Exss 3850 9 summer linear kinetics

EXSS 3850 Introduction to BiomechanicsEXSS 3850 Introduction to Biomechanics

Linear Kinetics – Forces Linear Kinetics – Forces Causing MovementCausing Movement

Paul DeVita, Ph.D. Biomechanics Laboratory East Carolina University Greenville, North Carolina

Linear KineticsLinear Kinetics

The study of forces and their effects on masses1) Force – a push or pull by one object onto another2) Effects – positive and negative accelerations, stabilize

object, apply stress on an object, rotate object3) Masses – the object under

consideration – a whole human or animal, an object being held in one’s hand, a body segment

Linear Kinetics and Isaac NewtonLinear Kinetics and Isaac Newton

Newton, b. 1642

Newtonian Mechanics or Newtonian Physics – describe how things move.

Three Laws of Motion applied to all nearly all objects in the universe.

Has problems with the very largest (i.e. fastest = galaxies and expansion of the universe) and smallest objects (nuclear particles).

Newtonian mechanics is used to analyze how tiny, one celled organisms move, how humans move, and how planets and solar systems move.

Force, By DefinitionForce, By DefinitionForce – a push or pull by one object onto another – always applied

through contact between two objects and termed, “Reaction Force.”

Force = Mass * AccelerationForce = Mass * Acceleration

F = m aF = m a

Force is a vector (magnitude & direction) and is measured in Newtons:

1 N = 1 kg m/s2 N = m * a

1 N = 0.225 Lbs. or 1 Lb. = 4.448 N

150 Lbs. = 667 N 200 Lbs. = 890 N 250 Lbs = 1,112 N

Never measure force in kg. Mass is measured in kg.

Vector Nature of Force – Magnitude and Vector Nature of Force – Magnitude and DirectionDirection

Force is a vector – The vector nature is seen in the direction of force relative to a bone.

Shear – force across an object

Compression – force into an object, squeezing the object

Tension – force away from the object, stretching the object

Patella-Femur compression 5,000 N in stair ascent

Squat has shear (5,000 N) and compression (10,000 N) on spine

Cruciate knee ligaments resist shear forces

Forces Exist In All SituationsForces Exist In All Situations

Forces Exist In All SituationsForces Exist In All Situations

We will concentrate on four very important forces:1) Weight2) Ground reaction force3) Muscle forces4) Joint forces

1) Weight – Force Due to Gravitational 1) Weight – Force Due to Gravitational Attraction Between The Earth and an ObjectAttraction Between The Earth and an Object

Downward gravitational force acting on all objects:Weight = mass x g

mass = amount of matter in an object (kg) g = gravitational acceleration (- 9.81 m/s2)

Weight is a force = mass x acceleration = a vectorDr. DeVita’s weight = 66 kg x -9.81 m/s2 = -647 N (~147 lbs)

Jumper’s weight:limits her jumping ability and height,stops her upward movement, andaccelerates her downward.

Weight Is Not Mass & Mass Is Not WeightWeight Is Not Mass & Mass Is Not Weight

Mass: scalar quantity measuring the amount of matter in an object

Barbell on Earth: Barbell mass is 4.5 kg. Barbell weighs 10 lbs = 44.5 N. Barbell in Space: Barbell mass is 4.5 kg. Barbell weighs 0 lbs = 0.0 N.

Weight: the force from the interaction between the planet’s mass and the object’s mass

Person’s mass is 70 kg. What is:– Person’s weight = 70 kg * -9.81 m/s2 = -883 N– Person’s mass on the moon = 70 kg– Person’s weight on the moon = 70 kg * -1.64 m/s = -115 N

Mass and weight are perfectly correlated thus it is easy to think they are equivalent. We will see how they are used differently in the physics used in biomechanics.

2) Ground Reaction Force (GRF) is…2) Ground Reaction Force (GRF) is…

…the force applied to a person form the supporting ground or floor. …the force that produces human movement around the environment (i.e. the force that

causes locomotion.…produced in response to the person’s weight plus any propulsive force generated by

muscles.

GRF propels runner

GRF stops vaulter

GRF propels jumper into the air

GRF propels pogo-er into the air

GRFs in WalkingGRFs in WalkingResultant GRF resolved into

vertical & horizontal components.

Vertical about 4 times larger than horizontal.

Heel strikeVertical GRF

Horizontal GRF

Up

Back

Forward

Late stance

No force the instant before floor contact

Large force at maximum knee

flexion – direction is up and slightly

backwards

Large force at maximum push-off – direction is up and

slightly forwards

Vertical – stops downward motion then creates upward motion

Horizontal – slows then accelerates the person

Early stance

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1000

1000-1000

-1000

1000

1000

1000

1000

Show Level-walking-3-speeds.cmo

Vertical GRFs in Walking and RunningVertical GRFs in Walking and Running

Running has higher force for a shorter duration.

Walking less “dynamic” than running – forces closer to bodyweight – walking is more similar to standing than to running

Bodyweight = 850 N

Vertical GRFs in Lean and Obese PeopleVertical GRFs in Lean and Obese People

Everyone who walks normally has, more or less, this basic shape: early and late force peaks above bodyweight and a force minimum in midstance below bodyweight.

Obese vs. lean individuals have more weight pushing down and greater GRF pushing up in response.

Bodyweight = 850 N

Lean

Vertical GRF in Jumping and LandingVertical GRF in Jumping and Landing

Vertical GRF in jumping propels (accelerates) by pushing person upward with large magnitude.

Jump video & GRF.MOV

Vertical GRF in landing stops (accelerates) by pushing person upward with large magnitude.

Vertical GRF both produces and stops movement.

3) Muscle & 4) Joint Forces3) Muscle & 4) Joint Forces (done previously and (done previously and more to come)more to come)

Internal vs. External ForcesInternal vs. External Forces

Internal force – a force entirely within an object that does not cause the object to move.

External – a force applied from outside the object (i.e. from the environment). Only external forces can move an object through the environment. Weight, GRFs, contact with other object (a linebacker tackles a running back).

Object – must be clearly defined (see below and next slide).

Pole vaulting: Object is the vaulter.External forces: weight pulls the vaulter down and the pole pulls the vaulter up.

Weight lifting:Object is the dumb bellExternal forces: dumb bell’s weight pulls it down and the Hand reaction Force pushes the dumb bell up.

Internal vs. External ForcesInternal vs. External Forces

In vaulting the left lower extremity moves upward as the hip flexes. The object is now the left lower extremity. What Forces are external to it?

In the dumb bell bench press, the arm moves up. The object is now the arm. What Forces are external to it?

Pole vaulting: Object is the left lower extremity.External forces: lower extremity weight (white arrow) pulls the lower extremity down and the hip flexor muscles pull the extremity.

Muscle Force is EXTERNAL in this situation.

Weight lifting:Object is the right armExternal forces: arm weight pulls it down and shoulder muscles pull it up.

Muscle Force is EXTERNAL in this situation.

Muscle Force is External to ForearmMuscle Force is External to Forearm

Muscle force from outside of forearm and reaching into the forearm.

Muscle force accelerates the forearm in the upward direction.

MUST CAREFULLY DEFINE THE OBJECT.

Force Resolution – Identifying Force Resolution – Identifying Force ComponentsForce Components

Force Resolution: separation of a force into components:

1) Vertical and horizontal forces in environmental reference frame – used to analyze locomotion and other full body movements

2) Stabilizing and rotational forces in anatomic reference frame – used to analyze muscle forces on skeletal bones

Early stance

-1000

1000

1000

Biceps force

Rotating component

Stabilizing component

`

Force Resolution in the EnvironmentForce Resolution in the Environment

Environmental reference frame for general movement.

60°

20°

4,000 N at 60 to horizontal 4,000 N at 20 to the horizontal

Force hor = 4,000 N cos 60 = 2,000 N Force hor = 4,000 N cos 20 = 3,759 N

Force vert = 4,000 N sin 60 = 3,464 N Force vert = 4,000 N sin 20 = 1,368 N

Long Jump – more horizontal than vertical

High Jump – more vertical than horizontal

`

Anatomical reference frame for muscle forces:

= 30°

Biceps force = 2,000 N

Rotating

Stabilizing Calculate stabilizing and rotating components not horizontal and vertical

Stabilizing:

Force = 2,000 cos 30

= 1,879 N

Rotating:

Force = 2,000 sin 30

= 1,000 N

Rotating force < Stabilizing force because < 45

Anatomical Force ResolutionAnatomical Force Resolution

Newton’s Laws of Linear MotionNewton’s Laws of Linear Motion

The next ~30 slides explain Newton’s Laws of Motion. These laws describe the underlying causes of movement.

Two of these laws (#1 & #3) are conceptual and do not require mathematics. Law #2 will have much mathematics and IS OUR PRIMARY FOCUS.

Please note, we will discuss laws #1 and #3 first and then law#2.


I. Law of Inertia – An object will remain stationary or move with constant velocity until an external force is applied to the object

“Constant velocity” – implies straight line (direction) and constant speed

Inertia – measures on object’s resistance to motion.

Inertia = mass (kg)

Shot put has greater resistance – it is harder to accelerate. We can throw a softball farther. What would happen if we attempted to throw a shot put?

Perceiving the Law of InertiaPerceiving the Law of Inertia

The Elevator Test: stand in elevator with knees flexed about 20 and then press the UP button.

Upward force from elevator

What happens?

Perceiving the Law of InertiaPerceiving the Law of Inertia

The Seat Belt Test: what happens when you press on the brakes as you are driving or if you JAM on the brakes?

Brakes slow the car

Trunk accelerates forward relative to thighs and car. The more you JAM on the breaks, the greater the acceleration, the faster your trunk moves forward.

Law of Inertia and Inertial ForcesLaw of Inertia and Inertial ForcesInertial forces – motion-dependent forces (but really acceleration-dependent

forces)

Forces due to the acceleration of an object: in lifting an object we accelerate the object. The object applies force on us equal to its weight PLUS the inertial force. The faster we lift (i.e. the greater the acceleration), the greater the inertial force and the total force.

Thus lifting slowly reduces spinal force while lifting rapidly increases spinal forces.

Inertial force is important because of the extra load it places on humans in rapid movements, not because it is the force that caused the movement. The person applies the movement force on the object and the object applies the reaction force (weight + inertial force) back onto the person.

Law of Inertia and Inertial ForcesLaw of Inertia and Inertial Forces

Inertial forces and Grocery Bags – the paper bags are full and the food in them is heavy. Lift the bags slowly and they are fine. Lift too fast (i.e. accelerate too rapidly) and they rip. Why?

The heavy load and the high acceleration creates a large inertial force (f = m a) applied downward against the bags. We accelerate the bags and food up and the food resists with a downward force: the bag rips.

Inertial Forces important in lifting – total force can be separated into weight plus inertial force. While holding the barbell stationary, the inertial force is zero and total force equals barbell weight.

Inertial Forces in Bench Press: barbell weight is 1,330 N. All force above 1,330 N is inertial force due to acceleration in lift, especially important at start of lift.

Force = mg + ma (vertical)

= weight + inertial force

While holding, ma (vertical) =0

Inertial force in early lift during initial acceleration


Lifting too rapidly, especially with bad technique creates large inertial load against your trunk extensor muscles and lumbar discs.

The box may weigh 80 N (20 lbs.) but your trunk may weigh 400 N (100 lbs.) and the combined inertial force can be over 2,000 N (500 lbs.) in a fast lift.



III. Law of Reaction – When one object applies a force on a second object, the second object applies an equal and opposite force onto the first object

“equal and opposite” – equal magnitude and opposite direction

Basis for force platform measurements and Ground Reaction Forces

Force Plate in Balance Force Plate in Balance and Locomotionand Locomotion

Platform measures the reaction forces to the forces applied by the person. After release, the person must step and apply force onto floor (force plate) to maintain support.

Person with ACL injury, surgery, and brace walks over force plate to analyze gait.

Walking direction

Vertical force

Mediolateral force

Anteroposterior force

Platform measures the reaction forces to the forces applied by the person in 3 dimensions

Force Platforms and the Law of ReactionForce Platforms and the Law of Reaction

To walk, we push down and back on the floor and the floor pushes up and forward on us. The external GRF causes locomotion.

Force Plate in Jumping…as we knowForce Plate in Jumping…as we know

Newton’s Laws of MotionNewton’s Laws of Motion

II. Law of Acceleration – a force will accelerate an object in the direction of the force, at a rate inversely proportional to the mass of the object

Force = mass x acceleration or F = m a

The basis for all biomechanics – forces cause motion

Force – a pushing or pulling effect on an object

This force is an EXTERNAL force

Law of Acceleration & and the Law of Acceleration & and the Impulse-Momentum RelationshipImpulse-Momentum Relationship

Law of Acceleration describes change in momentum of the object, a change in the quantity of motion.

F = m a

Positive acceleration – increase quantity of motion

Negative acceleration – decrease quantity of motion

Momentum is the Quantity of Motion or Mass in Motion

Momentum = mass * velocity in kg*m / s

Momentum = Mass * VelocityMomentum = Mass * Velocity

Momentum depends on the mass of the object and its velocity.

Momentum does not equal Mass (see Mr. Elephant)

Law of Acceleration restated:

F = m * a

F = m * (vf – vi) / time

F * time = m * (vf – vi) - Impulse-Momentum equation

Interpretation: impulse changes momentum – force applied for a period of time can either increase or decrease the velocity of an object.

Law of Acceleration & and the Law of Acceleration & and the Impulse-Momentum RelationshipImpulse-Momentum Relationship

Impulse Changes MomentumImpulse Changes Momentum

When impulse and momentum are in opposite directions, impulse will reduce momentum, as in tackling.

When impulse and momentum are in the same directions,

impulse will increase momentum, as in javelin.

http://www.youtube.com/watch?v=PMtrMhGDFtU

Impulse Changes MomentumImpulse Changes MomentumHuman activities are quick, short duration movements. Since time potion of impulse is low than force portion is high. Muscle forces are high.

Quick actions to increase momentum

Quick actions to decrease momentum

Force and Time in Impulse and Athletic SkillForce and Time in Impulse and Athletic Skill

Novice athletes – beginners – tend to exert force over shorter periods of time. Beginning golfers swing with only the upper body. This motion is a quicker, jerkier motion, that does not produce the highest impulse.

Skilled athletes exert force over longer times. They build up more force using more muscle groups. Skilled golfers use lower extremities more. This motion is smooth, lengthy, and it produces high impulse – the golf club moves faster and more accurately.

Vertical Impulse in RunningVertical Impulse in Running

Vertical impulse is the area under the Force-Time curve (gray area) = total effect of the applied force.

Measured in Newton*seconds (Ns)

In this example, impulse from vertical GRF = 300 Ns during the stance phase of running with half occurring during flexion and half during extension phases.

At heel strike (the start of stance phase), person’s momentum was downward. Upward force from ground reduces this momentum until the person stops at midstance (hip, knee flexion & ankle dorsiflexion all stop at vertical line). Additional impulse after midstance propels the person upward, increasing momentum.

150 Ns 150 Ns

-1.5 m/s 0.0 m/s +1.5 m/s Vertical velocity

Heel Strike Mid-stance Toe Off

Horizontal Impulse in RunningHorizontal Impulse in Running

Braking impulse reduces horizontal momentum (i.e. velocity) – impulse & momentum in opposite directions.

Propelling impulse increases horizontal momentum (i.e. velocity) – impulse & momentum in same direction.

Is this person speeding up or slowing down?

Negative force is backwards

Positive force is forwards

Horizontal Impulse Horizontal Impulse in Runningin Running

Runner’s mass = 70 kg

Initial velocity (vi) = 4.00 m/s

Braking imp. = -18 Ns

Propelling imp = 20 Ns

What is runner’s velocity at midstance and at toe off?

Calculations on next slide-400

-300

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-100

0

100

200

300

400

0 0.05 0.1 0.15 0.2

Time (s)

Forc

e (N

)

Imp= -18 Ns

Imp = 20 Ns

Heel Strike Midstance Toe off

4.00 m/s ? m/s ? m/s Horizontal velocity

Horizontal Impulse Horizontal Impulse in Runningin Running

-400

-300

-200

-100

0

100

200

300

400

0 0.05 0.1 0.15 0.2

Time (s)

Forc

e (N

)

Imp= -18 Ns

Imp = 20 Ns

Heel Strike Midstance Toe off

4.00 m/s ? m/s ? m/s Horizontal velocity

Braking imp. = -18 Ns

-18 Ns = 70 kg (vf – 4.00 m/s)

-18 Ns / 70 kg + 4.00 = vf

3.75 m/s = vf at midstance

Propelling imp = 20 Ns

20 Ns = 70 kg (vf – 3.75 m/s)

20 Ns / 70 kg + 3.75 = vf

4.04 m/s = vf at toe off

Horizontal Impulse in RunningHorizontal Impulse in Running

-400

-300

-200

-100

0

100

200

300

400

0 0.05 0.1 0.15 0.2

Time (s)

Forc

e (N

)

-18 Ns

20 Ns

Vertical Impulse in JumpingVertical Impulse in Jumping

Bodyweight is critical value

Assess impulse from BW

Calc. velocity at 3 points

mass = 65.7 kg0

200

400

600

800

1000

1200

1400

1600

0 200 400 600 800

Time (ms)

Forc

e (N

)

-59 Ns

59 Ns 196 Ns

V = 0.00 m/s V = -0.91 m/s V = 0.00 m/s V = 3.02 m/s

Vertical Impulse in JumpingVertical Impulse in Jumping

Jump video & GRF.MOV

Impulse – Momentum RelationshipImpulse – Momentum Relationship

Shows the underlying physics demonstrating how forces cause objects to move and how forces cause objects to stop moving.

Impulse represents the total effect of a force applied over time. In human movement, time intervals are typically short and forces are typically high.

Momentum represents the quantity of motion and is a function of the mass and the velocity of the moving object.

Law of Acceleration and Inverse DynamicsLaw of Acceleration and Inverse Dynamics

Inverse Dynamics – an analysis that calculates unknown forces inside the human body.

Forces in joints, muscles, bones, ligaments, etc

Direct measurement is best but not many people volunteer to have force transducers surgically implanted into their bodies. Weird, huh?

Measurement of Forces Measurement of Forces Inside the Human BodyInside the Human Body

Buckle transducer surgically inserted onto Achilles tendon in humans (Gregor et al, early 1980s) and in cats (still being done).

Fiber optic cable inserted through Achilles tendon in humans and other animals (started about 1995 and continuing).

Measurement of Forces Inside Measurement of Forces Inside the Human Bodythe Human Body

Achilles tendon forces along with GRFs during walking with buckle and fiber optics. Achilles force looks just like ankle torque during walking.

Swing Stance

Ant/Post GRF

Vertical GRF

Slow Fast

Inverse Dynamics AnalysisInverse Dynamics AnalysisInverse Dynamics – combines position and acceleration

data from video motion analysis and force data from force platforms or other force sensors to calculate internal forces. Most commonly used in locomotion but

also in rowing, cycling and other activities.

Inverse Dynamics AnalysisInverse Dynamics AnalysisInverse Dynamics uses two basic physics tools: a Free Body Diagram (FBD) and

Equations of motion.

Free Body Diagram – a diagram showing an object and all the forces applied to the object at a single instant in time.

FBDs of a person standing - all drawings are equivalent:

mg

Fvmg

Fv

mg = weight

Fv = vertical floor reaction force

mg

Fv Fv

mg

Inverse Dynamics AnalysisInverse Dynamics AnalysisFBD of a running

person:

mg

Fv

mg

Fh

Wind resistance

FBD of the leg of a running person:

Knee Vert. & Hor. Joint Reaction Forces – Thigh pushing on Leg

Ankle Vert. & Hor. Joint Reaction Forces - Foot Pushing on Leg

Vert. & Hor. GRF

Segment CoM about 43% from proximal end

The person is one object and it has one weight

Inverse Dynamics AnalysisInverse Dynamics AnalysisEquation of motion – the physics equation that describes the free body diagram.

The equation that shows the forces (kinetics) and their effects on the mass (the acceleration or kinematics).

The particular equation of motion is simply a re-working of the law of Acceleration, F = ma.

mg

Fv

Equation of motion for the standing person:

FFvv = ma = mavv (sum of the vertical forces = mass x vertical

acceleration)

mass = 70kg, av = 0 (standing person has mass but no accel.)

-mg + Fv = 0-mg + Fv = 0 (equation of motion for a standing (equation of motion for a standing person)person)

Fv = mg (the floor applies an upward force equal to the person’s weight during standing)

Fv = 70kg (9.81m/s2) = 687 N

Inverse Dynamics AnalysisInverse Dynamics Analysis

mg

FBD of a the leg of the running person:

Knee Vert. & Hor. Joint Reaction Forces

Ankle Vert. & Hor. Joint Reaction Forces

Segment CoM about 43% from proximal end

Inverse Dynamic Analysis to calculate the force under a standing person? Why bother? Buy a bathroom scale for that.

Ahhh, but we do need this analysis to identify unknown forces applied to our joints or ligaments or generated by our muscles.

Need data describing characteristics of each body segment (location inn space, mass, location of the center of mass in the segment - See next slide).

Kinematic chain of the lower extremity and individual body segments:

Kinematic chain

The objects or masses in this analysis are each of the individual body segments.

3. Goal – calculate unknown ankle joint forces.

Start with distal segment – the foot and analyze ankle, then knee, then hip joints.

External forces applied to a segment include segment weight, force from contact with ground, and joint reaction force from contacting body segment (i.e. the leg).

2.1.GRF v

GRF h

GRFv

GRFh

Ankle v

Ankle h

Subject walking up the ramp.

Video to produce position and acceleration data. Force plate to measure the known external forces.

See analysis on next few slides and on board.


White line is force plate. Curves are vertical and ant-post GRFs.

Data used in the I.D. analysis in next few slides:

Masses and moment of inertias:

Subject: 70 kg Foot: 1.7 kg, 0.0023 kgm2 Leg: 3.44 kg, 0.0044 kgm2

Accelerations:

Foot vertical: 2.47 m/s2 Foot horizontal: 4.70 m/s2

Foot rotational: -52.5 rad/s2

Leg vertical: 1.30 m/s2 Leg horizontal: 9.23 m/s2

Leg rotational: -10.3 rad/s2

Av – large & down: the body weight plus inertial force of accelerating body mass upward push down on the foot.

The upward GRF is larger than the downward ankle reaction force – THUS THE FOOT AND PERSON MOVE UPWARD.

Ankle Joint ForcesAnkle Joint Forces

Vertical Ankle Joint Reaction Force (JRF)

Av: Fv = mav

GRFv – mg + Av = mav

975 – (1.07) (9.81) + Av = (1.07) (2.47)

Av = -961 N

Foot

Ankle

-961 N Av

mg

Note: Weight applied at the center

of mass

GRFv = 975 N

Vertical Direction:

Ah – small and backward: the foot pushes the body forward & the body pushes back on the foot at the ankle.

The forward GRF is larger than the backward ankle reaction force – THUS THE FOOT AND PERSON MOVE FORWARD.

Ankle Joint ForcesAnkle Joint Forces

Horizontal Ankle Joint Reaction Force (JRF)

Ah: Fh = mah

GRFh + Ah = mah

162 + Ah = (1.07) (4.7)

Ah = -157 N

GRFh = 162 N

Foot

Ankle

-157 NAh

Horizontal Direction:

Goal: calculate unknown knee joint forces.

4.

Net force at of leg onto foot is reversed for foot onto leg. Leg pushed down and back on foot and foot pushes up and forward on leg.

This is the Law of Reaction – one object pushes a second and the second push back on the first.

Ankle v

Ankle h

Knee vKnee h

Leg mg

Knee Joint ForcesKnee Joint Forces

Vertical Knee Joint Reaction Force (JRF)

Kv: Fv = mav

Av – mg + Kv = mav

961 – (3.44) (9.81) + Kv = (3.44) (1.30)

Kv = -922 N

Av = 961 N

Leg

Knee

Kv

Kv – large & down: the body weight plus inertial force of accelerating body mass upward push down on the knee

The upward ankle force is larger than the downward knee force – THUS THE LEG AND PERSON MOVE UPWARD.

Ankle

Note: Ankle JRFs reversed onto leg (the

law of reaction)

mg

-922 N

Vertical Direction:

Knee Joint ForcesKnee Joint Forces

Horizontal Knee Joint Reaction Force (JRF)

Kh: Fh = mah

Ay + Kh = mah

157 + Kh = (3.44) (9.23)

Kh = -125 N

Ah = 157N

Leg

Knee

Kh – small and backward: the leg pushes the body forward & the body pushes back on the leg at the knee.

The forward ankle force is larger than the backward knee force – THUS THE LEG AND PERSON MOVE FORWARD.

Ankle

Note: Ankle JRFs reversed onto leg (the

law of reaction)

Kh

-125 N Horizontal Direction:

Joint Reaction Forces from Inverse Joint Reaction Forces from Inverse DynamicsDynamics

Forces calculated through the stance phase. The position and acceleration of the body segments are derived from each video frame. The ground reaction forces are applied to the foot and the analysis calculates the ankle JRF. The procedure is repeated for leg and knee and then thigh and hip.

Newton’s Laws of Motion - SummaryNewton’s Laws of Motion - Summary

Three laws describing linear kinetics (We will also learn the

analogous laws for angular kinetics.)

Second law, the law of acceleration, is the basis for most Biomechanics

All laws apply to all biomechanical situations, but each situation may best be analyzed with a subset of the laws

Vsevolod Meyerhold’s

Biomechanical Theater in

Russia, 1922

Energy, Work, and PowerEnergy, Work, and Power

An alternative analysis to the dynamic analysis of F=ma for understanding the mechanics of physical systems

Provides insight into motion in terms of a combination of kinematics (position & velocity) and kinetics (force)

Provides insight into muscle mechanics in terms of contraction types, roles of muscles, sources of movement

EnergyEnergyEnergy has many forms – chemical, nuclear, electrical,

mechanical, and more

Energy is often transformed from one form to another:

Electricity is used to spin CDs (the spinning CD has mechanical energy);

Chemical energy in ATP is used to produce the, “power stroke” and slide actin over myosin

Energy is a scalar variable that reflects the “energetic state” of the object – we measure how much or how little energy an object has at one point in time.

Energy, Conceptually Speaking….Energy, Conceptually Speaking….The biomechanical concept of energy is exactly like the English concept: if someone is

energetic biomechanically, that person is active, rambunctious, full of life, so to speak. If someone has low energy biomechanically, that person is tired, slow, lazy, lethargic, so to speak.

We can assess human movement by assessing the energy in a person or a body segment and how that energy increases or decreases:

Concentric contractions increase energy in our bodies and in objects we manipulate – they raise our position and/or increase our velocity or an object’s position and velocity – the high jump has concentric contractions to lift us and give us vertical velocity.

Eccentric contractions decrease energy in our bodies and in objects we manipulate – they lower our position and/or decrease our velocity or an object’s position and velocity – landing from a jump has eccentric contractions to carefully lower ourselves after hitting the floor, lowering our position.

Energy, Biomechanically Speaking….Energy, Biomechanically Speaking….

Mechanical energy is the capacity to do work – if a person has energy the person can do work: the javelin thrower runs up the runway and has developed high energy – she now can do much work on the javelin and throw it far.

The capacity to do work means the thrower does work on the javelin – this work increases the energy of the javelin and it flies…flies…flies…

Energy, Technically Speaking….Energy, Technically Speaking….

Mechanical energy is the capacity to do work and work is the product of force and displacement

Work = Force * Displacement

Therefore, mechanical energy is the capacity to move objects

Energy = Zero or positive value (a scalar), Joules = J

1 J is very small – move fingers a few centimeters?

133 J lifts 150 lb (666 N) person up one step (20 cm). It takes 1,330 J of energy for this person to ascend 10 steps.

(We will return to Work-Energy relation in a few slides)

Forms of Mechanical EnergyForms of Mechanical Energy

Two basic forms of mechanical energy:

Potential energy – energy due to position above the floor or ground – the gymnast has high P.E.

Kinetic energy – energy due to person’s mass and velocity – sprinters have high K.E.

Potential Energy Potential Energy (or Gravitational Potential (or Gravitational Potential

Energy) Energy)

Potential Energy = energy of position = energy associated with the weight (mg) of an object and its height (h) above the floor.

P.E. = mgh in Joules

Runner’s body has some P.E.: P.E. = 50 kg (9.81 m/s2) (1 m) = 490 J

Vaulter has more P.E. P.E. = 80 kg (9.81 m/s2) (3 m) = 2,354 J

Velocity does not matter, only vertical position.

1 m

3 m

Potential Energy and WorkPotential Energy and Work

How does Potential Energy have the capacity to do work?

Roller coasters exploit P.E. by lifting people to great heights, increasing their P.E., then letting the P.E. work on the people to create large and frightening velocity.

Potential Energy and WorkPotential Energy and Work

Elite bowlers use large hyperextension at shoulder to lift ball and add energy to it. This P.E. can then be converted to greater ball

velocity at release.

Elite divers leap high to increase P.E. before final bending of the springboard. Higher P.E. produces greater bending and a larger springing action to propel the diver higher into the air.

http://www.youtube.com/

watch?v=sjf6pLmNYkI

Linear Kinetic EnergyLinear Kinetic Energy

Kinetic Energy = energy of motion = energy associated with the mass and velocity of an object

Linear K.E. = ½ mv2 in Joules

Jumper’s body has Linear K.E. at touchdown onto board:

K.E. = ½ (65 kg) (7.4 m/s)2 = 1,780 J

Related to linear momentum = mv – if an object has momentum, it has kinetic energy

Kinetic Energy and WorkKinetic Energy and WorkHow does Kinetic Energy have the

capacity to do work?

Large K.E. in the rolling bowling ball scatters the pins.

The large kinetic energy in the swinging bat propels the ball over the outfield wall.

In both cases, athlete did work on the implement (bowling ball or bat) and the implement did work on the next object (pins or baseball).

Three Primary Work Scenarios in Three Primary Work Scenarios in Human MovementHuman Movement

1) Muscles do work on the skeleton – concentrically they increase its height or velocity and eccentrically they decrease its height or velocity.

2) Skeleton does work on external objects – increasing or decreasing their height or velocity

3) The ground or floor does work on our skeleton – GRFs increase or decrease our energy

Work – Changing EnergyWork – Changing Energy

Work represents the change in energy of an object

Work occurs when energy changes

Work occurs when objects are raised or lowered (change in P.E.) or when their velocity changes (change in K.E.)

Work = Total Energy = (mgh + ½ mv2) in = Joules

Work – Energy Theorem:

Force * Distance = (mgh + ½ mv2)

Work – Changing Energy in JumpingWork – Changing Energy in JumpingWork = Total Energy = (mgh + ½ mv2)

work = final energy – initial energy =

(P.E.f – P.E.i) + (K.E.f – K.E.i)

= (mghf – mghi) + (½ mv2f – ½ mv2

i )

= (61*9.81*1.4 – 61*9.81*1.1) + (0.5*61*3.022 – 0)

= (838 J – 658 J) + (278 J – 0 J)

= 180 J + 278 J

= 458 J Energy was increased through the concentric contractions of muscles. Muscles did positive work on the skeletal system.

Jumper’s mass = 61 kg

CM height = 1.1 m at start & 1.4 m at take off

0

200

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600

800

1000

1200

1400

1600

0 200 400 600 800

Time (ms)

Forc

e (N

)

-59 Ns

59 Ns 196 Ns

V = 0.00 m/s V = -0.91 m/s V = 0.00 m/s V = 3.02 m/s

Initial floor contact

Work – Changing Energy in LandingWork – Changing Energy in Landing

Final position

Jumper’s mass = 61 kg

CM height = 1.4 m at start & 1.1 m at end

Work = Total Energy = (mgh + ½ mv2)


(P.E.f – P.E.i) + (K.E.f – K.E.i)

= (mghf – mghi) + (½ mv2f – ½ mv2

i )

= (61*9.81*1.1 - 61*9.81*1.4) + (0 - 0.5*61*3.022)

= (658 J – 838 J) + (0 J - 278 J)

= -180 J - 278 J

= -458 J Energy was decreased through the eccentric contractions of muscles. Muscles did negative work on the skeletal system.

Work and Cyclic MovementsWork and Cyclic Movements

Work = Total Energy = (mgh + ½ mv2)


(P.E.f – P.E.i) + (K.E.f – K.E.i)

Final position and velocity = initial position and velocity – Energy does not change, no net work was done.

Cyclic activity has no net work and no change in energy.

Humans perform equal amounts of positive and negative work through our 24 hour, cyclic lifestyles – we balance concentric and eccentric contractions (mostly).

Power – Rate of WorkPower – Rate of Work (or Rate of Changing Energy) (or Rate of Changing Energy)

Power represents the rate at which work is being done.

Work occurs when energy changes and it occurs at various rates – i.e. fast or slow, high or low

The power used in lifting depends on how fast or slowly the lift occurred.

Strength training emphasizes high force at low speeds – has low power. Power training emphasizes moderate forces at moderate speeds – has high power.

Power – Rate of WorkPower – Rate of Work (or Rate of Changing Energy) (or Rate of Changing Energy)

P = Work / time = Force * displ. / time = Force * velocity

in Watts (W)

0.20 m

40 N

Work = Force * displacement = 0.20 m (40N)

= 8 Nm = 8 J of work

Lift in 0.5 s: P = Work/time = 16 WLift in 1.0 s: P = Work / time = 8 WLift in 2.0 s: P = Work / time = 4 W

(We are not emphasizing power in this section)

Power During LiftingPower During Lifting

End of Linear Kinetics section.

Extra slides

Skeletal-Muscle Models & Force ResolutionSkeletal-Muscle Models & Force Resolution

Skeletal-muscle models used to calculate individual muscle forces in different movements and the effects of illness and injury on these forces.

Glitsch & Bauman, 1998

Pandy & Shelburne, 1998

Muscle Forces From Muscle ModelMuscle Forces From Muscle Model

Glitsch & Bauman, 1998

Vas. RF.

Measured Achilles Tendon Measured Achilles Tendon Forces and Ankle Net TorqueForces and Ankle Net Torque

Ankle torque curve similar to achilles tendon force curves. Gastroc EMG shows this muscle active in mid-late stance.

Can estimate Achilles tendon force from net torque: Torque/Achilles lever arm: 98 Nm / 0.05 m = 1960 N. Measured forces peak value ~2200 N. Estimate is reasonable.

Measurement and Prediction of Measurement and Prediction of Forces Inside the Human BodyForces Inside the Human Body

Sonomicrometery to measure muscle fiber lengths, forces transducer to measure tendon force. Biewener et al on many birds and other animals.

Measurement and Prediction of Measurement and Prediction of Forces Inside the Human BodyForces Inside the Human Body

Demonstrate isometric or even shortening contraction of muscle fibers during muscle eccentric contraction.


We will do the analysis on the front board.

Large knee flexion creates large patella-femoral compressive forces:

4000 N stair descent, kicking 7000 N,parallel squat 14,900 N.

How much in Bodyweights?

Compression under the Patella Compression under the Patella

Shear and Compressive Spinal ForcesShear and Compressive Spinal Forces

PCL and ACL Resist Knee Shear ForcesPCL and ACL Resist Knee Shear Forces

ACL prevents anterior tibial displacement relative to the femur,

PCL prevents posterior tibial displacement.

Normal ligament function is to resist joint shear forces.

Inertial Forces in JumpingInertial Forces in Jumping (like lifting)(like lifting)

One Subject - Low and High Jumps

0

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1200

1400

1600

1800

0 100 200 300 400 500 600 700

Time (ms)

Fo

rce

(N)

Low Jump

High Jump

Horizontal Force & Velocity Horizontal Force & Velocity in Throwingin Throwing

Vertical impulse is the area under the Force-Time curve.

Velocity starts at 0.0 m/s. As impulse builds or increases over time the ball velocity & momentum increase.

During middle phase, force and therefore impulse are low and ball velocity & momentum are almost constant.

During final phase and due to rapid internal shoulder rotation, force & impulse are high and ball velocity & momentum increase rapidly.

Water Polo Ball Force & Velocity

0

20

40

60

80

100

0.000 0.068 0.136 0.204 0.272 0.340 0.408

Time (s)

Fo

rce

(N)

0

5

10

15

20

Ant/PostForceAnt/PostVelocity

V = 0.0 m/s V = 5.4V = 4.2 V = 18.0

Vel

oci

ty (

m/s

)

Energy & Work on a TrampolineEnergy & Work on a Trampoline

Person has high energy at instant of contact with trampoline – mostly K.E. due to falling velocity & some P.E.

Person’s energy does work on the trampoline and pushes it down, stretching the trampoline spring – person loses K.E. & P.E.

Then trampoline’s stretch does work on person – person gains K.E. & P.E. and flies into air.

Inability of Gravity to Change Inability of Gravity to Change Energy or Do WorkEnergy or Do Work

Total Energy = P.E. + K.E.

= mgh + ½ mv2

Changes while on the trampoline but constant during flight phases

As person rises through air, K.E. is converted to P.E. As person falls, P.E. is converted to K.E.

Person leaves trampoline and then hits trampoline a few moments later with the same total energy.

1) Force is a vector – therefore its direction is crucial - - vertical GRFs cause only vertical accelerations, - stabilizing muscle forces compress joints but do not rotate body

segments

2) Magnitude – how large or small is the force? Will it create favorable or unfavorable stress?

3) Point of application - where is the force applied to the body?- Lower limbs can withstand large forces – landing from a vertical jump- Head cannot withstand such large forces – causes concussion

Biomechanical Issues About ForcesBiomechanical Issues About Forces

3) Line of action of a force – In which direction is the force relative to the body segments?- does the force create a flexor or extensor torque?- does the force create compression or shear at a joint?

4) Rate of force application – is the force applied slowly or rapidly? – impact forces in running are applied very rapidly, lifting forces are applied relatively slowly

6) Frequency – how often is the force applied? GRFs are applied at 1 Hz (once a second) in walking and at 2-4 Hz in running. Seat vibrations occur at 60 Hz in truck driving (Ohhh, their aching backs!)

Biomechanical Issues About ForcesBiomechanical Issues About Forces

Ahhh, the Law of Reaction is Important in the Shot PutAhhh, the Law of Reaction is Important in the Shot Put

As you applied a large force onto the shot put, it applies an equally large force back on you. No wonder it would destroy our shoulder if we tried to throw the put.

As we just learned, the inertial load is much lower in softball vs. shot put. Thus the reaction force in softball is low and not injurious.

Force Composition: Combination of two or more forces into resultant or total force:

e.g. calculate total muscle force from component muscles

e.g. calculate the joint compressive force from many muscles

Two Processes Used to Better Two Processes Used to Better Understand the Effects of ForcesUnderstand the Effects of Forces

Force Composition for Shoulder MusclesForce Composition for Shoulder Muscles

What is total rotating force from both muscles (F resultant which is perpendicular to the arm)?

Fmc = Clavicular portion of pectoralis major = 2,000 N at β = 40°

Fms = Sternal portion of pectoralis major = 2,500 N at θ = 20°

Fres.

= 2,000 N

= 2,500 N


Fmc = Clavicular portion of pectoralis major = 2,000 N at β = 40°

Perpendicular force (to arm):

Cos 40° = Perp. Force / 2,000 N

Perp. Force from Fm,c = 0.766 * 2,000 N = 1,532 N

Perp. Force

= 2,000 N

Total Perpendicular Resultant Force = 1,532 N + 1,879 N = 3, 411N

From 4,500 N of total muscle force(the sum of the two components)


Fms = Sternal portion of pectoralis major = 2,500 N at θ = 20°

Perpendicular force (to arm):

Cos 20° = Perp. Force / 2,000 NPerp. Force from Fm.s =

0.940 * 2,000 N = 1,879 NPerp. Forceθ

= 2,500 N

Composition of Muscle Forces to Joint LoadsComposition of Muscle Forces to Joint Loads

Resultant joint forces during walking and running from muscle forces and musculo-skeletal model

Exss 3850 9 summer linear kinetics

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Transcript of Exss 3850 9 summer linear kinetics