Chapter 11 Angular Kinematics of Human Movement

Chapter 11
Angular Kinematics of
Human Movement
Basic Biomechanics, 4 th edition
Susan J. Hall
Presentation Created by
TK Koesterer, Ph.D., ATC
Humboldt State University

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

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

Measuring Angles
• Filmed images
• Videotapes and films of human
movement
• Computer software

11-1

Relative versus
Absolute Angles
Relative angle:
• Anatomical reference position
Absolute angle:
• Horizontal reference
• Vertical reference

11-2

11-3

Tools for Measuring
Body Angles
Goniometer:
• One arm fixed to protractor at 0 0
• Other arm free to rotate
• Center of goniometer over joint center
• Arms aligned over longitudinal axes
Electrogoniometer (elgon):
Inclinometers:

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

11-4

Angular Kinematic Relationships
Angular Distance & Displacement
• Assessed as difference of initial & final
positions
– Counterclockwise is positive
– Clockwise is negative
• Human’s also indicate with joint-related
terminology
• Measured in
– Degrees, radians, or revolutions

Radian

Angular Kinematic Relationships
Angular Velocity
Angular velocity = angular displacement ω = θ
change in time
Δt
Units: deg/s, rad/s, rev/s, & rpm

Angular Kinematic Relationships
Angular Acceleration
Angular acceleration = change in angular velocity
change in time
α = Δ ω
Δt
Units: deg/s 2 , rad/s 2 , & rev/s 2

Angular Kinematic Relationships
Angular Motion Vectors
• Right hand rule
Average vs. Instantaneous Angular
Quantities
• Angular speed, Velocity, & Acceleration

Right Hand Rule

Relationship Between
Linear and Angular Motion
d = rӨ
Radius of rotation:
• Linear distance & radius of rotation same
units
• Angular distance in radians

Radius of Rotation

Linear and Angular Velocity
V = rω m/s = (m) (rad/s)
• 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
However, the magnitude of the angular velocity
figures as heavily as the length of the radius
of rotation in determining the linear velocity of
a point on a swinging implement

Linear and Angular Acceleration
Tangential acceleration:
a t = v 2 - v 1 / t
a t = rα
Radial acceleration:
a r = v 2 / r
a t
a r

Summary
• The angular kinematic quantities - angular
displacement, angular velocity, and angular
acceleration - possess the same
interrelationship as their linear counterparts
• Angular kinematics variables may be
quantified for the relative angle formed by the
longitudinal axes of two body segment
articulating at a joint, or for the absolute
angular orientation of a single body segment
with respect to a fixed reference line

The End