chapter 5 torques and moments of force torques and moments of force maintaining equilibrium or...

Chapter 5Chapter 5Chapter 5Chapter 5

Torques and Moments of Torques and Moments of ForceForce

Maintaining Equilibrium or Maintaining Equilibrium or Changing Angular MotionChanging Angular Motion

To this junctureTo this junctureTo this junctureTo this juncture

• Analysis focused on linear motion Analysis focused on linear motion (translation)(translation)• kinematicskinematics: position, change of position, rate of : position, change of position, rate of

change of position, accelerationchange of position, acceleration• kineticskinetics: Newton’s 3 laws of linear motion: Newton’s 3 laws of linear motion

• F = maF = ma

• Ft = Ft = mv mv

• Fd = Fd = KE + KE + GPE GPE

What about Rotation?What about Rotation?What about Rotation?What about Rotation?

• All points on a body or object move in All points on a body or object move in circles (or parts of circles) about the same circles (or parts of circles) about the same fixedfixed central line or central line or axisaxis• body spins around an axis (real or imaginary)body spins around an axis (real or imaginary)

• Force ==> linear motionForce ==> linear motion

• ????? ==> angular motion????? ==> angular motion

Line of actionLine of actionrelative to axis of rotationrelative to axis of rotation


• Centric forceCentric force• line of action passes through the axis of rotationline of action passes through the axis of rotation• tends to cause tends to cause translationtranslation



• Centric forceCentric force

• Eccentric forceEccentric force• line of action line of action does notdoes not pass through the axis of pass through the axis of

rotationrotation



• Centric forceCentric force

• Eccentric forceEccentric force

• Force coupleForce couple• two eccentric forcestwo eccentric forces

TorqueTorqueTorqueTorque

• DefinitionDefinition• the turning effect of a forcethe turning effect of a force• the tendency of a force to cause rotationthe tendency of a force to cause rotation

What factors affectthe tendency

of the force to cause rotation???


• DefinitionDefinition• the turning effect of a forcethe turning effect of a force• the tendency of a force to cause rotationthe tendency of a force to cause rotation

Moment ArmMoment Arm(lever arm)(lever arm)

Moment ArmMoment Arm(lever arm)(lever arm)

Perpendiculardistancefrom line of action of a force to a specifiedaxis of rotation

Effect ofEffect ofchangingchangingthe line of the line of action of action of forceforce

Effect ofEffect ofchangingchangingthe line of the line of action of action of forceforce

To describe a torqueTo describe a torqueTo describe a torqueTo describe a torque

• Specified axis of rotationSpecified axis of rotation

• Torque magnitude (F x r)Torque magnitude (F x r)• units: Newtons x meters (Nm)units: Newtons x meters (Nm)• foot x pound (ft-lb)foot x pound (ft-lb)

• Direction (sense) of the torqueDirection (sense) of the torque• clockwise (-) clockwise (-) • counterclockwise (+)counterclockwise (+)

ExamplesExamples of of Torque Torque


Click on thepicture to goto a good website



Show themoment arm andidentify the sensefor each forceon each figure

Sculling: offsetting torques Sculling: offsetting torques to create translationto create translation

Sculling: offsetting torques Sculling: offsetting torques to create translationto create translation

Are allthreedesignsequal in nettorquecreatedat thestern??

ADLs must consider torque ADLs must consider torque for safety and conveniencefor safety and convenience

ADLs must consider torque ADLs must consider torque for safety and conveniencefor safety and convenience

Medicine caps mustbe removable by thedisadvantaged, butinoperable by kids.


• Rotary force that produces angular Rotary force that produces angular acceleration. acceleration.

• An increase in the magnitude of the applied An increase in the magnitude of the applied force, or in the perpendicular distance of the force, or in the perpendicular distance of the force's line of action to the axis of rotation, force's line of action to the axis of rotation, results in an increase in the acting torque. results in an increase in the acting torque.


• The greater the amount of torque acting at The greater the amount of torque acting at the axis of rotation, the greater the tendency the axis of rotation, the greater the tendency for rotation to occur and the greater the for rotation to occur and the greater the angular acceleration of a given body.angular acceleration of a given body.

Muscle TorqueMuscle TorqueMuscle TorqueMuscle Torque• Muscle applies force by?Muscle applies force by?

Muscle TorqueMuscle TorqueMuscle TorqueMuscle Torque• Muscle applies force by creating Muscle applies force by creating

tension on bonestension on bones

• Muscle crosses a joint or jointsMuscle crosses a joint or joints• brachialis and biceps brachiibrachialis and biceps brachii• soleus and gastrocnemiussoleus and gastrocnemius• other examples????other examples????

Muscle TorqueMuscle TorqueMuscle TorqueMuscle Torque

• Moment arm Moment arm - shortest (perpendicular) - shortest (perpendicular) distance between a force's line of action and distance between a force's line of action and an axis of rotation. an axis of rotation.

• The moment arm for a muscle with respect The moment arm for a muscle with respect to a joint center is the perpendicular to a joint center is the perpendicular distance between the muscle's line of action distance between the muscle's line of action and the joint center. and the joint center.

Muscle TorqueMuscle TorqueMuscle TorqueMuscle Torque• Muscle applies force by creating Muscle applies force by creating

tension on bonestension on bones

• Muscle crosses a joint or jointsMuscle crosses a joint or joints

• Muscle has a moment arm Muscle has a moment arm

BorelliBorelliBorelliBorelli


• As a joint moves through a range of motion, As a joint moves through a range of motion, there are changes in the moment arms of the there are changes in the moment arms of the muscles crossing the joints.muscles crossing the joints.

• For any given muscle, the moment arm is For any given muscle, the moment arm is largest when the angle of pull on the bone is largest when the angle of pull on the bone is closest to closest to 90 degrees90 degrees. .

Elbow at 90Elbow at 90oo of flexion of flexionElbow at 90Elbow at 90oo of flexion of flexion


• Changes in a moment arm directly affect Changes in a moment arm directly affect the joint torque that a muscle generates. the joint torque that a muscle generates.

• For a muscle to generate a constant joint For a muscle to generate a constant joint torque during an exercise, it must produce torque during an exercise, it must produce more force as its moment arm decreases.more force as its moment arm decreases.

CoupleCoupleCoupleCouple

• A pair of equal, oppositely directed forces A pair of equal, oppositely directed forces that act on opposite sides of an axis of that act on opposite sides of an axis of rotation to produce torque.rotation to produce torque.


• Concentric torque Concentric torque - when net torque and - when net torque and joint movement occur in the same direction.joint movement occur in the same direction.

• Eccentric torque Eccentric torque - torque in the direction - torque in the direction opposite joint motion.opposite joint motion.


• Movement speed Movement speed - when other factors - when other factors remain constant, increased movement speed remain constant, increased movement speed is associated with increased resultant joint is associated with increased resultant joint torque during exercise such as the squat. torque during exercise such as the squat.


• However, increased movement speed However, increased movement speed during weight training is generally during weight training is generally undesirable because increased speed undesirable because increased speed increases not only the muscle tension increases not only the muscle tension required, but also the likelihood of incorrect required, but also the likelihood of incorrect technique and subsequent injury. technique and subsequent injury.


• Acceleration of the load early in the Acceleration of the load early in the performance of a resistance exercise also performance of a resistance exercise also generates momentum, which means that the generates momentum, which means that the involved muscles need not work as hard involved muscles need not work as hard throughout the range of motion as would throughout the range of motion as would otherwise be the case. otherwise be the case.


• For these reasons it is both safer and more For these reasons it is both safer and more effective to perform resistive exercises at effective to perform resistive exercises at slow controlled movement speeds.slow controlled movement speeds.


• During eccentric contractions, muscle and During eccentric contractions, muscle and bone function as a second class lever.bone function as a second class lever.

Strength training and torqueStrength training and torqueBiceps CurlBiceps Curl

Strength training and torqueStrength training and torqueBiceps CurlBiceps Curl

• Muscle as torque generatorMuscle as torque generator• moment arm changes through ROMmoment arm changes through ROM• muscle’s ability to create force changes through muscle’s ability to create force changes through

ROM ROM (Read Chapter 12 in McGinnis)(Read Chapter 12 in McGinnis)

• External forces as torque generatorsExternal forces as torque generators• segment weightsegment weight• handheld weight (dumbbell)handheld weight (dumbbell)

Strength training and torqueStrength training and torqueStrength training and torqueStrength training and torque

Calculate Extensor Muscle Calculate Extensor Muscle ForceForce


Forces: P (hand held load) = 90 NW (HAT weight) = 80 N

Moment ArmsLw = 25 cmLp = 60 cmLm = 5 cm



Clockwise torque:

-90 N * 60 cm = ?

-90 N * 0.60 m = -54 Nm

-80 N * 25 cm = ?

-80 N * .25 m = -20 Nm

(-54 Nm) + (-20Nm) = -74 Nm



T = 0

-74 Nm = F * 5 cm

-74 Nm = F * 0.05 m

F = -74Nm ÷ 0.05 m

F = 1500 N

Additional calculationsAdditional calculationsAdditional calculationsAdditional calculations

Measuring torque to assess the effects of Lifetime Fitness

Torque Decline with AgeTorque Decline with AgeTorque Decline with AgeTorque Decline with Age

Athletes vs SedentaryAthletes vs SedentaryAthletes vs SedentaryAthletes vs Sedentary

Power DeclinePower DeclinePower DeclinePower Decline

Torque &

BaseballPitching

Forces and TorquesForces and Torquesin Equilibriumin Equilibrium

Forces and TorquesForces and Torquesin Equilibriumin Equilibrium

• Static EquilibriumStatic Equilibrium• sum of forces on the body = 0sum of forces on the body = 0

F = 0F = 0

• sum of torques on the body = 0sum of torques on the body = 0 T = 0T = 0

Human MachinesHuman MachinesHuman MachinesHuman Machines

• Torques and Moments of ForceTorques and Moments of Force


• The human body has many structures that The human body has many structures that function in a machine-like fashionfunction in a machine-like fashion


• When analyzing human machines, it is When analyzing human machines, it is important to recall Newton’s 3 Laws of important to recall Newton’s 3 Laws of motion.motion.• Law of InertiaLaw of Inertia• Law of AccelerationLaw of Acceleration• Law of Action-reactionLaw of Action-reaction

Functions of a MachineFunctions of a MachineFunctions of a MachineFunctions of a Machine

• Provide mechanical force advantage.Provide mechanical force advantage.

• Provide speed of motion advantage.Provide speed of motion advantage.

• Provide range of motion advantage.Provide range of motion advantage.

• Change the direction of the resistive force.Change the direction of the resistive force.

• Balance two or more forces.Balance two or more forces.


• Levers.Levers.• Bones and muscles.Bones and muscles.

• Wheel and axle.Wheel and axle.• Vertebrae and ribs.Vertebrae and ribs.

• Pulley.Pulley.• Femur (quads), patella, and tibia.Femur (quads), patella, and tibia.

Classes of LeversClasses of LeversClasses of LeversClasses of Levers

First ClassFirst Class

RM

Sit-up

Looking upward

Rising up on your toes*

Classes of LeversClasses of LeversClasses of LeversClasses of LeversSecond ClassSecond Class

R

M

Lowering a weight held in the hand eccentrically

Classes of LeversClasses of LeversClasses of LeversClasses of LeversThird ClassThird Class

M R

Lifting a weight held in the hand concentrically

http://www.dynamicscience.com.au/tester/solutions/hydraulicus/humanbody.htm

**Please note that the "Class 2 lever in the body" detailed above is not correct. It has been pointed out that the fulcrum will be the ankle during any plantarflexion movement and not the contact with the ground, making it a third class lever (1st). At the present time we are unable to identify a class 2 lever in the body. This example of a level 2 lever is provided in a number of Physical Education books.

Class 1 Lever in the Body

Class 2 Lever in the Body**

Class 3 Lever in the Body


• Most muscle-bone systems of the human body are Most muscle-bone systems of the human body are also of the third class for concentric contractions, also of the third class for concentric contractions, with the muscle supplying the applied force and with the muscle supplying the applied force and attaching to the bone at a short distance from the attaching to the bone at a short distance from the joint center compared to the distance at which the joint center compared to the distance at which the resistance supplied by the weight of the body resistance supplied by the weight of the body segment or that of a more distal body segment segment or that of a more distal body segment

acts. acts.

Mechanical advantage, ROM, and Speed Mechanical advantage, ROM, and Speed of Motionof Motion

Mechanical advantage, ROM, and Speed Mechanical advantage, ROM, and Speed of Motionof Motion

• The moment arm of an applied force can The moment arm of an applied force can also be referred to at the force arm, and the also be referred to at the force arm, and the moment arm of a resistance can be referred moment arm of a resistance can be referred to as the resistance arm.to as the resistance arm.


• Skilled athletes in many sports intentionally Skilled athletes in many sports intentionally maximize the length of the effective maximize the length of the effective moment arm for force application to moment arm for force application to maximize the effect of the torque produced maximize the effect of the torque produced by muscles about a joint. by muscles about a joint.


• The longer the radius of rotation, the greater The longer the radius of rotation, the greater the linear velocity of the racket head or the linear velocity of the racket head or hand delivering the pitch, and the greater hand delivering the pitch, and the greater the resultant velocity of the struck or the resultant velocity of the struck or thrown ball.thrown ball.


• The force-generating capability of a muscle The force-generating capability of a muscle is affected by muscle length, cross-sectional is affected by muscle length, cross-sectional area, moment arm, angle of attachment, area, moment arm, angle of attachment, shortening velocity, and shortening velocity, and state of training. state of training.

TorqueTorqueTorqueTorque• The angle of maximum mechanical The angle of maximum mechanical

advantage for any muscle is the angle at advantage for any muscle is the angle at which the most rotary force can be produced. which the most rotary force can be produced.

• The maximum mechanical advantages for The maximum mechanical advantages for the brachialis, biceps, and brachioradialis the brachialis, biceps, and brachioradialis occur between angles at the elbow of occur between angles at the elbow of approximately 75 and 90 degrees.approximately 75 and 90 degrees.


• As joint angle and mechanical advantage As joint angle and mechanical advantage change, muscle length also changes.change, muscle length also changes.

• Variable resistance training devices are Variable resistance training devices are designed to match the resistance offered to designed to match the resistance offered to the torque-generating capability of the the torque-generating capability of the muscle group as it varies throughout muscle group as it varies throughout a a range of motion.range of motion.


• The term isokinetic implies constant The term isokinetic implies constant angular velocity at a joint when applied to angular velocity at a joint when applied to exercise machinery.exercise machinery.

Equations of static Equations of static equilibriumequilibrium

Equations of static Equations of static equilibriumequilibrium

• EquilibriumEquilibrium is a state characterized by is a state characterized by balanced forces and torques.balanced forces and torques.

•

• In keeping with Newton's first law, a body In keeping with Newton's first law, a body in equilibrium is either motionless or in equilibrium is either motionless or moving with constant velocity. moving with constant velocity.

EquilibriumEquilibriumEquilibriumEquilibrium

• Whenever a body is completely motionless, Whenever a body is completely motionless, it is in it is in static equilibriumstatic equilibrium..

• Three conditions must be met for a body to Three conditions must be met for a body to be in a state of static equilibrium: be in a state of static equilibrium: 1) The sum of all vertical forces (or force 1) The sum of all vertical forces (or force

components) acting on the body must be 0,components) acting on the body must be 0,

EquilibriumEquilibriumEquilibriumEquilibrium

2) the sum of all horizontal forces (or force 2) the sum of all horizontal forces (or force components) acting on the body must be 0, and components) acting on the body must be 0, and

3) the sum of all torques must be 0.3) the sum of all torques must be 0.

• The application of any unopposed (net) The application of any unopposed (net) force to a body results in acceleration of the force to a body results in acceleration of the body.body.

Equations of dynamic Equations of dynamic equilibriumequilibrium

Equations of dynamic Equations of dynamic equilibriumequilibrium

• Bodies in motion are considered to be in a Bodies in motion are considered to be in a state of state of dynamic equilibriumdynamic equilibrium, with all forces , with all forces acting resulting in equal and oppositely acting resulting in equal and oppositely directed inertial forces.directed inertial forces.

• A balance exists between applied forces and A balance exists between applied forces and inertial forces for a body in motion.inertial forces for a body in motion.

Center of gravityCenter of gravityCenter of gravityCenter of gravity

• A unique point around which the body's A unique point around which the body's mass and weight are equally distributed in mass and weight are equally distributed in all directions. all directions.

• The CG of a perfectly symmetrical object of The CG of a perfectly symmetrical object of homogeneous density and therefore homogeneous density and therefore homogeneous mass and weight distribution, homogeneous mass and weight distribution, is at the exact center of the object. is at the exact center of the object.

Center of GravityCenter of GravityCenter of GravityCenter of Gravity

• Theoretical point about which the force of Theoretical point about which the force of gravity is considered to be evenly gravity is considered to be evenly distributed.distributed.

• It can also be considered the body’s balance It can also be considered the body’s balance point.point.


• If the object is a homogeneous ring, the CG If the object is a homogeneous ring, the CG is located in the hollow center of the ring. is located in the hollow center of the ring.

• However, when mass distribution within an However, when mass distribution within an object is not constant, the CG shifts in the object is not constant, the CG shifts in the direction of greater mass. direction of greater mass.


• It is also It is also possible for an possible for an object's CG to object's CG to be located be located physically physically outside of the outside of the object.object.


• Location of the CG of the human body is Location of the CG of the human body is complicated by the fact that its constituents complicated by the fact that its constituents (such as bone, muscle, and fat) have (such as bone, muscle, and fat) have different densities and are unequally different densities and are unequally distributed throughout the body. distributed throughout the body.


• The location of a body's CG is of interest The location of a body's CG is of interest because, mechanically, a body behaves as because, mechanically, a body behaves as though all of its mass were concentrated at though all of its mass were concentrated at the CG. the CG.


• For example, when the human body acts as For example, when the human body acts as a projectile, the body's CG follows a a projectile, the body's CG follows a parabolic trajectory, regardless of any parabolic trajectory, regardless of any changes in the configurations of the body changes in the configurations of the body while in air.while in air.


• The strategy of lowering the CG prior to The strategy of lowering the CG prior to takeoff enables the athlete to lengthen the takeoff enables the athlete to lengthen the vertical path over which the body is vertical path over which the body is accelerated during takeoff, thus facilitating accelerated during takeoff, thus facilitating a high vertical velocity at takeoff. a high vertical velocity at takeoff.


• The speed and angle of takeoff primarily The speed and angle of takeoff primarily determine the trajectory of the performer's determine the trajectory of the performer's CG during the jump.CG during the jump.

• The only other influencing factor is air The only other influencing factor is air resistance, which exerts an extremely small resistance, which exerts an extremely small effect on performance in the jumping effect on performance in the jumping events.events.

ApplicationApplicationApplicationApplication

Methods of locating the Methods of locating the CGCG

Methods of locating the Methods of locating the CGCG

• Every time the body changes configuration, its Every time the body changes configuration, its weight distribution and CG location are changed. weight distribution and CG location are changed.

• The location of the CG of a multi-segmented The location of the CG of a multi-segmented object is more influenced by the positions of the object is more influenced by the positions of the heavier segments than by those of the lighter heavier segments than by those of the lighter

segments.segments.


• Balance method Balance method - uses reaction board.- uses reaction board.


• Segmental method Segmental method - procedure for - procedure for determining total body center of mass determining total body center of mass location based on the masses and center of location based on the masses and center of mass locations of the individual body mass locations of the individual body segments. segments.


• The segmental method is most commonly The segmental method is most commonly implemented through a computer program implemented through a computer program that reads x,y coordinates of joint centers that reads x,y coordinates of joint centers from a file created by a digitizer.from a file created by a digitizer.

Stability and BalanceStability and BalanceStability and BalanceStability and Balance

• StabilityStability - resistance to disturbance of - resistance to disturbance of equilibrium.equilibrium.

• BalanceBalance - ability to control - ability to control

equilibrium.equilibrium.


• Different mechanical factors affect a body's Different mechanical factors affect a body's stability. stability.

• According to Newton's second law of According to Newton's second law of motion, the more massive an object is, the motion, the more massive an object is, the greater the force required to produce a greater the force required to produce a given acceleration. given acceleration.


• Football lineman who Football lineman who are expected to are expected to maintain their maintain their positions despite the positions despite the forces exerted on forces exerted on them by opposing them by opposing lineman are therefore lineman are therefore more mechanically more mechanically stable if they are more stable if they are more massive. massive.


• In contrast, gymnasts In contrast, gymnasts are at a disadvantage are at a disadvantage with greater body with greater body mass because mass because execution of most execution of most gymnastic skills gymnastic skills involves disruption of involves disruption of stability.stability.


• The greater the amount of friction between The greater the amount of friction between an object and the surface, or surfaces it an object and the surface, or surfaces it contacts, the greater the force requirement contacts, the greater the force requirement for initiating or maintaining motion.for initiating or maintaining motion.

Base of SupportBase of SupportBase of SupportBase of Support

• Area bound by the outermost regions of Area bound by the outermost regions of contact between a body and support surface contact between a body and support surface or surfaces.or surfaces.


• When the line of action of a body’s weight When the line of action of a body’s weight moves outside the base of support, a torque moves outside the base of support, a torque is created that tends to cause angular motion is created that tends to cause angular motion of the body, thereby disrupting stability of the body, thereby disrupting stability with the CG falling toward the ground.with the CG falling toward the ground.


• The larger the base of support is, the less The larger the base of support is, the less the likelihood that this will occur.the likelihood that this will occur.


• The horizontal location of the CG relative to the The horizontal location of the CG relative to the base of support can also influence stability.base of support can also influence stability.

• The closer the horizontal location of the CG to the The closer the horizontal location of the CG to the boundary of the base of support, the smaller the boundary of the base of support, the smaller the force required to push it outside the base of force required to push it outside the base of support, thereby disrupting equilibrium.support, thereby disrupting equilibrium.


• Alternatively, if a horizontal force must be Alternatively, if a horizontal force must be sustained, stability is enhanced if the CG is sustained, stability is enhanced if the CG is positioned closer to the oncoming force, positioned closer to the oncoming force, since the CG can be displaced farther before since the CG can be displaced farther before being moved outside the base of support.being moved outside the base of support.


• The height of the CG relative to the base of The height of the CG relative to the base of support can also affect stability.support can also affect stability.

• The higher the positioning of the CG, the The higher the positioning of the CG, the greater the potentially disruptive torque greater the potentially disruptive torque created if the body undergoes an angular created if the body undergoes an angular displacement.displacement.

Principles of Mechanical Principles of Mechanical StabilityStability


When other factors are held constant, a body’s When other factors are held constant, a body’s ability to maintain equilibrium is increased ability to maintain equilibrium is increased by the following:by the following:

• Increasing body massIncreasing body mass

• Increasing friction between the body and the Increasing friction between the body and the surface or surfaces contactedsurface or surfaces contacted



• Increasing the size of the base of support in Increasing the size of the base of support in the direction of the line of action of an the direction of the line of action of an external force.external force.

• Horizontally positioning the CG near the Horizontally positioning the CG near the edge of the base of support on the edge of the base of support on the oncoming external force.oncoming external force.



• Vertically positioning the center of gravity Vertically positioning the center of gravity as low as possible.as low as possible.

chapter 5 torques and moments of force torques and moments of force maintaining equilibrium or...

Documents