⚙️ Sway, No Foot Rise (please don't do this)

This model visualizes the biomechanical moment when a dancer standing on the Right Foot (RF) begins a clockwise (CW) leg swing of the Left Leg, using a simplified 2D simulation.

Free Foot Arc during sway with no foot rise

🧠 Summary

  • The model simulates a dancer standing on their RF with their Left Hip positioned 18" to the side.
  • The left leg extends from the hip linearly over 0.666 seconds, growing from 0" to 38" (full leg length).
  • The leg swings CW from -90° to 0°, centered at the RF.
  • The projected Center of Gravity (COG) of the leg segment is calculated and plotted, taking mass contribution into account.
  • The expulsion point is when the projected COG exits the Center of Support (COS) boundary.

📐 Parameters

  • Total body mass: 70 kg
  • Leg mass %: 16%
  • Hip width (fixed): 18"
  • Leg length: 38"
  • Duration of sweep: 0.666s
  • Sweep angle: -90° to 0° (CW)

📈 Key Results

  • COG exits COS at ≈ 45.6°
  • At this point:
    • The effective leg length is ≈ 56 inches
    • The projected COG is outside the safe zone, indicating loss of balance
    • The line from rotation center through projected COG intersects with the leg arc
    • Hypotenuse (distance from RF to projected COG) ≈ {calculated}
    • The plot includes:
    • Fixed arc (hip path)
    • Growing leg arc (tip)
    • Projected COG trajectory
    • COS violation marker (purple X)
    • Line from origin to expulsion point
    • Intersection point with leg arc and leg length at that moment

🔬 Equations

  • Leg extension:
    leg_extension = leg_length * (t / duration)

  • Mid-leg COG offset:
    mid_leg_offset = 0.5 * leg_extension

  • Hip position:
    hip_x = hip_width * cos(θ)
    hip_z = hip_width * sin(θ)

  • COG of leg:
    cog_x = hip_x + mid_leg_offset * cos(θ)
    cog_z = hip_z + mid_leg_offset * sin(θ)

  • Projected COG:
    proj_x = (leg_mass * cog_x) / total_mass
    proj_z = (leg_mass * cog_z) / total_mass

🟦 COS Boundaries

  • COS width: ±1.5"
  • COS depth: ±2.5"
  • COG is considered out of bounds if:
    abs(x_proj) > 1.5 or abs(z_proj) > 2.5

🌀 Orientation

The final plot is:

  • Flipped horizontally to match dance perspective
  • Rotated 90° CW so FLOD appears as upward Z-axis

🚩 Conclusion

This plot clearly demonstrates that the COG shifts outside of the support zone before any significant rotation has occurred. The body is already in the process of falling unless a counteracting force (frame, upper body torque, or foot adjustment) is applied.

This forms the basis of the "Poise Disruption Point" — a biomechanical moment when rotational intent exceeds stability margin. We will use this for future balance and sway charts.