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Cross Sectional Approach
To Applied Anatomy
1
Table of Contents
Introduction
What is Biomechanics
Definition
Areas of study
Anatomy
Terminology
Planes & Axes
Muscle actions
Bones
Joints
Types
Actions
Cross sectional Anatomy
How to read a slice
Joints
Ankle
Knee
Hip
Pelvis
Shoulder
Shoulder Girdle
Elbow
Wrist
Mechanics
Levers/Pulleys
Vectors
Projectile Motion
Forces
FBD
Forces on an incline plane
Work, Power & Energy
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Introduction
Definition – Biomechanics is the application of mechanical principles to
biological systems. (James Hay).
Biomechanists must have a strong background in anatomy, motor control,
physiology and mechanics. They apply this knowledge in many areas including (but not
restricted too):
Sport optimization – improvement of sport skills and training protocols (Fosbury Flop)
Rehabilitation – development of training protocols and equipment
Occupational/Ergonomics – Job optimizations, occupational injury reduction
Equipment design – sports shoes, safety equipment (helmets, padding), bats, golf clubs
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Anatomy
To have a strong background in biomechanical anatomy you must resign yourself
to do two things: (1) memorize the movement capabilities of each joint and (2) where
each muscle crosses the joint. This is not traditional anatomy or kinesiology where you
are asked to memorize the origin, insertion, action and innervation of a muscle set.
Rather, through your memorization of the location of the muscle with respect to the joint
axes, you will be able to determine the joint action that each muscle produces in
concentric, eccentric and isometric muscle actions.
Terminology
Anatomical Neutral – this is reference position of the human body, it consists of a
person standing, with arms down at the sides with the palms facing forward.
Proximal – A position closer to the midline in reference to another structure
Distal – A position further from the midline in reference to another structure
Dorsal – The top of the foot or the back of the hand
Superior – A position higher in the vertical direction in reference to another
structure
Inferior – A position lower in the vertical direction in reference to another
structure
Origin – Traditional term used to refer to the attachment site of a muscle that does
not move. In the past it has been referred to the proximal attachment.
Insertion - Traditional term used to refer to the attachment site of a muscle that
does move. In the past it has been referred to the distal attachment.
Agonist – The muscle most responsible for the joint action.
Antagonist – The muscle that performs the opposite joint action of the agonist.
Anterior – A position more toward the front of the body in reference to another
structure
Posterior - A position more toward the back of the body in reference to another
structure
Superficial - A position more toward the surface of the body in reference to
another structure
Deep - A position more toward the inside of the body in reference to another
structure
Active – A joint action that is performed by the muscles that cross that joint
Passive – A joint action that is performed by muscles that do not cross that joint
Resistive – Joint action performed against an external resistance
Range of Motion (ROM) – the angular distance through which a joint can be
moved, either actively or passively.
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Planes and Axes
Planes are slices in space that continue on, infinitely, in all directions. With
regard to anatomy, planes divide the body into panels within which movement occurs.
The real power of anatomical planes is that they unify the language that is used to
describe a movement to someone who may not be able to see the movement being
performed. The three anatomical planes are:
Sagital plane – which separates the body into right and left sections.
Frontal plane – which separated the body into front (anterior) and back (posterior)
sections.
Transverse/Horizontal plane – which separates the body into top (superior) and body
(inferior) sections.
Red – Sagital
Blue - Transverse
Yellow - Frontal
*It is important to note that these planes can be placed anywhere within the body, not
necessarily at the midpoints. However, where these 3 planes intersect when they are
placed so that they do separate the body into halves, is called the Center of Gravity.
Perpendicular to each plane is an axis about which motion occurs within that
plane. This statement implies that only rotational motion occurs within planes, and this is
true for human movement, since the human body is a series of rigid links. The only
motion that can occur at a joint is rotation. The axes about which this rotation occurs will
be perpendicular to the plane in which this motion occurs. The three axes are:
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Bilateral – this axes passes from right to left (or left to right) and is perpendicular to the
sagital plane. Motion that occurs in the sagital plane will always be motion about the
bilateral axis.
Anterio-posterior – this axis passes from front to back (or back to front) and is
perpendicular to the frontal plane. Motion that occurs in the frontal plane will always be
motion about the anterior-posterior axis.
Polar – this axis passes from top to bottom (or bottom to top) and is perpendicular to the
transverse plane. Motion that occurs in the transverse plane will always be motion about
the polar axis.
Examples –
(1) Standing in anatomical neutral – the elbow flexes, that is to say the elbow bends
to bring the hand closer to the shoulder – this motion will occur in the sagital
plane about the bilateral axis.
(2) Standing in anatomical neutral – the arms swung upward, mimicking the arm
motion associated with the jumping jack – this motion occurs in the frontal plane
about the anterior-posterior axis.
(3) Standing in anatomical neutral – the head is rotated from side to side, in the “no”
movement – this motion occurs in the transverse plane about the polar axis
Muscle Actions
Muscles act as strings that are attached to the segments of our body. You could
think of them as if they were oddly placed strings of a marionette. But as strings,
muscles can only get longer or shorter based on the demands of the task (and usually the
load being moved).
There are 3 true muscles actions:
Concentric – muscle action in which the muscle shortens, under tension.
Eccentric – muscle action in which the muscle lengthens, under tension.
Isometric – muscle action in which the length of the muscle remains the same, under
tension.
This book will focus on these three muscle actions. However, the reader should be aware
that there are three externally controlled muscle actions as well, that are primarily used in
rehabilitation:
Isokinetic – muscle action in which the length of the muscle changes at the same speed
through out the range of motion (same speed, variable resistance)
Isotonic – muscle action in which the tension of the muscle remains the same throughout
the entire range of motion (variable speed, same resistance)
Isoinertial – muscle action in which the external load remains the same throughout the
entire range of motion.
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Bones –
There are 5 types of bones in the body:
Irregular – Irregular bones are bones that an asymmetrical shape. They are generally in a
position to withstand direct loading and provide for limited range of motion.
Flat – Flat bones are those bones that have relatively large, smooth areas. Due to their
position in the body the flat arrangement.
Short – Small, compact shaped bones (i.e., the length and width are comparable). They
are designed to fit into unique spaces within the body, that often house gliding joints.
Long – These bones have a long central shaft and are topped at either end with load
bearing surfaces. The length of these bones are disproportional to the width of the bone.
These bones are designed to provide longer levers, through out the body.
Sesamoid – These bones are sometimes included in the flat bone group. However, it is
the purpose of this bone that requires a unique category. While these bones are usually
small, and flat in general shape, they are positioned through out the body so as to provide
the joint a fulcrum to work against. The purpose of these bones are: (1) protection and
(2) increasing mechanical advantage.
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Joints
Joint Actions
These are the general joint action terms:
Flexion – these joint motions move the segments, in such a manner as to “roll” them up.
Overall, these joint motions will bring the segments closer to a position that mimics the
fetal position.
Extension – these joint motions move the segments, in such a manner as to “unroll” them.
Overall, these joint motions will bring the segments back from a fetal and closer to an
anatomical position.
Abduction – the segment is moved away from the midline of the body
Adduction – the segment is moved away toward the midline of the body
Internal Rotation – the segment is rotated about its long axis with the anterior surface
moving toward the midline of the body
External Rotation - the segment is rotated about its long axis with the anterior surface
moving away the midline of the body
These joint action terms only become valuable when they can be applied to specific joints
within the body.
Certain joints have special names for their joint actions because of the unique design and
motions of the joint. Remember, this is all about unifying the vocabulary, so that
everyone speaks the same anatomical language.
Special Joint Action Names:
Ankle
Dorsiflexion – in which the distance between the top of the foot and the lower leg
is decreased.
Plantar flexion – in which the distance between the top of the foot and the lower
leg is increased.
Inversion – in which the big toe is moved upward and toward the midline of the
body (this is the classic ankle sprain posture)
Eversion – in which the big toe is moved downward and away from the midline of
the body
Hip/Shoulder
Horizontal Abduction – with the segment flexed, the segment is moved in the
transverse plane, away from the midline
Horizontal Adduction - with the segment flexed, the segment is moved in the
transverse plane, toward the midline
Circumduction – this a is a combination movement that includes flexion,
extension, abduction and adduction. In this motion the segment sweeps out a cone, in a
multiplanar motion (note, there is no rotation associated with this motion).
Pelvis – the motions are defined by the motion of the anterior, superior iliac crest (ASIC)
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Anterior Pelvic Rotation – the ASIC moves anteriorly (in the sagital plane)
Posterior Pelvic Rotation – the ASIC moves poteriorly (in the sagital plane)
Left Transverse Pelvic Rotation – the left ASIC moves posteriorly (in the
transverse plane)
Right Transverse Pelvic Rotation - the right ASIC moves posteriorly (in the
transverse plane)
Left Lateral Pelvic Rotation – the left ASIC moves superiorly (in the frontal
plane)
Right Lateral Pelvic Rotation – the right ASIC moves superiorly (in the frontal
plane)
Lumbar
Left Lateral Flexion (bending) (returning to neutral is reduction)
Right Lateral Flexion (bending) (returning to neutral is reduction)
Shoulder Girdle (Scapula) – these motions are described by the motion of the entire of
scapula
Upward Rotation – the inferior angle moves upward and laterally
Downward Rotation – the inferior angle moves downward and medially
Protraction (Abduction) – the scapula moves away from the midline
Retraction (Adduction) – the scapula moves toward the midline
Elevation – the scapula moves upward
Depression – the scapula moves downward
Radio-Ulna Joint
Pronation – this joint position can be identified by the thumb location. When the
thumb is positioned on the medial side of the elbow, the radio-ulna joint is in pronation.
Supination – this joint position can be identified by the thumb location. When the
thumb is positioned on the lateral side of the elbow, the radio-ulna joint is in supination.
Wrist
Radial Deviation – when the angle between the thumb and the radius decreases.
Ulna Deviation – when the angle between the pinky and the ulnar decreases.
Joint Types
Synarthrotic – non-movable, Ex-sutures
Amphiarthrotic – slightly movable
Syndesmosis – (ligaments) – between the (1) tibia/fibula, (2) metacarpals,
(3) metatarsals, (interoseous mebrane)
Synchondrosis – (cartilage) – pubis symphysis
Diathrotic- based on how many axes the articulating bones can move.
1) Gliding (Arthrodial) – nonaxial, carpals, tarsals, Distal Radio-Ulnamotion consists of movement of one bone past another, without an
axis
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2) Pivot (Trochoid) – uniaxial, atlas and axis (C1 & C2 – cervical
vertebrea) – Proximal Radio-ulna
3) Oids
a) Condyloid – biaxial, one is concave, one is convex. Two
degrees of motion. Allows for passive rotation – but has no muscles that
can cause this rotation
b) Ellipsoid – biaxial, one is concave, one is convex. Two degrees
of motion. Does NOT allow for passive rotation. Ex- Radial-Carpal
4) Saddle – both sides of articulation are concave. First CarpalMetacarpal joint (in the thumb it is at the BASE of the anatomical
snuff box)
5) Hinge – uniaxial. Can only flex and extend
6) Ball and Socket – triaxial. The rounded surface of one bone fits into the
“cup” of a second articulating bone. Ex – hip, shoulder
Least movable
Most movable
Joints
Gliding
Hinge
Pivot
Condyloid
Ellipsoid
Saddle
Ball & socket
Axis
0
1
1
2
2
3
3
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Planes
1
1
1
2
2
3
3
Bones –
MEDIAL
SIDE
Talus
Navicular
Cuneiforms
-there are 3
of them
Calcaneus
Cuboid
Metatarsals
Femur
Femur
Patella
Fibula
Tibia
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Humerus
Thumb
Side
Radius
Metacarpals
Ulna
Carpals
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Cross Sectional Anatomy
This is a unique way of looking at anatomy. It will not be the standard origin, insertion,
action and innervation that are the hallmarks of traditional anatomy. Here, we are talking
about how the location of muscles produce motion. Specifically, how these muscles
cross the joint. If it you know how (where) the muscle crosses a joint with reference to
that joint’s axis of rotation, then you will know what motion that muscle will produce at
the joint.
When approaching cross sectional anatomy, there are several steps that we will use:
Using the ankle as an example:
Anterior
(1) Imagine that you are looking at
a slice, taken at the joint center
(2) Divide the slice into 4 quadrants
Dorsiflexion
(3) Assign joint actions to quadrants
(5) Determine muscle-joint action
relationships
Eversion
Medial
Inversion
(4) Position muscles in appropriate
quadrants
Plantar flexion
Rules:
(1) Muscles in a quadrant produce all motions associated with that quadrant
(2) Muscles that are on a line produce only the joint motion assigned to that side of
the axis. However, if muscles are on adjacent axes they can work synergistically
to produce a combined joint motion.
(3) Muscles grouped in boxes work together and are usually called upon together.
(4) All muscles are indicated for concentric muscle actions.
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This picture shows a superior
view of how the cross sectional
circle is drawn at the ankle.
Dorsiflexion/Inversion
Dorsiflexion/Eversion
This picture identifies what
joint action is associated with
which quandrant.
Plantarflexion/Inversion
Plantarflexion/Eversion
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This picture
demonstrates
which muscles
contribute to
which joint
motions.
Muscle Assignment
Anterior
Ankle
EHL
Dorsiflexion/Inversion
EDL
Dorsiflexion/Eversion
TA
PT
Medial
TP
PB
FDL
PL
Plantarflexion/Inversion
Plantarflexion/Eversion
FHL
Soleus
Gastrocnemius
Abbreviation
EDL
PT
PB
PL
FHL
FDL
TP
TA
EHL
Gastroc
Soleus
Muscle
Extensor Digitorum Longus
Peroneus Tertius
Perneus Brevis
Peroneus Longus
Flexor Hallicus Longus
Flexor Digitorum Longus
Tibialis Posterior
Tibialis Anterior
Extensor Hallicus Longus
Gastrocnemius
Soleus
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Knee – While the knee is often considered a hinge joint for simplicity, the knee is
actually a helical joint and allows for many motions. For the purposes of learning the
muscles, the knee will be considered to be able to flex and extend, as well as internally
and externally rotate. The inclusion of joint actions in a plane other than sagital requires
an addition to the circles. The first circle reveals those muscles associated with flexion
and extension. The second circle demonstrates those muscles associated with internal
and external rotation. The third circle will demonstrate all four motions together.
Anterior
Flexion
Flexion
VM
RF
VI
VL
Medial
SAR
BF
Gr
SM
ST
Extension
Pop
Extension
Gastroc
16
Anterior
VM
Medial
RF
VI
Blue = External rotation
Red = Internal rotation
VL
SAR
BF
Gr
SM
External Rotation
ST
Internal Rotation
Pop
Gastroc
Notice that if the muscles on the medial side were to pull “down”, they would cause the
circle to rotate medially, therefore, these muscles are responsible for internal rotation of
the knee. Likewise, if the Biceps Femoris were to pull “down”, it would rotate the circle
laterally, therefore, these muscles are responsible for external rotation of the knee.
17
The next circle is the combination of the linear and the rotation circles for the knee, and
the only you need to remember.
Anterior
VM
Extension
RF
VI
VL
Extension
Medial
SAR
BF
Gr
SM
ST
Flexion/Internal Rotation
Flexion/External Rotation
Pop
Gastroc
Abbreviation
RF
VM
VI
VL
BF
Sar
Gr
SM
ST
Pop
Gastroc
Muscle
Rectus Femoris
Vastus Medialis
Vastus Intermedius
Vastus Lateralis
Biceps Femoris
Sartorious
Gracilis
Semimembranosus
Semitendinosus
Popliteus
Gastrocnemius
18
Hip – Just like the knee there are motions in more than just the sagital plane. One could
make a circle for the linear (flexion/extension, abduction/adduction) and a separate circle
for the rotations (internal/external). However, that’s not the way the body works, so
below is one circle that has it all.
Anterior
Sar,
RF, IS
Flexion/Abduction
AL
AB
TFL
Pect
PF
Gr
a
Medial
Adduction
Glut Med
Glut Min
Gmax
Extension/Adduction
Extension/Adduction
AM
SM, ST, BF
Blue = Internal rotators
Red = External rotators
Extension
Abbreviations
AL
AB
Pect
Sar
RF
IS
TFL
Glut min
Glut med
PF
SM
ST
BF
Gmax
AM
Gr
19
GS
OI
GI
OE
QF
Note – This box is a set of
external rotators. They are
positioned outside of the
critical circle because they do
not contribute to the linear
motions at all.
Muscle
Adductor Longus
Adductor Brevis
Pectineus
Sartorious
Rectus Femoris
Illiopsoas
Tensor Fascia Latae
Gluteus Minimus
Gluteus Medius
Piriformis
Semi-membranosus
Semi-tendinosus
Biceps Femoris
Gluteus Maximus
Adductor Magnus
Gracilis
Pelvis – the pelvic/hip/lumbar combination allows for a great deal of motion, so we have
broken out the hip, pelvis and lumbar motion creators separately. However, the muscles
that are responsible for motion of the pelvis to femur are the muscles already presented at
for the hip (femur to pelvis motion). This points out the trap of saying the proximal
attachment is the origin and the distal attachment is the insertion. It is movement
dependent. Sometimes the femur about the pelvis (hip flex/ext, hip abd/adduction,
int/external rotation) and sometimes the pelvis moves about the femur (ant/posterior
pelvic girdle rotation, right/left lateral pelvic girdle rotation, right/left transverse pelvic
girdle rotation).
Anterior/posterior pelvic girdle rotation
Anterior pelvic girdle rotation – forward tilting of the pelvis, both anterior,
superior, iliac crests (ASIC) moves forward. This happens naturally when you extend the
hip.
Posterior pelvic girdle rotation – backward tilting of the pelvis, both ASICs
moves backward. This happens naturally with hip flexion.
Lumbar
Thisflexion
is the= side
posterior pelvic girdle
rotation
Lumbar extension =
anterior pelvic
girdle rotation
Erector
Spinae
Abdominals
Pelvis
Hamstrings
Hip
Flexors
Hip extension =
posterior pelvic girdle
rotation
20
Hip flexion = anterior
pelvic girdle rotation
(sagital) view
Right/Left Lateral Pelvic Girdle Rotation
Right lateral pelvic girdle rotation – the right ASIC rises
Left lateral pelvic girdle rotation – the left ASIC rises
Spine
NOTE: Feet are on the
ground. Pelvis will
move with respect to
the fixed femur
(weight bearing), as
well as the lumbar.
Eerctor
Spinae
Abdominals
Hip
Abuctors
Hip
Adductors
Anterior View
Transverse Pelvic Rotation
Left transverse pelvic girdle rotation – the left ASIC moves backward
Right transverse pelvic girdle rotation – the right ASIC moves backward
Example: A right handed batter will have left, transverse pelvic girdle rotation,
left hip internal rotation and right hip external rotation.
Lumbar
Spine
NOTE: feet not on
the ground. The
pelvis will rotate
with respect to the
lumbar.
External
Obliques
Internal
Obliques
Pelvis
21
Transverse Pelvic and Hip Rotation
Spine
Anterior
Left
Internal
Rotators
Right
Internal
Rotators
Pelvis
L
leg
Left
External
Rotators
R
leg
Right
External
Rotators
Superior View
*The reason the right hip internal rotators are used to right transverse pelvic girdle
rotation is because the internal rotators originate toward the midline of the pelvis. The
internal and external rotators are already noted on the hip circle.
22
NOTE: feet on
the ground.
The femur is
fixed and the
pelvis is going
to move
Motion Review
Joint action = anterior pelvic
girdle rotation
1)
Muscle action = eccentric
Muscle group = hip extensors
Start
Finish
2)
Joint action = posterior
pelvic girdle rotation
Muscle action = concentric
Start
Muscle group = abdominals
Finish
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3)
Joint action = left transverse pelvic
girdle rotation
Muscle action = concentric
Start
Muscle group = Left Internal Hip
Rotators, Right External Hip Rotators
Right internal
NOTE: the feet are still facing
forward and there is no change in
joint position between the trunk
and the pelvis.
Finish
24
4)
Joint action = right lateral pelvic girdle
rotation
Muscle action = concentric
Muscle group = right abdominals and
right erector spinea as well as the left hip
abductors and right hip adductors
Start (Anterior View)
Finish (Anterior View)
25
Scapula – Elevation, depression, protraction, retraction
Elevation
LS,
UT
Elevation/Protraction
Rhom
Elevation/Retraction
UT
Rhom
LS
SA
Protraction
SA
LT
Pect
Minor
Depression/Retraction
Pect
Minor
LT
Depression/Protraction
Blue = Downward rotation
Red = Upward rotation
Abbreviations
UT
LS
SA
Pect Minor
LT
Rhom
Muscles
Upper Trapezius
Levator Scapula
Serratus Anterior
Pectoralis Minor
Lower Trapezius
Rhomboids
26
Shoulder- Glenohumeral Joint (flexion/extension & abd/adduction, internal/external
rotation)
Anterior
Blue = Internal rotation
Red = External rotation
BB
CB
AD
Pect
Maj
MD
Medial
Supra
Lat
PD
Tmaj
TB
Infra
T Minor
Abbreviations
BB
AD
MD
PD
Supra
Lat
T Maj
TB
CB
Pect Maj
Muscles
Biceps Brachii
Anterior Deltoid
Middle Deltoid
Posterior Deltoid
Supraspinatus
Latissimus Dorsi
Teres Major
Triceps Brachii
Coracobrachialis
Pectoralis Major
27
Note: The
infraspinatus and the
Teres Minor are
outside of the circle
because they do not
contribute to linear
motion at the shoulder
Elbow – Flexion & Extension
BR
Flexion
Flexion
BB
T
h
u
m
b
Brach
TB
Ancon
Extension
Extension
Abbreviations
BR
BB
Brach
TB
Ancon
Muscles
Brachioradialis
Biceps Brachii
Brachialis
Triceps Brachii
Anconeus
Elbow – Pronation/Supination
PT
Abbreviations
PT
PQ
Sup
BB
Muscles
Pronator Tere
Pronator Quadratus
Supinator
Biceps Brachii
BB
PQ
Sup
Blue = Pronators
Red = Supinators
28
T
h
u
m
b
Wrist – the arm is held in anatomical neutral, so the thumb is on the lateral side of the
hand.
Anterior
Flexion/Ulnar Deviation
Flexion/Radial Deviation
PL
FD
FCU
FCR
T
h
u
m
b
Medial
ED
ECU
ECR
Ulnar
Deviators
Extension/Radial Deviation
Extension/Ulanr Deviation
Abbreviations
PL
FD
FCR
ECR
ED
ECU
FCU
Muscles
Palmaris Longus
Flexor Digitorum
Flexor Carpi Radialis
Extensor Carpi Radialis
Extensor Digitorum
Extensor Carpi Ulnaris
Flexor Carpi Ulnaris
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Radial
Deviators
Mechanics
Simultaneous/Sequential
Movement within the body is often described as being Simultaneous or
Sequential. These two terms describe how the segments of the body are moving. In
Simultaneous movements all segments move at the same time, in the same direction.
This sort of movement is best suited for moving large loads and accurate movements.
Example, consider pushing a refrigerator across the kitchen, all body segments are
moving together. In Sequential movements the segments are moved one at a time. This
type of movement is utilized when a person tried to throw, kick or punch. In these
movements the body will use a process called Proximal to Distal Sequencing (P-D). P-D
is characterized by the proximal segment achieving maximum velocity, followed by the
next distal segment and so on, until the velocity is “summed” at the last segment. Debate
exists about how the body achieves this pattern but there is no debate that this is the
process that the body utilizes.
Levers
The body is a series of semi- rigid links. As a result, the articulations can
be modeled after the simple machine called levers. All simple machines must serve one
or more of the following four functions:
(1) Balance 2 or more forces
(2) Change direction of the applied force
(3) Favor speed and range of motion
(4) Favor force production
Levers consist of 5 primary components.
(1) Applied (motive) Force – in the body this represents the muscle force
(2) Force moment arm
(3) Axis of rotation – point about which the system rotates
(4) Resistance Force – in the body, the load to be overcome
(5) Resistance moment arm
Moment arm – the moment arm is defined as the perpendicular distance from the
point of force application to the axis of rotation.
Moments are “turning forces”. Forces that produce rotation. Within the body,
therefore, they are the forces that cause one segment to rotate about its articulation with
another. This force (the moment) is the product of the magnitude of the force and that
forces moment arm.
Classification – while levers have 5 components, only three are used to classify them:
The Force (F) , the Axis (A) and the Resistance (R ). The order of these 3 components
indicates which class of lever being discussed.
First Class
Second Class
Third Class
F
A
R
A
R
F
R
F
A
30
First Class LeverF-A-R
In this type of the lever the axis is always between the force and the resistance. This is the
most versatile lever because it can be manipulated to serve all four of the functions of a
simple machine.
F
R
A
Function 1 – Balances 2 forces - in the current arrangement, it is apparent that the force
and the resistance can be balanced, if the force and the resistance were equal and the
distance between the axis of rotation and the force and resistance are the same.
Function2 – Changes the effective direction of the applied force. If the force is pushing
down, it is apparent that the resistance will go up.
Function 3 – Favors speed and range of motion. In order for this to be true, we have to
alter the above diagram, by moving the axis closer to the applied force.
F
R
A
In this new configuration, it should be apparent that moving the force a small distance
will cause the resistance to move a greater distance than the force is moved.
Furthermore, since the force and the resistance are connected by a rigid link, the time it
takes to move the force the small distance is the same time that it will take to move the
resistance through the greater distance.
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Function 4- Favors force production – In order for this to be true, we have to alter the
diagram by moving the axis closer to the resistance.
F
R
A
The advantage of this new configuration is the force moment arm is considerably
longer than the resistance moment arm. This allows a smaller force to move a larger
load.
Examples within the body of a first class lever –
Example 1-
F
A
R
F – is supplied by the neck extensors
A – is supplied by the spine/skull articulation
R – is supplied by the weight of the head, considered to act at the
center of gravity of the skull
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Second Class Lever –
A–R–F
In this class lever, the resistance is ALWAYS closer to the axis of rotation than
the force. This means that the force lever arm will always be longer than the resistance
moment arm. This configuration therefore favors force production, since a smaller force
can move a larger load due to the longer moment arm of the force.
R
F
A
While this is most efficient configuration, it is the least common within the body.
Example 1 – Push-up
A – is supplied by the feet
R – is supplied by the center
of gravity
F – is supplied by the arms
A
R
F
Example 2 – The toe raise
A – is supplied by the toes
R - is supplied by the COG
F –is supplied by the calf
muscles
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F R A
Third class lever
R-F-A
In this class of lever the force is ALWAYS closer to the axis. This configuration
while favoring the resistances advantage, does allow for favoring speed and range of
motion. Consider the diagram below. Notice that if the force is moved a small amount
the resistance will move a much greater amount. In addition, since the small distance of
the force and the larger distance of the resistance must occur in the same time, so the
resistance will move faster than the force.
R
F
A
This is the most common configuration in the body.
Example – Bicep curl
A – is supplied by the elbow
F – is supplied by muscle force
R – is supplied by the load in the hand
F
A
R
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Vectors
Scalar quantities have magnitude only (mass, time, distance and speed)
Vector quantities have magnitude and direction (velocity, acceleration and force)
If a person were to walk 3 m due east, then
Scalar– 3m
Vector – 3m (E)
3m
Since it is not always easy to decide which direction a drawing is facing a method was
needed to indicate direction better than north, south, east and west. So, the physicists
turned the world of mathematics and Rene Descartes and his Cartesian plane.
II
X–
Y+
III
X–
Y+
I
X+
Y+
IV
X+
Y-
Since the person walked 3m to the right, we could also say that they walked 3m in
the positive x-direction. Now, signs take on the meaning of direction and NOT of
magnitude.
Consider a person who walks along the following path.
i
f
3m
3m
Scalar – 8 m
Vector - + 2m
2m
The vector value is the sum of the vector distances indicated by the diagram
-3m + 2m + 3m = +2m
Of course the tradition method of determining the resultant vector is to draw a
vector (a line that represents magnitude and direction) from the tail of the first vector to
the tip of the last vector. In this case, a vector would be drawn from the i to the f.
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Left to be done –
Vector addition
Resultant
Vector resolution
Projectile Motion –
Projectile motion is a special case of uniform acceleration, and as a result, the
equations developed for uniform acceleration hold. The first equation is the definition of
the velocity, but is included in this list as it will be a useful equation
v
s
t
v
a
this can also be written as s  vt
f
v
i
t
this can also be written as v f  v i  at
v 2f  v i2  2as
s  v i t  1 2 at 2
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