Chapter 11 - Illinois State University

advertisement
Chapter 6
Angular Kinematics
Describing Objects in Angular
Motion
Illinois State University
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.
Illinois State University
Angles
• An angle is formed by the intersection
of two lines, two planes, or a line and a
plane.

Illinois State University
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.
Illinois State University
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.
Illinois State University
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.
Illinois State University
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.
Illinois State University
Tools for measuring body
angles
• Goniometers are commonly used by
clinicians for direct measurement of
relative joint angles on a live human
subject.
Illinois State University
Tools for measuring body
angles
• Other instruments available for
quantifying angles relative to the
human body are the electrogoniometer
and the Leighton flexometer.
Illinois State University
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.
Illinois State University
(a) Laser scan. (b) Body segments. (c) Joint centers.
Illinois State University
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).
Illinois State University
Angular kinematic
relationships
• The counterclockwise direction is
regarded as positive, and the clockwise
direction is regarded as negative.
Illinois State University
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.
Illinois State University
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.
Illinois State University
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.
Illinois State University
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).
Illinois State University
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.
Illinois State University
Angular Kinematics
• Angular motion vectors:
• Right hand rule - procedure for
identifying the direction of an angular
motion vector.
Illinois State University
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
Illinois State University
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
Illinois State University
Illinois State University
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.
Illinois State University
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.
Illinois State University
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.
Illinois State University
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.
Illinois State University
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.
Illinois State University
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.
Illinois State University
Centripetal acceleration
• The linear acceleration directed toward
the axis of rotation.
• Centripetal force is the force that causes
centripetal acceleration.
Illinois State University
Anatomical
Movement
Terminology
Illinois State University
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.
Illinois State University
Analyzing Human Movement
•consistent descriptive terms
•accurately describe actions
•identify critical actions
Illinois State University
Standard reference
terminology:
Anatomical
reference
position.
Is this position
neutral?
“palms forward” requires
muscle activity
Illinois State University
Directional terms:
• Superior
Illinois State University
• Inferior
Directional terms:
• Superior
• Anterior
Illinois State University
• Inferior
• Posterior
Directional terms:
• Superior
• Anterior
• Medial
Illinois State University
• Inferior
• Posterior
• Lateral
Directional terms:
•
•
•
•
•
•
•
•
•
•
Superior
Anterior
Medial
Proximal
Superficial
Inferior
Posterior
Lateral
Distal
Deep
Illinois State University
Anatomical reference planes
Cardinal planes:
• Sagittal plane
• Frontal plane
• Transverse plane
• Oblique planes
http://www.sohp.soton.ac.uk/biosci/anatomy1.htm
Illinois State University
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.
Illinois State University
Joint Movement Terminology
Sagittal plane movements:
• Flexion
• Extension
• Hyperextension
• Dorsiflexion
• Plantar flexion
Axis????
Illinois State University
Frontal plane movements
• Abduction
• Adduction
• Lateral flexion - sideways rotation of
the trunk.
• Elevation of the shoulder girdle.
• Depression of the shoulder girdle.
Axis????
Illinois State University
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.
Illinois State University
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.
Illinois State University
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????
Illinois State University
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????
Illinois State University
Special movements:
• Circumduction - combination of
flexion/extension,
abduction/adduction
– finger circling in a raised position.
– hip
– knee
Illinois State University
Special Movements
• Supination of the foot - inversion,
adduction, and plantar flexion.
• Pronation of the foot - eversion,
abduction, and dorsiflexion.
Illinois State University
Download