United States [US] units) or in radians
(International System of Units [SI units]).

ROTATORY MOTION
• The magnitude of rotatory motion that a body
segment moves through or can move through is
known as its range of motion (ROM).
• The most widely used standardized clinical method
of measuring available joint ROM is goniome- try,
with units given in degrees.

TRANSLATORY MOTION
• Translatory motion or displacement of a segment is quantified
by the linear distance through which the object or segment is
displaced.The units for describing translatory motions are the
same as those for length.The SI system’s unit is the meter (or
millimeter or cen- timeter); the corresponding unit in the US
system is the foot (or inch).
For example, the 6- minute walk6 (a test of functional status in
individuals with cardiorespiratory problems) measures the
distance (in feet or meters) someone walks in 6 minutes. Smaller
full body or segment displacements can also be measured by
three-dimensional motion analysis systems.

Rate of Displacement
• Displacement per unit time regardless of direction is known as
speed, whereas displacement per unit time in a given direction is
known as velocity. If the velocity is changing over time, the change
in velocity per unit time is acceleration. Linear velocity (velocity of a
trans- lating segment) is expressed as meters per second (m/sec) in
SI units or feet per second (ft/sec) in US units; the corresponding
units for acceleration are
• meters per second squared (m/sec2) and feet per second squared
(ft/sec2). Angular velocity (velocity of a rotating segment) is
expressed as degrees per second (deg/sec), whereas angular
acceleration is given as degrees per second squared (deg/sec2).

• An electrogoniometer or a three-dimensional
motion analysis system allows documentation of the
changes in displacement over time.

Definition of Forces
• Whether a body or body segment is in
motion or at rest depends on the forces
exerted on that body.
• A force, simplistically speaking, is a push or
a pull exerted by one object or substance on
another. Any time two objects make
contact, they will either push on each other
or pull on each other with some magnitude
of force

THEORETICAL CON- CEPT” FORCES
• A force (F) is described by the acceleration (a)
of the object to which the force is applied,
with the acceleration being directly pro-
portional to the mass (m) of that object;
• Because mass is measured in kilograms (kg)
and acceleration in m/sec2, the unit for force
is actually kg-m/sec2

External forces
• External forces are pushes or pulls on the
body that arise from sources outside the
body. Gravity (g), the attraction of the
Earth’s mass to another mass, is an external
force that under normal conditions
constantly affects all objects.

Internal forces
• Internal forces are forces that act on
structures of the body and arise from the
body’s own structures
• A few common examples are the forces
produced by the muscles (pull of the biceps
brachii on the radius), the ligaments (pull of a
ligament on bone), and the bones (the push of
one bone on another bone at a joint). Some
forces, such as atmospheric pressure (the push
of air pressure), work both inside and outside
the body, but— in our definition—are
considered external forces

ForceVectors
• All forces, despite the source or the object acted
on, are vector quantities.
• 1) has its base on the object being acted on (the
point of application),
• (2) has a shaft and arrowhead in the direction of
the force being exerted and at an angle to the
object acted on (direction/orientation), and
• (3) has a length drawn to represent the amount
of force being exerted (magnitude).

THE FORCE OF GRAVITY
• the force of gravity can be fully
described by point of application,
action line/direction/orientation, and
magnitude
• Unlike other forces that may act on
point or limited area of contact, gravity
acts on each unit of mass that
composes an object.

CENTER OF GRAVITY (COG)
• The force of gravity acting on an object or segment
is considered to have its point of application at the
CoM or center of gravity (CoG) of that object or
segment—the hypothetical point at which all the
mass of the object or segment appear to be
concentrated. Every object or segment can be
considered to have a single CoM.
• In a symmetrical object, the CoM is located in the
geometric center of the object (Fig. 1-18A). In an
asym- metrical object, the CoM will be located
toward the heavier end because the mass must be
evenly distrib- uted around the CoM

LINE OF GRAVITY (LOG).
• Although the direction and
orientation of most forces vary with
the source of the force, the force of
gravity acting on an object is always
vertically downward toward the
center of the earth.The gravitational
vector is commonly referred to as the
line of gravity (LoG).

SEGMENTAL CENTERS OF MASS AND
COMPOSITION OF GRAVITATIONAL FORCES
• Each segment in the body
can be considered to have
its own CoM and LoG. the
gravitational vectors
(LoGs) acting at the CoMs
of the arm, the forearm,
and the hand segments
(vectors GA, GF, and GH,
respectively).

RESULTANT FORCE & COMPOSITION OF FORCES.
• The new vector will have the
same effect on the
combined forearm-hand
segment as the original two
vectors and is known as the
resultant force. The process
of combining two or more
forces into a single resultant
force is known as
composition of forces.

Center of Mass of the Human Body
• When all the segments of the body
are combined and considered as a
single rigid object in anatomic
position, the CoM of the body lies
approximately anterior to the second
sacral vertebra (S2).
• The precise location of the CoM for a
person in anatomic position depends
on the proportions (weight
distribution) of that person.

Cont,.
• If a person really were a rigid object, the CoM would
not change its position in the body, regardless of
whether the person was standing up, lying down, or
leaning forward. Although the CoM does not change
its location in the rigid body as the body moves in
space, the LoG changes its relative position or
alignment within the body.

(BASE OF SUPPORT [BOS])
• the LoG is between the person’s feet (base of
support [BoS]) as the person stands in anatomic
position; the LoG is parallel to the trunk and limbs. If
the person is lying down (still in anatomic position),
the LoG projecting from the CoM of the body lies
perpendicular to the trunk and limbs, rather than
parallel as it does in the standing position.

CONT,.
• A person is not rigid and does not remain in
anatomic position. Rather, a person is constantly
rearranging segments in relation to each other as
the person moves.With each rearrangement of body
segments, the location of the individual’s CoM will
potentially change.The amount of change in the
location of the CoM depends on how
disproportionately the segments are rearranged.

ALTERATIONS IN MASS OF AN OBJECT OR
SEGMENT
• The location of the CoM of an object
or the body depends on the
distribution of mass of the object.
The mass can be redistributed not
only by rearranging linked segments
in space but also by adding or taking
away mass. People certainly gain
weight and may gain it
disproportionately in the body (thus
shifting the CoM).

CENTER OF MASS, LINE OF GRAVITY, AND STABILITY
• However, the point of application, action
line, and direction remain accurate. By
extending the football player’s LoG , we can
see that the LoG is anterior to his BoS; it
would be impossible for the player to hold
this pose. For an object to be stable, the
LoG must fall within the BoS. When the LoG
is outside the BoS, the object will fall.

Cont,.
• When the BoS of an object is large, the
LoG is less likely to be displaced outside
the BoS, and the object, consequently, is
more stable. When a person stands with his
or her legs spread apart, the base is large
side to side, and the trunk can move a
good deal in that plane without displacing
the LoG from the BoS and without falling
over

INTRODUCTIONTO STATICS AND DYNAMICS
• The primary concern when looking at
forces that act on the body or a
particular segment is the effect that the
forces will have on the body or segment.
If all the forces acting on a segment are
“balanced”, the segment will remain at
rest or in uniform motion.

Statics
• If the forces are not “balanced,” the
segment will accelerate. Statics is the
study of the conditions under which
objects remain at rest.

Dynamics
• Dynamics is the study of the
conditions under which objects move.

Newton’s Law of Inertia
• Newton’s first law, the law of inertia,
identifies the conditions under which an
object will be in equilibrium. Inertia is the
property of an object that resists both the
initiation of motion and a change in motion
and is directly proportional to its mass.
• The law of inertia states that an object will
remain at rest or in uniform (unchanging)
motion unless acted on by an unbalanced
(net or resultant) force.

• Newton’s law of inertia (or law of
equilibrium) can be restated thus: For
an object to be in equilibrium, the sum
of all the forces applied to that object
must be zero.
• ∑F =0

Newton’s Law of Acceleration
The magnitude of acceleration of a moving
object is defined by Newton’s second law, the
law of acceleration. Newton’s second law
states that the acceleration (a) of an object is
proportional to the net unbalanced (resultant)
forces acting on it (Funbal) and is inversely
proportional to the mass (m) of that object:

Translatory Motion in Linear and Concurrent
Force Systems
• The process of composition of forces is used to determine
whether a net unbalanced force (or forces) exists on a segment,
because this will determine whether the segment is at rest or in
motion.
• Furthermore, the direction/orientation and location of the net
unbalanced force or forces determine the type and direction of
motion of the segment.
• The process of composition of forces was oversimplifiedThe
process of composition depends on the relationship of the
forces to each other: that is, whether the forces are in a linear,
concurrent, or parallel force system.

Linear Force System
• A linear force system exists whenever two or more forces
act on the same segment, in the same plane, and in the
same line (their action lines, if extended, overlap). Forces
in a linear force system are assigned positive or negative
signs.
• Forces applied up (y-axis), forward or anterior (z-axis), or
to the right (x- axis) will be assigned positive signs,
whereas forces applied down, back or posterior, or to the
left will be assigned negative signs.

Determining Resultant Forces in a Linear
Force System
• All forces in the same linear force system can be composed into
a single resultant vector.
• The resultant vector has an action line in the same line as that of
the original composing vectors, with a magnitude and direction
equivalent to the arithmetic sum of the composing vectors.
• Because the vectors in a linear force system are all co-linear and
coplanar, the point of application of the resultant vector will lie
along the common action line of the composing vectors, and the
resultant will have the same orientation in space as the
composing vectors.

• capsuloligamentous structures are best visualized
as string or cords with some elasticity that can
“pull” (not “push”) on the bones to which they
attach. a schematic representation of the capsu-
loligamentous structures that join the femur and
the tibia. [Side-bar: In reality, the capsule surrounds
the adjacent bones, and the ligamentous
connections are more complex.]We will nickname
the structures “Acapsule” (anterior capsule) and
“Pcapsule” (posterior capsule), understanding that
these two forces are representing the pull of both
the capsule and the capsular ligaments at the knee

DISTRACTION FORCE.
• the net downward force ofWbLf and GLf would tend
to move the leg-foot segment away from the femur,
minimizing or eliminating the contact of the femur
with the leg-foot segment. A net force that moves a
bony segment away from its adjacent bony segment
is known as a distraction force.

COMPRESSIVE FORCE
• Joint reaction forces are dependent on the existence
of one force on each of the adjacent joint segments
that is perpendicular to and directed toward its joint
surface.The two forces that cause joint reac- tions
forces are known as compression forces.

CONCURRENT FORCE SYSTEM
• It is quite common for forces applied to an object to have
action lines that lie at angles to each other.
• The net effect, or resultant, of concurrent forces appears
to occur at the common point of application (or point of
intersection). Any two forces in a concurrent force system
can be composed into a single resultant force with a
graphic process known as composition by parallelogram.

COT,..
• The resultant has the same point of application
as the original vectors and is the diagonal of the
parallelogram. If there are more than two
vectors in a concurrent force system, a third
vector is added to the resultant of the original
two through the same process.The sequential
use of the resultant and one of the original
vectors continues until all the vectors in the
original concurrent force system are accounted
for.

Newton’s Law of Reaction
• When two objects touch, both must touch
each other and touch with the same
magnitude. Isaac Newton noted this
compulsory phenomenon and concluded
that all forces come in pairs that are
applied to contacting objects, are equal in
magnitude, and are opposite in direction.
This is known as Newton’s third law,

• When one object applies a force to the
second object, the second object must
simultaneously apply a force equal in
magnitude and opposite in direction to that
of the first object.These two forces that are
applied to the two contacting objects are an
interaction pair and can also be called
action-reaction (or simply reaction)
forces.

GRAVITATIONALANDCONTACT
FORCES
• We generally assume when we get on a scale
that the scale shows our weight .A person’s
weight (gravity-on-person [GP]), however, is
not applied to the scale and thus cannot act on
the scale.What is actually being recorded on
the scale is the contact (push) of the “person-
on-scale” (PS) and not “gravity-on-person.”The
distinction between the forces GP and PS and
the relation between these two forces can be
established by using both Newton’s first and
third laws.

Additional Linear Force Considerations
• the ability of the capsule to pull on the leg-foot
segment is dependent on the amount of tension
that the capsule can withstand.This requires an
understanding of tensile forces and the forces that
produce them.

TENSILE FORCES
• Tension in the joint capsule, just like tension in
any passive structure (including relatively solid
materials such as bone), is created by opposite
pulls on the object. If there are not two opposite
pulls on the object (each of which is a tensile
force), there cannot be tension in the object.
Remembering that the connective tissue capsule
and ligaments are best analogized to slightly
elasticized cord, we first examine tension in a
cord or rope.

TENSILE FORCES ANDTHEIR REACTION FORCES
• Hands-on-rope (HR) is a tensile vector and,
therefore, must be equivalent in magnitude and
opposite in direction to the other tensile
vector, block-on-rope (BR). Not only is the
tensile vector block-on-rope (BR) equal to the
other tensile vector (HR), but tensile vector BR is
also equivalent in magnitude and opposite in
direction to its reaction force, rope-on-block
(RB) Consequently, as long as the rope can
structurally withstand the tension, the pull of
hands-on-rope (HR) will be transmitted through
the rope to an equivalent pull on the block (RB).

joint distraction
• The magnitude of pull of the capsule (and ligaments) on
the leg-foot segment would be neg- ligible as long as HLf
had a magnitude equal and opposite to that of GLf and
WbLf. As the upward support of the hand is taken away,
however, there would be a net unbalanced force down
on the leg-foot segment that would cause the leg-foot
segment to accelerate away from the femur.The pull or
movement of one bony segment away from another is
known as joint distraction.

Distraction Forces
• A joint distraction force cannot exist in isolation;
joint surfaces will not separate unless there is a
distraction force applied to the adjacent segment
in the opposite direction. As the leg-foot segment
is pulled away from the femur, any tension in the
capsule created by the pull of the leg-foot segment
on the capsule results in a second tensile vector in
the capsule (femur-on- capsule).

joint reaction forces
• When the two segments of a joint are pushed
together and “touch,” as occurs with the upward
support of the hand in the resulting reaction
(contact) forces are also referred to as joint reaction
forces. Joint reaction forces are contact forces that
result whenever two or more forces cause contact
between contiguous joint surfaces.

compression forces
• Joint reaction forces are dependent on the existence
of one force on each of the adjacent joint segments
that is perpendicular to and directed toward its joint
surface.The two forces that cause joint reac- tions
forces are known as compression forces.

Vertical and Horizontal Linear Force
Systems
• Newton’s law of inertia (or law of
equilibrium) can be broken down into
component parts:The sum of the vertical
forces (FV) acting on an object in
equilibrium must total zero (∑FV 0), and,
independently, the sum of the horizontal
forces (FH) acting on an object in
equilibrium must total zero (∑FH 0).

shear force
• A force (regardless of its source) that
moves or attempts to move one object on
another is known as a shear force (FS). A
shear force is any force (or the compo-
nent of a force) that is parallel to
contacting surfaces (or tangential to
curved surfaces) and has an action line in
the direction of attempted movement.

• A friction force (Fr) potentially exists on an
object whenever there is a contact force on
that object. Friction forces are always parallel
to contacting surfaces (or tangential to
curved surfaces) and have a direction that is
opposite to potential movement. For fric-
tion to have magnitude, some other force (a
shear force) must be moving or attempting to
move one or both of the contacting objects
on each other.

Static Friction
• The magnitude of a friction force on an object is always a
function of the magnitude of contact between the objects
and the slipperiness or roughness of the contacting
surfaces.
• When two contacting objects with shear forces applied to
each are not moving, the magnitude of friction on each
object is also proportional to the magnitude of the shear
forces.
• If the two objects are not moving (objects are static), the
maximum magnitude of the force of static friction (Frs)
on each object is the product of a constant value known
as the coefficient of static friction (’
S) and the magnitude
of the contact force

• The coefficient of static friction is a constant value for
given materials. For example, for ice on ice is
approximately 0.05; the value of for wood on wood is
as little as 0.25.5As the contacting surfaces become
softer or rougher, ’
S increases.As the magnitude of
contact (FC) between objects increases, so too does
the magnitude of potential friction.
• Increasing the pressure increases the contact force
between the hands and increases the maximum value
of friction (the coefficient of friction exmains
unchanged because the surface remains skin on skin)

kinetic friction
• Once an object is moving, the magnitude of the
force of kinetic friction (FrK) on the contacting
objects is a constant value, equal to the product
of the contact force (FC) and the coefficient of
kinetic friction (’)K
• The coefficient of kinetic friction (’
K) is always
smaller in magnitude than the coefficient of static
friction (’
S) for any set of contacting surfaces.

Kinetics—Considering Rotatory andTranslatory Forces
and Motions
• When an object is completely unconstrained (not at-
tached to anything), a single force applied at or through
the CoM of the object will produce linear displacement
regardless of the angle at which the force is applied

Torque, or Moment of Force
• When the force applied to an
unattached object does not pass
through the CoM, a combination
of rotation and translation will
result .To produce pure rotatory
motion (angular displacement), a
second force that is parallel to the
original force must be applied to
the object or segment.

• When a second force (FB2) equal in
magnitude and opposite in direction to
FB is applied parallel to FB (applied to
the same object at any other point), the
translatory motions of FB and FB2 will
offset each other (as they do in a linear
force system), and pure rotatory motion
will occur.

• Two forces that are equal in
magnitude, opposite in direction, and
applied to the same object at different
points are known as a force couple.

• A force couple will always produce pure rota-
tory motion of an object (if there are no other
forces on the object).The strength of rotation
produced by a force couple is known as torque
(T), or moment of force, and is a product of the
magnitude of one of the forces and the shortest
distance (which always will be the perpendicular
distance) between the forces:
• T =(F)(d)

Angular Acceleration
• If the torque created by the force couple is
unopposed (there are no other forces on the
segment), the result will be rotatory (or
angular) acceleration of the segment. Linear
(translatory) acceleration (a), as already
noted, is a function of net unbalanced force
and the mass (m) of the object
• (a = Funbal ÷ m).
• Angular acceleration is given in deg/sec2 and
is a function of net unbalanced torque and the
mass (m) of the object:

Angular Equilibrium
• When the torques on an object are
balanced (∑T = 0), the object must be
in angular (rotatory) equilibrium (no
resultant angular acceleration).
• We can now identify three conditions
that are independently necessary for
an object or segment to be com-
pletely at rest:

Parallel Force Systems
• Because the forces in a force couple are parallel
to each other, the two forces are part of a
parallel force system. A parallel force system
exists whenever two or more forces applied to
the same object are parallel to each other.
• The torque generated by each force is deter-
mined by multiplying the magnitude of that
force by its distance (MA) either from the point
of constraint of the segment or from an
arbitrarily chosen point on the segment (as long
as the same point is used for all forces).

Determining Resultant Forces in a
Parallel Force System
• The net or resultant torque produced by forces in the same parallel force
system can be determined by adding the torques contributed by each force
• Three forces are applied to an unconstrained segmentThe magnitudes of
F1, F2, and F3 are 5 N, 3 N, and 7 N, respectively.The MAs between F1, F2,
and F3 and an arbitrarily chosen point (Œ) are 0.25 m, 0.12 m, and 0.12 m,
respectively. F1 and F2 are applied in a clockwise direction, whereas F3 is
applied in a counterclockwise direction (in relation to the chosen point of
rotation).The resultant torque (T)

Bending Moments
• When parallel forces are applied
to an unsegmented object
(assumed to be rigid) in a way
that results in equilibrium
(neither rotation nor translation
of the segment), the torques, or
moments of force, applied to a
particular point on the object are
considered to be bending
moments.

torsional moment
• A torsional moment is sometimes
considered a spe- cial case (or
subcategory) of a torque, or moment of
force, whereby a so-called torsional force
creates (or tends to create) a rotation of a
segment around its long axis

Identifying the Joint Axis about
which Body Segments Rotate
• In the human body, the motion of a segment at a joint is
ultimately constrained by the articular structures, either by
joint reaction forces (bony contact) or by cap-
suloligamentous forces. Any translatory motion of a seg-
ment produced by a force (e.g., gravity) will be checked
before too long by the application of a new force (the push of
a joint reaction force or the pull of a joint capsule or
ligaments).

Meeting theThree Conditions for
Equilibrium
• We have now established that
everything that contacts a segment
of the body creates a force on that
segment and that each force has the
potential to create translatory
motion (vertical or horizontal),
rotatory motion (torque), or both.

Total Muscle ForceVector
• The force applied by a muscle to a
bony segment is actually the
resultant of the pull on a common
point of attachment of all the
fibers that compose the muscle.
Because each muscle fiber can be
represented by a vector that has
a common point of application
the fibers taken together form a
concurrent force system with a
resultant that represents the total
muscle force vector (Fms)

• Every muscle pulls on each of its attachments
every time the muscle exerts a force.
Therefore, every muscle creates a minimum of
two force vectors, one on each of the two (or
more) segments to which the muscle is
attached; each of the two (or more) vectors is
directed toward the middle of the muscle.The
type and direction of motion that results
from an active muscle contraction depends
on the net forces and net torques acting on
each of its levers.The muscle will move a seg-
ment in its direction of pull only when the
torque of the muscle exceeds the potential
opposing torques.

Anatomic Pulleys
• When the direction of pull of a muscle is
altered, the bone or bony prominence
causing the deflection forms an anatomic
pulley. Pulleys (if they are
• frictionless) change the direction without
changing the magnitude of the applied
force. As we will see, the change in action
line produced by an anatomic pulley (even
without affecting force) will have
implications for the ability of the muscle to
produce torque.

Anatomic Pulleys, Action Lines, and
Moment Arms
• A schematic representation of the
muscle and muscle force produced by
the middle deltoid muscle if the
muscle crosses two straight levers. B.
A more anatomic representation of
the bony levers to which the middle
deltoid muscle is attached, showing
its line of pull deflected away from
the joint axis by the anatomic pulley
of the humeral head.

Torque Revisited
• We are now ready to add the
quadriceps muscle force to Sam
Alexander’s leg-foot segment at the
point at which knee extension is to be
initiated in the weight boot example.
shows the pull of the quadriceps
muscle on the leg-foot segment (QLf).
In the force of gravity (GLf) and the
force of the weight boot (WbLf) are
represented as a single resultant
force, GWbLf, as was done.

Changes to Moment Arm of a Force

Angular Acceleration with
ChangingTorques

Moment Arm and Angle of
Application of a Force

Lever Systems, or Classes of
Levers
• One perspective used to assess the relative torques of internal and external forces
is that of lever systems, or classes of levers.
• A lever is any rigid segment that rotates around a fulcrum. A lever system exists
whenever two forces are applied to a lever in a way that produces opposing
torques.
• In a lever system, the force that is producing the resultant torque (the force acting
in the direction of rotation) is called the effort force (EF). Because the other force
must be creating an opposing torque, it is known as the resistance force (RF).
Another way to think of effort and resistance forces acting on a lever is that the
effort force is always the winner in the torque game, and the resistance force is
always the loser in producing rotation of the segment.
• The MA for the EF is referred to as the effort arm (EA), whereas the MA for the RF
is referred to as the resistance arm (RA).Once the effort and resistance forces are
identified and labeled, the position of the axis and relative sizes of the effort and
resistance arms determine the class of the lever.

first-class lever
• A first-class lever is a lever system in which the axis lies
between the point of application of the effort force and the
point of application of the resistance force, without regard
to the size of EA or RA. As long as the axis lies between the
points of application of the EF and RF, EA can be bigger
than RA (Fig. 1-69A), smaller than RA

• the feature of this order is stability, and
a state of equilibrium can be achieved
either with or without mechanical
advantage.
• One example of this type of lever is
demonstrated during nodding
movement of the head; the skull
represents the lever, the atlanto-
occipital joints the fulcrum, the weight
is situated anteriorly in the face, and
the effort is supplied by the
contraction of the posterior Neck
muscles, applied at their attachment
to the occipitalbone.

second-class lever
A second-class lever is a lever system in which the resistance
force has a point of application between the axis and the
point of application of the effort force, which always results
in EA being larger than RA between the axis and the point of
application of the effort force, which always results in EA
being larger than RA

• this is the lever of power as there must always be a
• mechanical advantage. An example in the lower limb
is
• demonstrated when the heels are raised to stand on
the
• toes.The tarsal and metatarsal bones are stabilized by
• muscular action to form the lever, the fulcrum is at the
• metatarsophalangeal join, and the weight of the body
is
• transmitted through the ankle joint to the talus.The
effort is
• applied at the insertion of the tendo- calcneum by the
• contraction of the calf muscle. In the arm, the action
of
• Brachioradialis muscle in flexing the elbow joint can

third-class lever
• A third-class lever is a lever system
in which the effort force has a point
of application between the axis and
the point of application of the
resistance force, which always
results in RA being larger than EA

• When the lever is the forearm, the fulcrum is the
• elbow joint, and when the effort is supplied by
the
• contraction of the Brachialis muscle applied at its
• insertion, and the weight is some object held in
the
• hands, it can be seen that a small amount of
• muscular contraction will be translated into
much
• more extensive and rapid movement at the
hand.
• The action of the Hamstring muscles in flexing
the
• knee is another simple example.

Mechanical Advantage
• Mechanical advantage (M Ad) is a measure of the mechanical
efficiency of the lever (the relative effec- tiveness of the effort
force in comparison with the resistance force).
• Mechanical advantage is related to the classification of a
lever and provides an understanding of the relationship
between the torque of an external force (that we can roughly
estimate) and the torque of a muscular force (that we can
estimate only in relation to the external torque).
• Mechanical advantage of a lever is the ratio of the effort arm
(MA of the effort force) to the resistance arm (MA of the
resistance force), or:

Trade-Offs of Mechanical Advantage
• It has already been observed that the majority of
the muscles in the human body, when contracting
concen- trically and distal lever free, work over a
shorter MA than does the external force on that
lever.To move a lever, a muscle must exert a
proportionally very large force to produce a
“winning” torque. It appears, then, that the
human body is structured inefficiently. In fact, the
muscles of the body are structured to take on the
burden of “mechanical disadvantage” to achieve
the goal of rotating the segment through space.

Limitations to Analysis of Forces
by Lever Systems
• Although the conceptual framework of lever
systems described here provides useful terms
and some additional insights into rotation of
segments and muscle function, there are
distinct limitations to this approach. Our
discussion of lever systems ignored the fact
that rotation of a lever requires at least one
force couple.An effort force and resistance
force are not a force couple because the effort
and resistance forces produce rotation in the
opposite (rather than the same) direction.

Force Components
• Resolving
Forces into
Perpendicula
r and Parallel
Components
• Perpendicula
r and Parallel
Force Effects

Determining Magnitudes of
Component Forces
• In a figure drawn to scale, the relative
vectors lengths can be used to ascertain
the net unbalanced forces. Because the
vectors are not drawn to scale in, the
relative magnitudes of Fy and Fx must be
determined by using trigonometric
functions of sines (sin) and cosines (cos)
that are based on fixed rela- tionships for
right (90) triangles.

Trigonometric Resolution of Forces
• The relation between the
lengths of the three sides in a
right (90) triangle is given by the
Pythagorean theorem: A2 B2
C2, where C is the length of the
hypotenuse of the triangle (the
side opposite the 90 angle) and
A and B are, respectively, the
lengths of the sides adjacent to
and opposite to the angle θ (Fig.
1-78A).According to the
theorem, it will hold that:

Force Components and theAngle of
Application of the Force

ranslatory Effects of Force
Components

Rotatory Effects of Force
Components
• Rotation Produced
by Perpendicular
Force Components
• Rotation Produced
by Parallel Force
Components

Total Rotation Produced by a
Force
• Levers in the human body are generally
treated as if the axis of rotation not only is
fixed but also lies in a direct line with the long
axis of the lever.When this is the case,
parallel components (Fx) will not contribute
to torque, and torque for each force can be
equivalently

Multisegment (Closed-Chain)
Force Analysis
The primary difference between the
weight boot and leg-press exercise is
that the leg-foot segment is “fixed” or
weight-bearing at both ends.The distal
end of the leg-foot segment is
constrained by its contact with the
footplate and is not free to move in
space; the proximal end is connected to
or contacting the femur and is also not
free to move in space.

Open and Closed Chains
• Whenever one
end of a seg-
ment or set of
segments is
free to move in
space, this is
referred to as
an open chain.

closed chain.
• When both ends of a segment or set
of segments are constrained in some
way (and not free to move in space),
this is referred to as a closed chain.

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