Torques and Moments of Force:

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Chapter 5

• Torques and Moments of Force
• Maintaining Equilibrium or Changing Angular Motion

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To this juncture

• Analysis focused on linear motion (translation)
• kinematics position, change of position, rate of
  change of position, acceleration
• kinetics Newtons 3 laws of linear motion
• F ma
• Ft ? mv
• Fd ? KE ? GPE

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What about rotation?

• All points on a body or object move in circles
  (or parts of circles) about the same fixed
  central line or axis
• body spin around an axis (real or imaginary)
• Force gt linear motion
• ????? gt angular motion

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Line of actionrelative to axis of rotation

• Centric force
• line of action passes through the axis of
  rotation
• tends to cause translation

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Line of actionrelative to axis of rotation

• Centric force
• Eccentric force
• line of action does not pass through the axis of
  rotation

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Line of actionrelative to axis of rotation

• Centric force
• Eccentric force
• Force couple
• two eccentric forces

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Torquehttp//www.tri-c.cc.oh.us/metro/faculty/gra
m/web/torque.htm

• Definition
• the turning effect of a force
• the tendency of a force to cause rotation

What factors affect the tendency of the force to
cause rotation???
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Torque

• Definition
• the turning effect of a force
• the tendency of a force to cause rotation

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Moment Arm(lever arm)
Perpendicular distance from line of action of a
force to a specified axis of rotation
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Effect ofchangingthe line of action of force
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To describe a torque

• Specified axis of rotation
• Torque magnitude (F x r)
• units Newtons x meters (Nm)
• foot x pound (ft-lb)
• Direction (sense) of the torque
• clockwise (-)
• counterclockwise ()

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Examples of Torque
Click on the picture to go to a good website
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Examples of Torque
Show the moment arm and identify the sense for
each force on each figure
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Sculling offsetting torques to create translation
Are all three designs equal in
net torque created at the stern??
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ADLs must consider torque for safety and
convenience
Medicine caps must be removable by
the disadvantaged, but inoperable by kids.
Click on the picture to go to a website with
more information.
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Torque

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

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Torque

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

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Muscle Torque

• Muscle applies force by?

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Muscle Torque

• Muscle applies force by creating tension on bones
• Muscle crosses a joint or joints
• brachialis and biceps brachii
• soleus and gastrocnemius
• other examples????

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Muscle Torque

• Moment arm - shortest (perpendicular) distance
  between a force's line of action and an axis of
  rotation.
• The moment arm for a muscle with respect to a
  joint center is the perpendicular distance
  between the muscle's line of action and the joint
  center.

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Muscle Torque

• Muscle applies force by creating tension on bones
• Muscle crosses a joint or joints
• Muscle has a moment arm

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Borelli
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Muscle Torque

• As a joint moves through a range of motion, there
  are changes in the moment arms of the muscles
  crossing the joints.
• For any given muscle, the moment arm is largest
  when the angle of pull on the bone is closest to
  90 degrees.

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Elbow at 90o of flexion
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Elbow at 135o of flexion
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Elbow at 45o of flexion
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Muscle Torque

• Changes in a moment arm directly affect the joint
  torque that a muscle generates.
• For a muscle to generate a constant joint torque
  during an exercise, it must produce more force as
  its moment arm decreases.

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Couple

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

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Muscle Torque

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

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Torque

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

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Torque

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

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Torque

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

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Torque

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

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Torque

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

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Strength training and torqueBiceps Curl

• Muscle as torque generator
• moment arm changes through ROM
• muscles ability to create force changes through
  ROM (Read Chapter 12 in McGinnis)
• External forces as torque generators
• segment weight
• handheld weight (dumbbell)

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Strength training and torque
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Calculate Extensor Muscle Force
Forces P (hand held load) 90 N W (HAT weight)
80 N Moment Arms Lw 25 cm Lp 60 cm Lm 5
cm
Great Web Site
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Calculate Extensor Muscle Force
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
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Calculate Extensor Muscle Force
?T 0 -74 Nm F 5 cm -74 Nm F 0.05 m F
-74Nm 0.05 m F 1500 N
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Additional calculations
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Measuring torque to assess the effects of
Lifetime Fitness
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Torque Decline with Age
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Athletes vs Sedentary
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Power Decline
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Torque Baseball Pitching
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Forces and Torquesin Equilibrium

• Static Equilibrium
• sum of forces on the body 0
• ? F 0
• sum of torques on the body 0
• ? T 0

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Human Machines

• Torques and Moments of Force

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Human Machines

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

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Human Machines

• When analyzing human machines, it is important to
  recall Newtons 3 Laws of motion.
• Law of Inertia
• Law of Acceleration
• Law of Action-reaction

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Functions of a Machine

• Provide mechanical force advantage.
• Provide speed of motion advantage.
• Provide range of motion advantage.
• Change the direction of the resistive force.
• Balance two or more forces.

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Human Machines

• Levers.
• Bones and muscles.
• Wheel and axle.
• Vertebrae and ribs.
• Pulley.
• Femur (quads), patella, and tibia.

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Classes of Levers

• First Class

R
M
Sit-up Looking upward Rising on your toes
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Classes of Levers

• Second Class

R
M
Lowering a weight held in the hand eccentrically
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Classes of Levers

• Third Class

R
M
Lifting a weight held in the hand concentrically
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Torque

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

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Mechanical advantage, ROM, and Speed of Motion

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

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Torque

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

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Torque

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

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Torque

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

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Torque

• The angle of maximum mechanical advantage for any
  muscle is the angle at which the most rotary
  force can be produced.
• The maximum mechanical advantages for the
  brachialis, biceps, and brachioradialis occur
  between angles at the elbow of approximately 75
  and 90 degrees.

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Torque

• As joint angle and mechanical advantage change,
  muscle length also changes.
• Variable resistance training devices are designed
  to match the resistance offered to the
  torque-generating capability of the muscle group
  as it varies throughout a range of motion.

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Torque

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

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Equations of static equilibrium

• Equilibrium is a state characterized by balanced
  forces and torques.
• In keeping with Newton's first law, a body in
  equilibrium is either motionless or moving with
  constant velocity.

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Equilibrium

• Whenever a body is completely motionless, it is
  in static equilibrium.
• Three conditions must be met for a body to be in
  a state of static equilibrium
• 1) The sum of all vertical forces (or force
  components) acting on the body must be 0,

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Equilibrium

• 2) the sum of all horizontal forces (or force
  components) acting on the body must be 0, and
• 3) the sum of all torques must be 0.
• The application of any unopposed (net) force to a
  body results in acceleration of the body.

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Equations of dynamic equilibrium

• Bodies in motion are considered to be in a state
  of dynamic equilibrium, with all forces acting
  resulting in equal and oppositely directed
  inertial forces.
• A balance exists between applied forces and
  inertial forces for a body in motion.

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Center of gravity

• A unique point around which the body's mass and
  weight are equally distributed in all directions.
  
• The CG of a perfectly symmetrical object of
  homogeneous density and therefore homogeneous
  mass and weight distribution, is at the exact
  center of the object.

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Center of Gravity

• Theoretical point about which the force of
  gravity is considered to be evenly distributed.
• It can also be considered the bodys balance
  point.

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Center of gravity

• If the object is a homogeneous ring, the CG is
  located in the hollow center of the ring.
• However, when mass distribution within an object
  is not constant, the CG shifts in the direction
  of greater mass.

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Center of gravity

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

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Center of gravity

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

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Center of gravity

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

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Center of gravity

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

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Center of gravity

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

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Center of gravity

• The speed and angle of takeoff primarily
  determine the trajectory of the performer's CG
  during the jump.
• The only other influencing factor is air
  resistance, which exerts an extremely small
  effect on performance in the jumping events.

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Application
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Methods of locating the CG

• Every time the body changes configuration, its
  weight distribution and CG location are changed.
• The location of the CG of a multi-segmented
  object is more influenced by the positions of the
  heavier segments than by those of the lighter
  segments.

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Center of gravity

• Balance method - uses reaction board.

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Center of gravity

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

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Center of gravity

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

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Stability and Balance

• Stability - resistance to disturbance of
  equilibrium.
• Balance - ability to control equilibrium.

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Stability and Balance

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

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Stability and Balance

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

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Stability and Balance

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

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Stability and Balance

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

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Base of Support

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

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Base of Support

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

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Base of Support

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

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Base of Support

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

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Base of Support

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

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Base of Support

• The height of the CG relative to the base of
  support can also affect stability.
• The higher the positioning of the CG, the greater
  the potentially disruptive torque created if the
  body undergoes an angular displacement.

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Principles of Mechanical Stability

• When other factors are held constant, a bodys
  ability to maintain equilibrium is increased by
  the following
• Increasing body mass
• Increasing friction between the body and the
  surface or surfaces contacted

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Principles of Mechanical Stability

• Increasing the size of the base of support in the
  direction of the line of action of an external
  force.
• Horizontally positioning the CG near the edge of
  the base of support on the oncoming external
  force.

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Principles of Mechanical Stability

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