Cross Sectional ApproachTo Applied Anatomy

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Table of Contents

IntroductionWhat is Biomechanics

DefinitionAreas of study

AnatomyTerminology

Planes & AxesMuscle actionsBonesJoints

TypesActions

Cross sectional AnatomyHow to read a sliceJoints

AnkleKneeHipPelvisShoulderShoulder GirdleElbowWrist

MechanicsLevers/PulleysVectorsProjectile MotionForces

FBDForces 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 equipmentOccupational/Ergonomics – Job optimizations, occupational injury reductionEquipment 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 structureDistal – A position further from the midline in reference to another structureDorsal – The top of the foot or the back of the handSuperior – A position higher in the vertical direction in reference to another

structureInferior – A position lower in the vertical direction in reference to another

structureOrigin – 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

structurePosterior - A position more toward the back of the body in reference to another

structureSuperficial - A position more toward the surface of the body in reference to

another structureDeep - 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 jointPassive – A joint action that is performed by muscles that do not cross that jointResistive – Joint action performed against an external resistanceRange 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 bodyAdduction – the segment is moved away toward the midline of the bodyInternal Rotation – the segment is rotated about its long axis with the anterior surface moving toward the midline of the bodyExternal 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 midlineHorizontal Adduction - with the segment flexed, the segment is moved in the

transverse plane, toward the midlineCircumduction – 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)

LumbarLeft 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 laterallyDownward Rotation – the inferior angle moves downward and mediallyProtraction (Abduction) – the scapula moves away from the midlineRetraction (Adduction) – the scapula moves toward the midlineElevation – the scapula moves upwardDepression – the scapula moves downward

Radio-Ulna JointPronation – 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.

WristRadial Deviation – when the angle between the thumb and the radius decreases.Ulna Deviation – when the angle between the pinky and the ulnar decreases.

Joint TypesSynarthrotic – non-movable, Ex-sutures Amphiarthrotic – slightly movable

Syndesmosis – (ligaments) – between the (1) tibia/fibula, (2) metacarpals, (3) metatarsals, (interoseous mebrane)

Synchondrosis – (cartilage) – pubis symphysisDiathrotic- based on how many axes the articulating bones can move.

1) Gliding (Arthrodial) – nonaxial, carpals, tarsals, Distal Radio-Ulna- motion 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) Oidsa) 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-Carpal4) Saddle – both sides of articulation are concave. First Carpal-

Metacarpal joint (in the thumb it is at the BASE of the anatomical snuff box)

5) Hinge – uniaxial. Can only flex and extend6) Ball and Socket – triaxial. The rounded surface of one bone fits into the

“cup” of a second articulating bone. Ex – hip, shoulder

Joints Axis PlanesLeast movable Gliding 0 1

Hinge 1 1Pivot 1 1Condyloid 2 2Ellipsoid 2 2Saddle 3 3

Most movable Ball & socket 3 3

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Bones –

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Femur

Fibula

Femur

Tibia

Patella

Talus

Calcaneus

Cuboid

NavicularCuneiforms-there are 3 of them

Metatarsals

MEDIAL SIDE

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Thumb SideRadius

Ulna

Humerus

Carpals

Metacarpals

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:

(1) Imagine that you are looking at a slice, taken at the joint center

(2) Divide the slice into 4 quadrants

(3) Assign joint actions to quadrants

(4) Position muscles in appropriate quadrants

(5) Determine muscle-joint action relationships

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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Anterior

Medial

Dorsiflexion

Plantar flexion

Eversion

Inve

rsio

n

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Dorsiflexion/EversionDorsiflexion/Inversion

Plantarflexion/EversionPlantarflexion/Inversion

This picture shows a superior view of how the cross sectional circle is drawn at the ankle.

This picture identifies what joint action is associated with which quandrant.

Muscle Assignment

Ankle

Abbreviation MuscleEDL Extensor Digitorum LongusPT Peroneus TertiusPB Perneus BrevisPL Peroneus LongusFHL Flexor Hallicus LongusFDL Flexor Digitorum LongusTP Tibialis PosteriorTA Tibialis AnteriorEHL Extensor Hallicus LongusGastroc GastrocnemiusSoleus Soleus

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TA

EHL EDL

PT

PB

PL

TP

FDL

FHL

Anterior

Medial

SoleusGastrocnemius

Dorsiflexion/Eversion

Plantarflexion/EversionPlantarflexion/Inversion

Dorsiflexion/Inversion

This picture demonstrates which muscles contribute to which joint motions.

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.

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RFVM VI VL

BFSAR

Gr

SM

ST

Pop

Gastroc

Anterior

Medial

FlexionFlexion

Extension

Extension

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.

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RFVM VI VL

BF

SAR

Gr

SM

ST

Pop

Gastroc

Anterior

Medial

External RotationInternal Rotation

Blue = External rotationRed = Internal rotation

The next circle is the combination of the linear and the rotation circles for the knee, and the only you need to remember.

Abbreviation MuscleRF Rectus FemorisVM Vastus MedialisVI Vastus IntermediusVL Vastus LateralisBF Biceps FemorisSar SartoriousGr GracilisSM SemimembranosusST SemitendinosusPop PopliteusGastroc Gastrocnemius

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RFVM VI VL

BFSAR

Gr

SM

ST

Pop

Gastroc

Anterior

Medial

ExtensionExtension

Flexion/Internal Rotation Flexion/External Rotation

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.

Abbreviations MuscleAL Adductor LongusAB Adductor BrevisPect PectineusSar SartoriousRF Rectus FemorisIS IlliopsoasTFL Tensor Fascia LataeGlut min Gluteus MinimusGlut med Gluteus MediusPF PiriformisSM Semi-membranosusST Semi-tendinosusBF Biceps FemorisGmax Gluteus MaximusAM Adductor MagnusGr Gracilis

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AM

AL AB

SM, ST, BF

Gmax

Gra

Pect

Sar, RF, IS

TFL

PF

Glut MedGlut Min

Anterior

Medial

GSOIGIOEQF

Flexion/Abduction

Adduction

Extension/AdductionExtension/Adduction

Extension 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

Blue = Internal rotatorsRed = External rotators

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 rotationAnterior 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.

This is the side (sagital) view

Right/Left Lateral Pelvic Girdle Rotation

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Pelvis

AbdominalsErectorSpinae

HipFlexors

Hamstrings

Lumbar extension = anterior pelvic girdle rotation

Hip extension = posterior pelvic girdle rotation

Lumbar flexion = posterior pelvic girdle rotation

Hip flexion = anterior pelvic girdle rotation

Right lateral pelvic girdle rotation – the right ASIC risesLeft lateral pelvic girdle rotation – the left ASIC rises

Transverse Pelvic RotationLeft transverse pelvic girdle rotation – the left ASIC moves backwardRight transverse pelvic girdle rotation – the right ASIC moves backwardExample: A right handed batter will have left, transverse pelvic girdle rotation,

left hip internal rotation and right hip external rotation.

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Spine

Eerctor Spinae

Abdominals

Hip AbuctorsHip

Adductors

Anterior View

LumbarSpine

Pelvis

External Obliques

InternalObliques

NOTE: Feet are on the ground. Pelvis will move with respect to the fixed femur (weight bearing), as well as the lumbar.

NOTE: feet not on the ground. The pelvis will rotate with respect to the lumbar.

Transverse Pelvic and Hip Rotation

*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.

Motion Review

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Anterior

Pelvis

Rleg

Lleg

Superior View

Spine

RightInternal Rotators

Left InternalRotators

RightExternalRotatorsLeft

External Rotators NOTE: feet on

the ground. The femur is fixed and the pelvis is going to move

Joint action = anterior pelvic girdle rotation

Muscle action = eccentric

Muscle group = hip extensors

1)

2)

3)

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StartFinish

Start

Finish

Joint action = posterior pelvic girdle rotation

Muscle action = concentric

Muscle group = abdominals

4)

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Start

Finish

Joint action = left transverse pelvic girdle rotation

Muscle action = concentric

Muscle group = Left Internal Hip Rotators, Right External Hip Rotators

NOTE: the feet are still facing forward and there is no change in joint position between the trunk and the pelvis.

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Start (Anterior View)

Finish (Anterior View)

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

Scapula – Elevation, depression, protraction, retraction

Abbreviations MusclesUT Upper TrapeziusLS Levator ScapulaSA Serratus AnteriorPect Minor Pectoralis MinorLT Lower TrapeziusRhom Rhomboids

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UT

LS

SA

PectMinor

LT

Rhom

LS, UT

SA

PectMinor

LT

Rhom

Protraction

Elevation

Elevation/Retraction

Depression/RetractionDepression/Protraction

Elevation/Protraction

Blue = Downward rotationRed = Upward rotation

Shoulder- Glenohumeral Joint (flexion/extension & abd/adduction, internal/external rotation)

Abbreviations MusclesBB Biceps BrachiiAD Anterior DeltoidMD Middle DeltoidPD Posterior DeltoidSupra SupraspinatusLat Latissimus DorsiT Maj Teres MajorTB Triceps BrachiiCB CoracobrachialisPect Maj Pectoralis Major

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BB

AD

MD

Supra

PD

TB

Lat

Tmaj

PectMaj

CB

InfraT Minor

Anterior

Medial

Blue = Internal rotationRed = External rotation

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

Abbreviations MusclesBR BrachioradialisBB Biceps BrachiiBrach BrachialisTB Triceps BrachiiAncon Anconeus

Elbow – Pronation/Supination

Abbreviations MusclesPT Pronator TerePQ Pronator Quadratus

Sup SupinatorBB Biceps Brachii

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BR

BB

Brach

TB

Ancon

PT

PQBB

Sup Thumb

Flexion

Flexion

Thumb

ExtensionExtension

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Blue = Pronators

Red = Supinators

Wrist – the arm is held in anatomical neutral, so the thumb is on the lateral side of the hand.

Abbreviations MusclesPL Palmaris LongusFD Flexor DigitorumFCR Flexor Carpi RadialisECR Extensor Carpi RadialisED Extensor DigitorumECU Extensor Carpi UlnarisFCU Flexor Carpi Ulnaris

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PL

FD

FCR

ECR

EDECU

FCU

Thumb

Anterior

Medial

Ulnar Deviators Radial

Deviators

Flexion/Radial Deviation

Extension/Radial Deviation

Flexion/Ulnar Deviation

Extension/Ulanr Deviation

MechanicsSimultaneous/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.

LeversThe 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 F A RSecond Class A R FThird Class R F A

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First Class Lever-

F-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.

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.

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.

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.

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F

A

R

F

A

R

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 – 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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F R

A

FA

R

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.

While this is most efficient configuration, it is the least common within the body.

Example 1 – Push-up

A – is supplied by the feetR – is supplied by the center

of gravityF – is supplied by the arms

Example 2 – The toe raise

A – is supplied by the toesR - is supplied by the COGF –is supplied by the calf

muscles

Third class lever

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FR

A

A RF

AF R

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.

This is the most common configuration in the body.

Example – Bicep curl

A – is supplied by the elbowF – is supplied by muscle forceR – is supplied by the load in the hand

Vectors

Scalar quantities have magnitude only (mass, time, distance and speed)

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FR

A

A

R

F

Vector quantities have magnitude and direction (velocity, acceleration and force)

If a person were to walk 3 m due east, then

Scalar– 3mVector – 3m (E)

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.

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.

Scalar – 8 mVector - + 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.

Left to be done –Vector additionResultantVector resolution

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3m

IX +Y +

IIX –Y +IIIX –Y +

IVX +Y -

3m

2m

3m

i f

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

this can also be written as

this can also be written as

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