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

(use Sway with Foot Rise instead)

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.

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 \(\times (\dfrac{t}{duration})\)

• 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:
  \(|x_{proj}| > 1.5\,\, or\,\,|z_{proj}| > 2.5\)