Angular Kinematics

1
Chapter 6

• Angular Kinematics
• Describing Objects in Angular Motion

2
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.

3
Angles

• An angle is formed by the intersection of two
  lines, two planes, or a line and a plane.

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4
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.

5
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.

6
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.

7
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.

8
Tools for measuring body angles

• Goniometers are commonly used by clinicians for
  direct measurement of relative joint angles on a
  live human subject.
• Other instruments available for quantifying
  angles relative to the human body are the
  electrogoniometer and the Leighton flexometer.

9
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.

10
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).

11
Angular kinematic relationships

• The counterclockwise direction is regarded as
  positive, and the clockwise direction is regarded
  as negative.

12
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.

13
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.

14
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.

15
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).

16
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.

17
Angular Kinematics

• Angular motion vectors
• Right hand rule - procedure for identifying the
  direction of an angular motion vector.

18
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

19
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

20
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.

21
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.

22
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.

23
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.

24
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.

25
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.

26
Centripetal acceleration

• The linear acceleration directed toward the axis
  of rotation.
• Centripetal force is the force that causes
  centripetal acceleration.

27

• Anatomical
• Movement
• Terminology

28
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.

29
Analyzing Human Movement

• consistent descriptive terms
• accurately describe actions
• identify critical actions

30
Standard reference terminology

• Anatomical reference position.
• Is this position neutral?
• palms forward requires muscle activity

31
Directional terms

• Superior

• Inferior

32
Directional terms

• Superior
• Anterior

• Inferior
• Posterior

33
Directional terms

• Superior
• Anterior
• Medial

• Inferior
• Posterior
• Lateral

34
Directional terms

• Superior
• Anterior
• Medial
• Proximal
• Superficial
• Inferior
• Posterior
• Lateral
• Distal
• Deep

35
Anatomical reference planes

• Cardinal planes
• Sagittal plane
• Frontal plane
• Transverse plane
• Oblique planes

http//www.sohp.soton.ac.uk/biosci/anatomy1.htm
36
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.

37
Joint Movement Terminology

• Sagittal plane movements
• Flexion
• Extension
• Hyperextension
• Dorsiflexion
• Plantar flexion

Axis????
38
Frontal plane movements

• Abduction
• Adduction
• Lateral flexion - sideways rotation of the trunk.
• Elevation of the shoulder girdle.
• Depression of the shoulder girdle.

Axis????
39
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.

40
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.

41
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????
42
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????
43
Special movements

• Circumduction - combination of flexion/extension,
  abduction/adduction
• finger circling in a raised position.
• hip
• knee

44
Special Movements

• Supination of the foot - inversion, adduction,
  and plantar flexion.
• Pronation of the foot - eversion, abduction, and
  dorsiflexion.