L31 - Interpreting Graphs

• Joint Rotation to Velocity pt 1:

  • Velocity is the 1st time derivative of displacement
  • It describes the rate of angular displacement in the joint
  • v = Δ s /Δ t or w = Δ 𝜃 / Δ t
  • Δt = something happen as a function of time (a waveform)
  • Position of joint at any point in time
  • If want to know what's going on at any point look at slope of curve (change in displacement), over that given time period
• Joint Rotation to Velocity pt 2:

  • Velocity is the 1st time derivative of displacement
  • It describes the rate of angular displacement in the joint
  • v = Δ s /Δ t or w = Δ 𝜃 / Δ t
  • Angular change/displacement = 𝜃2 - 𝜃1, over change in time t2 - t1
  • wk = 𝜃2 - 𝜃1 / t2 - t1
  • If we calculate put instantaneous velocity for each moment in time we get a waveform presented on the right
  • End up with velocity curve (w)
• Joint Rotation to Acceleration:

  • Acceleration is the 2nd time derivative of displacement (a waveform)
  • It describes the rate of change in angular velocity at a joint
  • a = vf - vi / tf - ti or a = wf - wi / tf - ti
  • a = w2 - w1 / t2 - t1
  • If we can calculate ur instantaneous acceleration for each moment in time we get a waveform presented on the right
  • Identify changes in movement during force development to identify slopes
  • Can look at curve (visualise) to see what is happening
  • Understanding how change in slopes relate to velocity & acceleration
• What the displacement waveform tells us about rate of change:

  • eg with a barbell
  • Thinking what does the waveform tell us about rate of change in displacement
  • Direction pos (flexion), neg (extension)
  • Direction of motion (y, z, x)
  • Change in motion (speeding up or slowing down; can occur in either direction)
  • Direction of acceleration
• What the displacement waveform tells us about rate of change:

  • Have flexion & extension pt 1
  • upward/pos direction (slope), can expect that speed is increasing in flexion direction (in pos axis), increasing in magnitude, prob some acceleration
  • Would expect some pos velocity is pos direction
  • The top of movement (max/peak flexon), are slowing down, stop moving in that direction, no change, about to change direction, still in pos direction but slowing down as reach peak of movement (0 point), still in flexion slowing down in moment time will be 0 at peak
  • Decreasing velocity
• What the displacement waveform tells us about rate of change:

  • Have flexion & extension pt 2
  • Moving into extension/down, moving in neg direction but steeper slope, so speeding up in neg direction (increase in velocity), direction is neg but magnitude is pos
  • Would expect to see reaching peak in neg velocity
  • No change, slowing down decreasing velocity back to 0 point (velocity), to end end of extension phase
  • Velocity is decreasing and back to 0
• What the displacement waveform tells us about rate of change:

  • Can do same thing with velocity to look at acceleration pt 1
  • Velocity is changing, pos slope (increase velocity), velocity increasing in pos direction
  • Expect to see positive acceleration
  • The peak of velocity, plateau in velocity, moving with constant velocity (not changing), still in pos direction (flexion)
  • Would expect that acceleration decreasing (no change in velocity, acceleration can’t change, so back to 0)
• What the displacement waveform tells us about rate of change:

  • Can do same thing with velocity to look at acceleration pt 2
  • Top of movement: 0 in velocity, velocity is decreasing (slowing down in flexion)
  • If velocity is decreasing so acceleration will go negative (deceleration)
  • Think of it as direction of push,
  • Increase in velocity in neg direction (speeding up in downward direction), if speeding up acceleration increasing
  • More acceleration in neg direction (still below 0 line because in extension direction)
• What the displacement waveform tells us about rate of change:

  • Can do same thing with velocity to look at acceleration pt 3
  • Plateau in velocity of neg movement, so no acceleration (0)
  • 0 velocity = 0 acceleration, back to 0 point
  • Have to slow down, decelerate as go down (but think of direction of push - give push in pos direction)
  • Decelerating but push in pos direction
• What the displacement waveform tells us about rate of change:

  • No change in angles, plateau in displacement/angle (midline), would expect velocity to be 0, bc/ plateau big downward slope in velocity so deceleration (in pos direction), & acceleration (in neg direction)
  • Represents when pos & neg come together
  • Top of linear portion of velocity (half way up slope), indicates peak of angular velocity
• Gait analysis example:

  • How many times changing direction (amount of 0 points in velocity & acceleration)
  • What's happening bw/ these points (directionally)
  • Greatest slope/displacement; greatest bump → magnitude of velocity