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Angular Kinematics

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Angular Kinematics D. Gordon E. Robertson, PhD, FCSB School of Human Kinetics University of Ottawa * Biomechanics Lab, University of Ottawa * Angular Kinematics ... – PowerPoint PPT presentation

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Title: Angular Kinematics


1
Angular Kinematics
  • D. Gordon E. Robertson, PhD, FCSB
  • School of Human Kinetics
  • University of Ottawa

2
Angular KinematicsDifferences vs. Linear
Kinematics
  • Three acceptable SI units of measure
  • revolutions (abbreviated r)
  • degrees (deg or º, 360º 1 r)
  • radians (rad, 2p rad 1 r, 1 rad 57.3 deg)
  • Angles are discontinuous after one cycle
  • Common to use both absolute and relative frames
    of reference
  • In three dimensions angular displacements are not
    vectors because they do not add commutatively
  • (i.e., a b ? b a)

3
(No Transcript)
4
Absolute or Segment AnglesUses Newtonian or
inertial frame of reference
  • Used to define angles of segments
  • Frame of reference is stationary with respect to
    the ground, i.e., fixed, not moving
  • In two-dimensional analyses, zero is a right,
    horizontal axis from the proximal end
  • Positive direction follows right-hand rule
  • Magnitudes range from 0 to 360 or
  • 0 to /180 (preferably 0 to /180) deg

5
Angle of Foot
6
Angle of Leg
7
Relative or Joint AnglesUses Cardinal or
anatomical frame of reference
  • Used to define angles of joints, therefore easy
    to visualize and functional
  • Requires three or four markers or two absolute
    angles
  • Frame of reference is nonstationary, i.e., can be
    moving
  • Origin is arbitrary depends on system used,
    i.e., zero can mean neutral position (medical)
    or closed joint (biomechanical)

8
Angle of Ankle
9
Angle of Knee
10
Absolute vs. Relative
  • knee angle
  • thigh angle
  • leg angle 180
  • 60(120)180
  • 120

11
Joint Angles in 2D or 3D
  • q cos1(ab)/ab
  • a and b are vectors representing two segments
  • ab product of segment lengths
  • ab dot product

12
Angular KinematicsFinite Difference Calculus
  • Assuming the data have been smoothed, finite
    differences may be taken to determine velocity
    and acceleration. I.e.,
  • Angular velocity
  • omegai wi (qi1 qi-1) / (2 Dt)
  • where Dt time between adjacent samples
  • Angular acceleration
  • alphai ai (wi1 wi-1) / Dt (qi2 2qi
    qi-2) / 4(Dt)2
  • or ai (qi1 2qi qi-1) / (Dt)2

13
3D AnglesEuler Angles
  • Ordered set of rotations
  • a, b, g
  • Start with x, y, z axes
  • rotate about z (a) to N
  • rotate about N (b) to Z
  • rotate about Z (g) to X
  • Finishes as X, Y, Z axes

14
Visual3D AnglesSegment Angles
  • Segment angle is angle of a segment relative to
    the laboratory coordinate system
  • x, y, z vs. X, Y, Z
  • z-axis longitudinal axis
  • y-axis perpendicular to plane of joint markers
    (red)
  • x-axis orthogonal to
  • y-z plane

15
Visual3D AnglesJoint Cardan Angles
  • Joint angle is the angle of a segment relative to
    a second segment
  • x1, y1, z1 vs. x2, y2, z2
  • order is x, y, z
  • x-axis is flexion/extension
  • y-axis is varus/valgus, abduction/adduction
  • z-axis is internal/external rotation

16
Computerize the Process
  • Visual3D, MATLAB, Vicon, or SIMI etc.
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