Kinematics and Kinetic Basic Kinematics and Kinetic Basic ConceptsConcepts

Lecture-2Lecture-2

Saifullah KhalidSaifullah KhalidLecturerLecturer

School of Physiotherapy,School of Physiotherapy,IPM&R, Dow University of Health Science, KarachiIPM&R, Dow University of Health Science, Karachi

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MassMass“ “ The quantity of matter The quantity of matter

in an object in an object ””

No variation in mass No variation in mass with regard to location or with regard to location or gravitational conditions gravitational conditions

““It represents the It represents the resistance to a change of resistance to a change of state of an objectstate of an object””

WeightWeight“ “ The force that results The force that results

from the action of a from the action of a gravitational field on a gravitational field on a massmass ” ”

Units:Units: Newton, Pound Newton, Pound force (lbf)force (lbf)

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InertiaInertia “ “ The resistance to a change of state during The resistance to a change of state during

rotation rotation ””

I = m × r I = m × r ²²

Units: Units: kilogram meter squared kilogram meter squared ((kg×mkg×m²²)), Slug inch , Slug inch squared squared (sl×in(sl×in²)²)

The Truck and Ladder

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Linear MotionLinear Motion

“ “ Motion in which all Motion in which all parts of the body travel parts of the body travel along parallel pathsalong parallel paths ” ”

Also calledAlso called Translation Translation

Rectilinear translationRectilinear translation Curvilinear translationCurvilinear translation

Angular MotionAngular Motion

“ “ Motion in which all Motion in which all particles in the body particles in the body travel in a circular travel in a circular mannermanner, , if the axis of if the axis of rotation is fixed rotation is fixed ””

If the If the axis of rotation is axis of rotation is

not fixednot fixed the motion is the motion is actually a actually a combination of combination of translation translation && rotation rotation

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DisplacementDisplacement “ “ The change in the position of a The change in the position of a

body”body” TranslationalTranslational Rotational changeRotational change Combined Combined

Translational change Translational change Example: Example: General movement of the General movement of the

human body human body Rotational changeRotational change

Example: Example: Motion of limbsMotion of limbs05/03/2305/03/23 55

VelocityVelocity ““The rate at which an The rate at which an

object changes its object changes its position”position”

AngularAngular & & Linear Linear VelocityVelocity

HorizontalHorizontal & &Vertical Vertical VelocityVelocity

SpeedSpeed "How fast an object is "How fast an object is

moving”moving”

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Linear velocityLinear velocity

“ “ The rate at which a The rate at which a body moves in a body moves in a straight linestraight line ” ”

Units:Units: Meters/second (Meters/second (m/sm/s)) Feet/second (Feet/second (ft/secft/sec or or

ft/sft/s), Miles per hour ), Miles per hour ((mphmph))

Angular VelocityAngular Velocity

“ “ The rate of change of The rate of change of angular displacement angular displacement with respect to timewith respect to time ” ”

Units:Units: Radians/sec Radians/sec ( rad/s )( rad/s ) degrees/sec degrees/sec (deg/sec(deg/sec or or

° /sec° /sec or or ° /s° /s ))

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AccelerationAcceleration “The rate of change of The rate of change of

velocity with respect to velocity with respect to timetime”

PositivePositive, , NegativeNegative, , ZeroZero valuesvalues

DecelerationDeceleration (Negative (Negative acceleration)acceleration)

Units:Units: (m/s(m/s²²), (ft/sec), (ft/sec² or ² or ft/sft/s²²), ),

(in/sec(in/sec² ² or in/sor in/s²²))

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Forces & MomentsForces & MomentsForces:Forces:

““A push or pull" that results from A push or pull" that results from physical contact between two objectsphysical contact between two objects

Common examples Force:Common examples Force: Muscles/tendons pull, ligaments pull, Muscles/tendons pull, ligaments pull,

friction, ground reaction, weight, joint friction, ground reaction, weight, joint forces and joint reaction forcesforces and joint reaction forces

Gravity is the only exception Gravity is the only exception

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Force & MomentsForce & Moments Forces from the abd. & add. muscles Forces from the abd. & add. muscles

act through their tendons, while the act through their tendons, while the hip joint reaction forcehip joint reaction force acts through acts through its respective joint COR its respective joint COR

In general, the point of application of In general, the point of application of a force is located with respect to a a force is located with respect to a fixed point on a body, usually the fixed point on a body, usually the joint CORjoint COR

This information is used This information is used to calculate to calculate thethe momentmoment due to that forcedue to that force

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Force & MomentsForce & MomentsMoment ...Moment ... The bending action of forceThe bending action of force In biomechanics, a moment In biomechanics, a moment

(M)(M) is typically is typically caused by a caused by a force acting at a distance force acting at a distance (r)(r) from the COR of a segment from the COR of a segment

M = r M = r ××FF A moment tends to cause a A moment tends to cause a

rotationrotation

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Moments & Moment ArmMoments & Moment Arm Torque …Torque … Synonymous with a momentSynonymous with a moment Effect of a force that tends Effect of a force that tends

to cause rotation about an to cause rotation about an axisaxis

Moment Arm …Moment Arm … ““The distance that is The distance that is

perpendicular perpendicular to the force vector”to the force vector”

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Force CoupleForce Couple “ “ An arrangement of two An arrangement of two

equal and opposite parallel equal and opposite parallel forces that tend to cause forces that tend to cause rotationrotation ””

Pure examples are rare in Pure examples are rare in musculoskeletal systemmusculoskeletal system

In general, muscles are In general, muscles are responsible for producing responsible for producing both forces both forces and and momentsmoments, , thus resulting in both thus resulting in both translationaltranslational and and rotational rotational motionmotion

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Muscle ForcesMuscle Forces

Three important parameters to consider the Three important parameters to consider the force of a muscle;force of a muscle;

OrientationOrientation, , MagnitudeMagnitude and and Point ofPoint of applicationapplication

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Clinical RelevanceClinical Relevance Muscles generate 2 types of forces Muscles generate 2 types of forces

Angular MotionAngular Motion ((RotationRotation)) Linear MotionLinear Motion ((TranslationTranslation) may ) may

be be StabilizingStabilizing or or destabilizing forcedestabilizing force Example Example …… Supraspinatus orientation & action …Supraspinatus orientation & action …

Stabilize head of humrus into Stabilize head of humrus into glenoid cavityglenoid cavity

Deltoid orientationDeltoid orientation & action …& action … Produces a Produces a destabilizing forcedestabilizing force that that

may result in may result in superior translationsuperior translation of of the humeral headthe humeral head

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FrictionFriction “ The tangential force acting

between two bodies in contact that opposes motion or impending motion ”

Static FrictionStatic Friction Kinetic FrictionKinetic Friction Coulomb FrictionCoulomb Friction

Friction b/w dry surfacesFriction b/w dry surfaces Most biomechanical analyses Most biomechanical analyses involve dry friction involve dry friction

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Joint ForcesJoint Forces “ “ The forces that exist between The forces that exist between

the Articular surfaces of the the Articular surfaces of the jointjoint ” ”

Joint forces are the result of Joint forces are the result of muscle forces, gravity, and muscle forces, gravity, and inertial forces inertial forces ((usually, muscle usually, muscle forces are responsible for the forces are responsible for the largest partlargest part))

Also called Bone on bone forces Also called Bone on bone forces ((not joint reaction forcesnot joint reaction forces))

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Joint Reaction ForcesJoint Reaction Forces “ The equal and opposite forces that

exist between adjacent bones at a joint caused by the weight and inertial forces of the two segments ””

A fairly A fairly abstract conceptabstract concept useful in useful in mathematical analysis but not much mathematical analysis but not much use in practiceuse in practice

Must not be confused with joint Must not be confused with joint forcesforces that include the effects of that include the effects of muscle actionmuscle action

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Ground Reaction ForcesGround Reaction Forces “ The forces that act on the

body as a result of interaction with the ground ”

According to Newton’s third According to Newton’s third law … law … ““Ground reaction forces are Ground reaction forces are

equal and opposite to those equal and opposite to those that the body is applying to that the body is applying to the ground” the ground”

Ground reaction forces can be Ground reaction forces can be measuredmeasured with a with a force force platformplatform

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Center of PressureCenter of Pressure “ “ Center of pressure is the point Center of pressure is the point

on a body where the total sum of on a body where the total sum of the pressure field acts,the pressure field acts, causing a causing a force to act through that pointforce to act through that point

Generally, the force is applied Generally, the force is applied over a diffuse area over a diffuse area e.g. the plantar e.g. the plantar aspect of the foot aspect of the foot

During Standing …During Standing … When pressure exists under both When pressure exists under both heels and balls of the foot, the heels and balls of the foot, the COPCOP will be in the will be in the mid-foot mid-foot RegionRegion

During Walking …During Walking … COPCOP moves under the foot moves under the foot 05/03/2305/03/23 2020

Free Body DiagramFree Body Diagram “ “ A diagram in which all the A diagram in which all the

forces and torques acting on a forces and torques acting on a body are identifiedbody are identified ” ”

This includes forces like This includes forces like gravitygravity, , frictional forcesfrictional forces, and , and reaction reaction forcesforces caused by contact with caused by contact with other objects other objects

The name originates from the The name originates from the fact that the body is “ fact that the body is “ freed freed ”” from its external contacts that are from its external contacts that are replaced by reaction forces replaced by reaction forces

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F is the force applied to the hand by the handle of the cable attached to the weight in the weight pan,W is the total weight of the lower arm acting at the center of gravity of the lower arm,FM1 is the force exerted by the biceps on the radius,FM3 is the force exerted by the brachioradialis muscles on the radius,FM2 is the force exerted by the brachialis muscles on the ulna, andFJ is the resultant reaction force at the humeroulnar and humeroradial joints of the elbow.

Example of free body diagram

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Newton’s LawsNewton’s Laws

Sir Isaac NewtonSir Isaac Newton (1642-1727)(1642-1727) IN-MO-REIN-MO-RE First Newton’s lawFirst Newton’s law (Law of (Law of InInertia)ertia) Second Newton’s lawSecond Newton’s law (Law of (Law of

MoMomentum)mentum) Third Newton’s lawThird Newton’s law (Law of (Law of

ReReaction)action)

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Newton’s LawsNewton’s Laws First law …First law … “ “ An object remains at rest or constant velocity unless An object remains at rest or constant velocity unless

acted upon by an unbalanced external forceacted upon by an unbalanced external force ”” Second law …Second law … “ “ If there is an unbalanced force acting on a object, it If there is an unbalanced force acting on a object, it

produces an acceleration in the direction of the force, produces an acceleration in the direction of the force, directly proportional to the force directly proportional to the force (f = ma)(f = ma)””

Third law ……Third law …… “ “ For every action (For every action (forceforce) there is a reaction () there is a reaction (opposing opposing

forceforce) of equal magnitude but in opposite direction) of equal magnitude but in opposite direction ””

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Newton’s LawsNewton’s Laws

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Modes of DeformationModes of Deformation

When an object (in static equilibrium) is When an object (in static equilibrium) is subjected to external force, there is some subjected to external force, there is some local shape change within the object called local shape change within the object called deformationdeformation

External forces may beExternal forces may beNormal forces Normal forces i.e. tensile or compressive i.e. tensile or compressive

forcesforcesShearShear i.e. tangential forces i.e. tangential forces

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Normal and shear stressesNormal and shear stresses Normal stress..Normal stress..The internal force that is opposite The internal force that is opposite

in the direction of externally in the direction of externally applied force and parallel to the applied force and parallel to the long axis of material or long axis of material or perpendicular to its cross sectionperpendicular to its cross section

It may be tensile stress or It may be tensile stress or compressive stresscompressive stress

Represented by Represented by σσ=F/A=F/A

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Shear stressesShear stresses

The intensity of internal The intensity of internal force that is opposite in the force that is opposite in the direction of external load but direction of external load but perpendicular to the long perpendicular to the long axis of material or coplanar axis of material or coplanar with its cross sectionwith its cross section

Represented by Represented by ττ= F/A= F/A

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Normal and Shear StrainsNormal and Shear Strains Strain…Strain… Measure of the degree of deformationMeasure of the degree of deformation Normal strainNormal strain….….The ratio of the change (increase or decrease) The ratio of the change (increase or decrease)

in length to the original (undeformed) lengthin length to the original (undeformed) lengthTensile or +ive strainTensile or +ive strainCompressive or –ive strainCompressive or –ive strain Denoted by Denoted by εε==ΔΔl/ll/l

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Shear strainShear strain

Related to distortions caused by shear Related to distortions caused by shear stresses stresses

Denoted with the symbol Denoted with the symbol γ = γ = d/h.d/h.

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STRESS-STRAIN DIAGRAMSSTRESS-STRAIN DIAGRAMS Different materials may Different materials may

demonstrate different stress demonstrate different stress strain relationshipsstrain relationships

Consider the stress-strain Consider the stress-strain diagram showndiagram shown

Labeled as O, P, E, Y, U & Labeled as O, P, E, Y, U & RR

Type of material, Type of material, temperature and load rate temperature and load rate can alter s-s relationshipcan alter s-s relationship

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ELASTIC AND PLASTIC ELASTIC AND PLASTIC DEFORMATIONSDEFORMATIONS

Elasticity is defined as the ability of a material to Elasticity is defined as the ability of a material to resume its original (stress-free) size and shape resume its original (stress-free) size and shape on removal of applied loadson removal of applied loads

An elastic material whose stress-strain diagram An elastic material whose stress-strain diagram is a straight line is called a linearly elastic is a straight line is called a linearly elastic material.material.

For such a material, the stress is linearly For such a material, the stress is linearly proportional to strainproportional to strain

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The slope of the stress-strain The slope of the stress-strain diagram in the elastic region is diagram in the elastic region is called the elastic or Young’s called the elastic or Young’s modulus of the material,modulus of the material,

denoted by E. so denoted by E. so σσ= Eε. = Eε. Plasticity implies permanent Plasticity implies permanent

deformations. Materials may deformations. Materials may undergo plastic deformations undergo plastic deformations following elastic deformations following elastic deformations when they are loaded beyond when they are loaded beyond their elastic limitstheir elastic limits

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VISCOELASTICITYVISCOELASTICITY Tissues in which the physical properties Tissues in which the physical properties

associated with the stress-strain curve associated with the stress-strain curve change(strain) as a function of time are change(strain) as a function of time are considered considered viscoelasticviscoelastic

Most tissues within the musculoskeletal system Most tissues within the musculoskeletal system demonstrate at least some degree of demonstrate at least some degree of Viscoelasticity Viscoelasticity

The stress-strain curve of a viscoelastic material The stress-strain curve of a viscoelastic material is also sensitive to the is also sensitive to the rate of loading of the rate of loading of the tissuetissue

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In general, the In general, the slope of a slope of a stress-strain relationship stress-strain relationship when placed under when placed under tension or compression tension or compression increases throughout its increases throughout its elastic range as the rate elastic range as the rate of the loading increasesof the loading increases

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Creep phenomenonCreep phenomenon

One phenomenon of a One phenomenon of a viscoelastic material is creepviscoelastic material is creep

creep describes a creep describes a progressive strain of a progressive strain of a material when exposed material when exposed to a to a constant load over timeconstant load over time

if the stress is held constant, if the stress is held constant, the strain increases with the strain increases with timetime

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Stress relaxation phenomenonStress relaxation phenomenon

Strain is maintained Strain is maintained at a constant levelat a constant level

while observing the while observing the stress response of stress response of the material.the material.

the stress decreases the stress decreases with time (relaxation)with time (relaxation)

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Center of Gravity and StabilityCenter of Gravity and Stability COGCOG :: ““The point at which all of the weight of that body to be The point at which all of the weight of that body to be

concentrated”concentrated” It changes on a body's shape and body mass distribution It changes on a body's shape and body mass distribution

changeschanges COGCOG in anatomical position … in anatomical position … approx. at the level of approx. at the level of

22ndnd sacral vertebra sacral vertebra

Importance of the location of a person’s COG Importance of the location of a person’s COG …… Important in athletics and other fast motionsImportant in athletics and other fast motions More important clinically i.e. for motions in which the More important clinically i.e. for motions in which the

acceleration is negligible, COG must be contained acceleration is negligible, COG must be contained within a person's base of support to maintain stability within a person's base of support to maintain stability

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Center of Gravity and StabilityCenter of Gravity and Stability When a person stands upright, When a person stands upright, his COG is post. to his toes, so his COG is post. to his toes, so there is a counterclockwise there is a counterclockwise moment at his toes. This is a moment at his toes. This is a stable positionstable positionAs the person bends forward, As the person bends forward, his COG moves anterior to his his COG moves anterior to his toes and the weight of his upper toes and the weight of his upper body produces a clockwise body produces a clockwise moment at his toes. Since there moment at his toes. Since there is no further anterior support, is no further anterior support, this moment is unbalanced and this moment is unbalanced and the man will fall forwardthe man will fall forward05/03/2305/03/23 3939

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