Angular Kinematics of Human Movement

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Presentation transcript:

Angular Kinematics of Human Movement Chapter 11 Angular Kinematics of Human Movement Basic Biomechanics, 6th edition By Susan J. Hall, Ph.D. © 2012 The McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill/Irwin

Basic Biomechanics, 6th edition Measuring Angles What is a relative angle? angle at a joint formed between the longitudinal axes of adjacent body segments AKA joint angle the straight, fully extended position at a joint is regarded as zero degrees Basic Biomechanics, 6th edition By Susan J. Hall, Ph.D.

Basic Biomechanics, 6th edition Measuring Angles The relative angle at the lead knee tends to be smaller during sprinting than during distance running. Basic Biomechanics, 6th edition By Susan J. Hall, Ph.D.

Basic Biomechanics, 6th edition Measuring Angles What is an absolute angle? angular orientation of a body segment with respect to a fixed line of reference (reference lines are usually vertical or horizontal) Basic Biomechanics, 6th edition By Susan J. Hall, Ph.D.

Basic Biomechanics, 6th edition Measuring Angles The absolute angle 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, 6th edition By Susan J. Hall, Ph.D.

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, 6th edition By Susan J. Hall, Ph.D.

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, 6th edition By Susan J. Hall, Ph.D.

Angular Kinematic Quantities Units of angular measure 90 degrees radians revolution 2 14 180 degrees  12 270 degrees 3 2 34 360 degrees 1revolution 2 Basic Biomechanics, 6th edition By Susan J. Hall, Ph.D.

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, 6th edition By Susan J. Hall, Ph.D.

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 Basic Biomechanics, 6th edition By Susan J. Hall, Ph.D.

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, 6th edition By Susan J. Hall, Ph.D.

 Relationships Between Linear and Angular Motion 1 1 2 2 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, 6th edition By Susan J. Hall, Ph.D.

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, 6th edition By Susan J. Hall, Ph.D.

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, 6th edition By Susan J. Hall, Ph.D.

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, 6th edition By Susan J. Hall, Ph.D.

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, 6th edition By Susan J. Hall, Ph.D.