Chapter 11 Angular Kinematics of

Human Movement

Basic Biomechanics, 4th 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 00

•  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/s2, rad/s2, & rev/s2

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:

at = v2 - v1 / t

at = rα

Radial acceleration:

ar = v2 / r

at

ar

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