1. Angular Kinematics of Human Movement
Chapter 11
Angular Kinematics of Human Movement
Basic Biomechanics, 7th edition
By Susan J. Hall, Ph.D.
© 2014 The McGraw-Hill Companies, Inc. All rights reserved.
McGraw-Hill/Irwin

2. Basic Biomechanics, 7th edition
Measuring Angles
A goniometer is used to measure the angle between body segments.
Basic Biomechanics, 7th edition
By Susan J. Hall, Ph.D.

3. Basic Biomechanics, 7th edition
Measuring Angles
Joint angles are measured as segment movement away from anatomical position. The straight, fully extended position at a joint is regarded as zero degrees
Basic Biomechanics, 7th edition
By Susan J. Hall, Ph.D.

4. Basic Biomechanics, 7th edition
Measuring Angles
What is a body segment angle of orientation?
Angular orientation of a body segment with respect to a fixed line of reference (usually horizontal or vertical).
Basic Biomechanics, 7th edition
By Susan J. Hall, Ph.D.

5. Basic Biomechanics, 7th edition
Measuring Angles
The angle of orientation of the trunk with respect to vertical is often a quantity of interest in studies of lifting as related to low back pain.
Basic Biomechanics, 7th edition
By Susan J. Hall, Ph.D.

6. Basic Biomechanics, 7th edition
Measuring Angles
The angle of orientation of the trunk with respect to horizontal and the angle of flexion at the knee.
Basic Biomechanics, 7th edition
By Susan J. Hall, Ph.D.

7. Angular Kinematic Quantities What is the instant center of rotation?
The path of the instant center of rotation at the knee during knee extension.
Basic Biomechanics, 7th edition
By Susan J. Hall, Ph.D.

8. Angular Kinematic Quantities
What is angular displacement?
Change in angular position
The directed angular distance from initial to final angular position
The vector equivalent of angular distance
Measured in units of degrees, radians, or rotations
Basic Biomechanics, 7th edition
By Susan J. Hall, Ph.D.

9. Angular Kinematic Quantities What is angular displacement?
When the forearm returns to original position at the completion of a curl exercise, the angular displacement at the elbow is zero.
Basic Biomechanics, 7th edition
By Susan J. Hall, Ph.D.

10. Angular Kinematic Quantities What is angular displacement?
A. The path of motion of a swinging pendulum. B. Angular distance is the sum of all angular changes. Angular displacement is the difference between the initial and final positions.
Basic Biomechanics, 7th edition
By Susan J. Hall, Ph.D.

11. Angular Kinematic Quantities
360º
180º
90º
Angles measured in degrees.
Basic Biomechanics, 7th edition
By Susan J. Hall, Ph.D.

12. Angular Kinematic Quantities
What is a radian?
radius
1 radian
The size of the angle subtended at the center of a circle by an arc equal in length to the radius of the circle.
Basic Biomechanics, 7th edition
By Susan J. Hall, Ph.D.

13. Angular Kinematic Quantities
Units of angular measure
90 degrees
radians
revolution 2 14
180 degrees  12
270 degrees
3 2 34
370 degrees
1revolution 2
Basic Biomechanics, 7th edition
By Susan J. Hall, Ph.D.

14. Angular Kinematic Quantities
How is the direction of angular motion identified?
The direction of rotational motion is identified as positive (counterclockwise) or negative (clockwise).
Basic Biomechanics, 7th edition
By Susan J. Hall, Ph.D.

15. Angular Kinematic Quantities
What is angular velocity?
The rate of change in angular position
angular displacement Angular velocity = time 
 = t
degrees radians
Measured in units of s or s
Basic Biomechanics, 7th edition
By Susan J. Hall, Ph.D.

16. Relationships Between Linear and Angular Motion
What is the relationship between linear and angular displacement?
The greater the radius between a given point on a rotating body and the axis of rotation, the greater the linear distance traveled by that point during an angular motion.
Basic Biomechanics, 7th edition
By Susan J. Hall, Ph.D.

17.  Relationships Between Linear and Angular Motion r1 r2 s2 s1 
The larger the radius of rotation (r), the greater the linear distance (s) traveled by a point on a rotating body.
s = r
Basic Biomechanics, 7th edition
By Susan J. Hall, Ph.D.

18. Relationships Between Linear and Angular Motion
A simple experiment in which a rotating stick simultaneously strikes three balls demonstrates the significance of the radius of rotation.
Basic Biomechanics, 7th edition
By Susan J. Hall, Ph.D.

19. Relationships Between Linear and Angular Motion
What is the relationship between linear and angular velocity?
Since velocity is displacement over time, linear and angular velocity are related by the same factor that relates displacement: the radius of rotation (r).
v = r
Basic Biomechanics, 7th edition
By Susan J. Hall, Ph.D.

20. Relationships Between Linear and Angular Motion
The greater the angular velocity of a baseball bat, the farther a struck ball will travel, other conditions being equal.
Basic Biomechanics, 7th edition
By Susan J. Hall, Ph.D.

21. Angular Kinematic Quantities
What is angular acceleration?
The rate of change in angular velocity
 ang.velocity
Angular acceleration = time
2 - 1
 = t
deg rad
Measured in units of s or s 2
Basic Biomechanics, 7th edition
By Susan J. Hall, Ph.D.

22. Relationships Between Linear and Angular Motion
What is the relationship between linear and angular acceleration?
The acceleration of a body in angular motion can be resolved into two perpendicular linear acceleration components.
Basic Biomechanics, 7th edition
By Susan J. Hall, Ph.D.

23. Relationships Between Linear and Angular Motion
What is tangential acceleration?
Component of acceleration of angular motion directed along a tangent to the path of motion
Represents change in linear speed
v2 - v1
at = t at
Basic Biomechanics, 7th edition
By Susan J. Hall, Ph.D.

24. Relationships Between Linear and Angular Motion
What is radial acceleration?
Component of acceleration of angular motion directed toward the center of curvature
Represents change in direction v2
ar = t ar
Basic Biomechanics, 7th edition
By Susan J. Hall, Ph.D.

25. Relationships Between Linear and Angular Motion
What is the relationship between units of measure of linear and angular motion?
Displacement
Velocity
Acceleration
Linear
meters
meters/second
Angular
radians
radians/second 2 2
Basic Biomechanics, 7th edition
By Susan J. Hall, Ph.D.