L13 - Angular Kinematics

• Angular Motion in Human Movement:

  • Muscles contract creating joint torques/moments & cause segment rotation
  • Linear movement can only be achieved through multi joint coordination
• Angular Motion in Human Movement:

  • All linear movement comes from angular motion (at different joints allowing to do things linearly)
• Angular Displacement:

  • Angular displacement = Δ𝜃
  • Δ𝜃 = 𝜃 final - 𝜃 initial
  • Δ𝜃 = 𝜃 f - 𝜃 i
  • = 250 degrees
  • Can be tricky with multiple revolutions
• Angular Displacement:

  • Angle something turns through, not a rate angle of the change
  • eg if ran 400 m loop = 0 angular displacement, or a backflip also 0/360 degrees
  • Don’t talk about distance
• Angular Displacement:

  • Red = rotation direction
  • Positive rotation if right hand rule, with thumb
  • Could be negative too (clockwise)
  • Depended on info & reference frame
• Angular Displacement Examples:

  • Snowboard rotations
  • Rotates around mediolateral (x) axis, positive direction around the x (as sideways in snowboarding, facing left, right foot forward)
  • Back flips
  • Mediolateral direction, left foot forward, rotate around y axis (negative)
  • Side flips, forwards
  • Right hand system = with anatomical position moves with you (fixed to anatomical position)
  • Around z axis, direction tight foot forward, positive direction
  • Doing 360 spins
• Angular displacement example

  • Find Δ𝜃 from p1 to p2
  • 𝜃1 = tan-1(3.93 m/0.69 m)
  • 𝜃1 = 80.0°

  
  

  • 𝜃2 = tan-1 (2.00 m/3.46 m)
  • 𝜃2 = 30.0° + 90° = 120°
  • Take angels from same reference eg right horizontal

  
  

  • p1 = relative to horizontal
  • p2 = relative to vertical
  • Want the same

  
  

  • Δ𝜃 = 𝜃2 - 𝜃1
  • Δ𝜃 = 120° - 80°
  • Δ𝜃 = 40°
• Angular Velocity:

  • Rate of change of angular displacement
  • w = Δ𝜃/Δ t
  • Units are deg/s (or rad/s)
  • Degrees per seconds
• Angular Velocity:

  • Angular velocity = rate of change
  • eg 360 degree rotation in 1 s = 360?
• Derivative Graphs:

  • Red lines - change in direction
  • eg increasing to decreasing slope
  • ⍵ = 0
  • When slope changes from neg to pos
  • Angular velocity will be 0 at these points
  • Green lines - change in curvature
  • eg valley to hill curvature
  • Peaks in angular velocity
• Angular Acceleration (𝜶):

  • Rate of change of angular velocity
  • 𝜶 = Δ w / Δ t
  • Units are deg/s^2 (or rad/s^2)
• Case Study - Golf Technique Analysis:

  • Electromagnetic sensor system
  • 5 sensors: L4, T3, lateral humerus, back of hand, centre of forehead
  • Anatomical landmarks identified using wand
  • Real time tracking
• Data Reduction:

  • 3 events in the swing

  1. Address (TA)
  2. Top of Backswing (TB)
  3. Impact (BC)

  • Segment linear & angular positions extracted at each event & displacements bw/ events
  • Get 3D positions
• Address Position - Angular Position:

  • Absolute reference frame (+ve x right, +ve y anterior, +ve z up)
  • Segment angle
• Address Position - Angular Position:

  • Database compared each golfer to professional golfers
  • Coordinate system
  • At the address position global reference frame was the lab
  • Thorax aligned with coordinate system
  • Around z axis, negative towards target = positive
  • Thorax may or may not be a problem
• Top of the Backswing Position - Angular Displacement:

  • Final displacement - from initial (angular position)
  • Head rotation doesn’t matter to much
• Address to Top of the Backswing - Linear Displacement:

  • Pos x to the back
• Movement Sequencing & Coordination:

  • Sequence of events
  • Sequence = hips, chest, lead arm, club