Chapter 11 Angular Kinematics of Human Movement

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Chapter 11Angular Kinematics of Human Movement

• Basic Biomechanics, 4th edition
• Susan J. Hall
• Presentation Created by
• TK Koesterer, Ph.D., ATC
• Humboldt State University

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Objectives

• Distinguish angular motion from rectilinear and
  curvilinear motion
• Discuss the relationship among angular kinematic
  variables
• Correctly associate associate angular kinematic
  quantities with their units of measure
• Explain the relationship between angular and
  linear displacement, angular and linear velocity,
  and angular and linear acceleration
• Solve quantitative problems involving angular
  kinematic quantities and the relationship between
  and linear quantities

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Observing the Angular Kinematics

• Clinicians, coaches, and teachers of physical
  activities routinely analyze human movement
• Based on observation of timing and range of
  motion
• Developmental stages of motor skills are based on
  analysis of angular kinematics

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Angular KinematicsMeasuring Angles

• Biomechanics use projection of images of body
  with dots marking joint centers and dots
  connected with segmental lines representing
  longitudinal axes of body segments. These can be
  filmed and converted to computer generated
  representation of motion.

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Relative versus Absolute Angles

• Relative angle the angle formed between two
  adjacent body segments
• Anatomical reference position relative angles
  are zero
• Absolute angle angular orientation of a single
  body segment with respect to a fixed line of
  reference
• Horizontal reference
• Vertical reference

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Relative
Absolute
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Tools for Measuring Body Angles

• Goniometer
• One arm fixed to protractor at 00
• Other arm free to rotate
• Center of goniometer over joint center
• Arms aligned over longitudinal axes
• Electrogoniometer (elgon)
• Inclinometers

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Instant Center of Rotation

• Instant Center
• Roentgenograms (x rays)
• Instrumented spatial linkage with pin fixation
• Example
• Instant center of the knee shifts during angular
  movement

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Angular Kinematic RelationshipsAngular Distance
Displacement

• Angular distance (? phi)
• Angular Displacement (theta ? )- Assessed as
  difference of initial final positions
• Counterclockwise is positive
• Clockwise is negative
• Measured in
• Degrees, radians, or revolutions

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Units of rotary motion

• Circumference of circle is 2pr
• 360 degrees is one revolution
• Radian the angle which includes an arc of a
  circle equal to the radius of the same circle
• 1 revolution 360 degrees 2 p radians
• 1 Radian 57.3 degrees
• Convert from deg to rad multiply by p/180
• Convert from rad to deg multiply by 180/ p

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Angular Kinematic Relationships Angular Speed
Velocity

• Angular speed (? sigma) angular distance
  ? ?
• change in time
  ?t
• Angular velocity (? omega) angular displacement
  ? ?
• change in time
  ?t
• Units deg/s, rad/s, rev/s, rpm

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Angular Kinematic Relationships Angular
Acceleration

• Angular acceleration (? alpha) change in
  angular velocity
• change in time
• ? ? ?
• ?t
• Units deg/s2, rad/s2, rev/s2
• Can be positive (speeding up) or negative
  (slowing down.

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Angular Kinematic Relationships

• Angular Motion Vectors
• Right hand rule curl the fingers of the right
  hand in the direction of the angular motion. The
  vector used to represent the motion is in the
  direction of the extended thumb
• Average vs. Instantaneous Angular Quantities
• Angular speed, Velocity, Acceleration
• In general, the instantaneous value is of more
  interest

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Relationship Between Linear and Angular
Quantities

• Linear and Angular Displacement
• The greater the distance of a given point on a
  rotating body is located from the axis of
  rotation, the greater the linear displacement of
  that point (TM 64)
• dr ?
• Linear displacement equals the product of radius
  of rotation (distance of the point from the axis
  of rotation) and the angular displacement
  quantified in radians.

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Relationship Between Linear and Angular
Quantities

• Linear and Angular Velocity
• Linear velocity of a point on a rotating body is
  the product of the length of the body (radius of
  rotation) and the angular velocity of the
  rotating body
• vr? (recall ? is angular velocity)
• With other factors constant, greater radius of
  rotation (distance between axis and contact
  point) causes greater linear velocity. (TM 23)

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Relationship Between Linear and Angular
Quantities

• Linear and Angular Velocity
• When linear velocity at the end of the radius is
  constant, radius length determines angular
  velocity. Once an object is engaged in rotary
  motion, linear velocity at the end of the radius
  stays the same due to conservation of momentum
• Shortening the radius will increase the angular
  velocity and lengthening it will decrease the
  angular velocity

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Relationship Between Linear and Angular
Quantities
a and b have moved same linear distanceAngular
displacement is greater for A than B. If
displacement for a and b take place in the same
time, Linear velocity would be equal, but A would
have greater angular velocity.
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Relationship Between Linear and Angular
Quantities

• Linear and Angular Acceleration
• The acceleration of a body in angular motion may
  be resolved into two perpendicular linear
  acceleration components. (TM74)
• Tangential acceleration the component of
  angular acceleration directed along a tangent to
  the path of motion that indicates change in
  linear speed
• at v2-v1/t

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Relationship Between Linear and Angular
Quantities

• Linear and Angular Acceleration
• The relationship between tangential acceleration
  and angular acceleration is
• at ra (recall a is angular acceleration)
• Radial acceleration the component of angular
  acceleration directed toward the the center
• ar v2/r v is linear velocity
• An increase in the linear velocity of the moving
  body or a decrease in the radius of curvature
  increases radial acceleration

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Relationship Between Linear and Angular
Quantities

• Linear and Angular Acceleration
• The restraining force of the cable in the hammer
  throw and the throwers arm in the discus throw
  cause radial acceleration toward the center of
  the curvature throughout the motion.
• When the thrower releases the implement,
  radial acceleration no longer exists and the
  implement follows the path tangent to the curve
  at that instant.