Chapter 6
Angular Kinematics
Describing Objects in Angular
Motion
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Angular Motion
• In angular motion, or rotational motion
around an axis, the axis of rotation is a
line, real or imaginary, oriented
perpendicular to the plane in which the
rotation occurs, like the axle for the
wheels of a cart.
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Angles
• An angle is formed by the intersection
of two lines, two planes, or a line and a
plane.

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Measuring angles
Relative versus absolute angles:
• Relative angle - angle at a joint formed
between the longitudinal axes of
adjacent body segments.
• Relative angles should be measured on
the same side of a given joint.
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Measuring angles
• The straight, fully extended position at
a joint is regarded as 0 degrees.
• When joint ROM is quantified, it is the
relative joint angle that is measured.
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Measuring angles
• Absolute angle - angular orientation of
a body segment with respect to a fixed
line of reference.
• Absolute angles should be consistently
measured in the same direction from a
single reference - either horizontal or
vertical.
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Measuring angles
• The relative angle at the knee is
measured between adjacent body
segments and the absolute angle of the
trunk is measured with respect to the
right horizontal.
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Tools for measuring body
angles
• Goniometers are commonly used by
clinicians for direct measurement of
relative joint angles on a live human
subject.
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Tools for measuring body
angles
• Other instruments available for
quantifying angles relative to the
human body are the electrogoniometer
and the Leighton flexometer.
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Instant center of rotation
• The location of the exact center of
rotation at the joint changes slightly
when joint angle changes.
• The instant center is the precisely
located center of rotation at a joint at a
given instant in time.
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(a) Laser scan. (b) Body segments. (c) Joint centers.
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Angular distance and
displacement:
• Angular displacement is measured as
the sum of all angular changes
undergone by a rotating body.
• It is the change in angular position and
is defined by both magnitude and
direction (vector quantity).
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Angular kinematic
relationships
• The counterclockwise direction is
regarded as positive, and the clockwise
direction is regarded as negative.
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Angular kinematic
relationships
• Three units of measure are commonly
used to represent angular displacement
and angular distance.
• The degree, the radian (equal to 57.3
degrees), and the revolution.
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Angular kinematic
relationships
• Radians are often quantified in
multiples of pi.
• Pi is a mathematical constant equal to
approximately 3.14, which is the ratio of
the circumference to the diameter of a
circle.
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Angular speed and velocity
• Angular speed is a scalar quantity and
is defined as the angular distance
covered divided by the time interval
over which the motion occurred.
• Angular velocity is calculated as the
change in angular position or the
angular displacement that occurs
during a given period of time.
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Angular speed and velocity
• Units of angular speed and angular
velocity are degrees per second (deg/s),
radians per second (rad/s), revolutions
per second (rev/s), and revolutions per
minute (rpm).
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Angular acceleration
• The change in angular velocity
occurring over a given time.
• Units are degrees per second squared
(deg/s2), rad/s2, and rev/s2.
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Angular Kinematics
• Angular motion vectors:
• Right hand rule - procedure for
identifying the direction of an angular
motion vector.
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Average versus instantaneous
angular quantities
• Angular speed, velocity, and
acceleration may be calculated as
instantaneous or average values,
depending on the length of the time
interval selected.
 =  / t
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Relationships between linear and
angular displacement
• Radius of rotation - distance from the
axis of rotation to a point of interest on
a rotating body.
• The greater the distance a given point
on a rotating body is located from the
axis of rotation, the greater the linear
displacement undergone by that point.
– P 152 Fig 6.7
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Relationships between linear and
angular velocity
• The same type of relationship exists
between the angular velocity of a
rotating body and the linear velocity of
a point on that body at a given instant
in time.
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Relationships between linear and
angular velocity
• With all other factors held constant, the
greater the radius of rotation at which a
swinging implement hits a ball, the
greater the linear velocity imparted to
the ball.
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Relationships between linear and
angular acceleration
• The acceleration of a body in angular
motion may be resolved into two
perpendicular linear acceleration
components.
• These components are directed along
and perpendicular to the path of
angular motion at any point in time.
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Relationships between linear and
angular acceleration
• Tangential acceleration - component of
angular acceleration directed along a
tangent to the path of motion that
indicates change in linear speed.
• At the instant that a thrown ball is
released, its tangential and radial
accelerations become equal to 0 because
a thrower is no longer applying force.
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Relationships between linear and
angular acceleration
• The second component of angular
acceleration represents the rate change
in direction of a body in angular
motion.
• This component is called radial
acceleration, and is always directed
toward the center of curvature.
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Relationships between linear and
angular acceleration
• An increase in linear velocity or a
decrease in the radius of curvature
increases radial acceleration (choking
up on a bat).
• Thus, the smaller the radius of
curvature, the more difficult it is for a
cyclist to negotiate the curve at a high
velocity.
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Centripetal acceleration
• The linear acceleration directed toward
the axis of rotation.
• Centripetal force is the force that causes
centripetal acceleration.
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Anatomical
Movement
Terminology
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Analyzing Human Movement
• In order to analyze motion, we have to
be able to consistently describe it.
• We need to accurately describe which
body parts are moving and the
direction(s) in which they are moving.
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Analyzing Human Movement
•consistent descriptive terms
•accurately describe actions
•identify critical actions
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Standard reference
terminology:
Anatomical
reference
position.
Is this position
neutral?
“palms forward” requires
muscle activity
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Directional terms:
• Superior
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• Inferior
Directional terms:
• Superior
• Anterior
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• Inferior
• Posterior
Directional terms:
• Superior
• Anterior
• Medial
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• Inferior
• Posterior
• Lateral
Directional terms:
•
•
•
•
•
•
•
•
•
•
Superior
Anterior
Medial
Proximal
Superficial
Inferior
Posterior
Lateral
Distal
Deep
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Anatomical reference planes
Cardinal planes:
• Sagittal plane
• Frontal plane
• Transverse plane
• Oblique planes
http://www.sohp.soton.ac.uk/biosci/anatomy1.htm
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Anatomical Reference Axes
• Medio-lateral (ML) axis (frontal,
transverse)
• Anteroposterior (AP) axis (sagittal axis)
• Longitudinal axis (vertical)
• Axes are always perpendicular to their
respective plane of motion.
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Joint Movement Terminology
Sagittal plane movements:
• Flexion
• Extension
• Hyperextension
• Dorsiflexion
• Plantar flexion
Axis????
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Frontal plane movements
• Abduction
• Adduction
• Lateral flexion - sideways rotation of
the trunk.
• Elevation of the shoulder girdle.
• Depression of the shoulder girdle.
Axis????
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Frontal plane movements
• Radial deviation - rotation of the hand
at the wrist in the frontal plane toward
the thumb.
• Ulnar deviation - rotation of the hand at
the wrist in the frontal plane toward the
little finger.
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Frontal Plane Movements
• Eversion of the foot - outward rotation
of the sole of the foot.
• Inversion of the foot - inward rotation
of the sole of the foot.
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Transverse plane movements:
• Left rotation of the head, neck, and
trunk.
• Right rotation of the head, neck, and
trunk.
• Medial rotation of the arm or leg.
Axis????
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Transverse plane movements:
• Lateral rotation of the arm or leg.
• Supination and pronation of the
forearm.
• Horizontal abduction and adduction
– horizontal extension and flexion
Axis????
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Special movements:
• Circumduction - combination of
flexion/extension,
abduction/adduction
– finger circling in a raised position.
– hip
– knee
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Special Movements
• Supination of the foot - inversion,
adduction, and plantar flexion.
• Pronation of the foot - eversion,
abduction, and dorsiflexion.
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