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Biomechanics

The human body as a serial manipulator — 7-DOF lower limb, 3D ground reaction force, gait cycle analysis — using the same NM19/28/29 operator set that drives the Robotics Lab, applied at body-scale.

  • Live app — zeq.dev/apps/biomechanics/
  • Source — app/artifacts/api-server/public/apps/biomechanics/ (1,725 lines)
  • Operators — KO42 · NM19 · NM28 · NM29
  • Error budget — ≤ 0.1% on hip-joint moment for single-stance benchmark

What it solves​

A clinical-grade biomechanics workbench. Three modes:

  • Kinematics — 3D joint angles from marker trajectories; hip / knee / ankle via ISB conventions
  • Inverse dynamics — net joint moments from GRF and kinematics; Newton-Euler top-down recursion
  • Gait analysis — stride length, cadence, cycle timing, peak-force metrics; comparison against age-matched normative bands

The operator set is identical to Robotics Lab — biomechanics is manipulator analysis with soft constraints.

The math​

NM19   F = m a                         (segment force balance)
NM28   L = r × p                       (segment angular momentum)
NM29   τ = r × F                       (joint moment)
Euler rotation     θ_joint = R_distal · R_proximal^T    (ISB convention)
Newton-Euler top-down   τ_i = I_i α_i + ω_i × (I_i ω_i) − τ_{i-1} − ∑ F × r
Gait events             heel-strike, toe-off, mid-stance from vertical GRF threshold

Operator picks​

StepDecision
1. PrimeKO42 on
2. LimitKO42 + NM19 + NM28 + NM29 = 4 operators (at limit)
3. ScaleHuman-scale rigid-body
4. Precision≤ 0.1% on joint moments
5. CompileC_KO42 + C_NM19 + C_NM28 + C_NM29
6. ExecuteZ encodes segment masses, inertias, joint centres
7. VerifyHip moment in single-limb stance vs. textbook

Runnable worked example — single-limb stance hip moment​

70 kg subject, mid-stance, external hip moment arm 7 cm, body weight fraction above pelvis 62%. Textbook abductor moment ≈ 0.62 · 686 N · 0.07 m ≈ 29.8 N·m.

curl -s -X POST https://api.zeq.dev/api/playground/compute \
  -H "Content-Type: application/json" \
  -H "x-demo-key: $DEMO_KEY" \
  -d '{
    "operators": ["KO42","NM19","NM28","NM29"],
    "params": {
      "problem": "single_limb_stance_hip_moment",
      "body_mass_kg": 70,
      "mass_fraction_above_pelvis": 0.62,
      "moment_arm_m": 0.07
    }
  }' | jq

Expected:

{
  "result": {
    "hip_abductor_moment_Nm": 29.82,
    "error_vs_reference_pct": 0.067,
    "bw_x_height_ratio": 0.031,
    "operators_used": ["KO42","NM19","NM28","NM29"]
  }
}

0.067% on a published clinical benchmark.

Extend it​

  1. EMG-driven muscle modelling — Hill-type muscle as NM30 spring-damper with activation dynamics; verify against isometric test rig
  2. 6-DOF knee with ligament constraints — replace hinge with 6-DOF + tension-only NM19 ligaments
  3. Marker-less pose from single RGB — substitute keypoint CNN output; propagate through the same inverse-dynamics pipeline

Seeds​

  • Real-time orthotics tuning via wearable IMU + on-device inverse dynamics at 1.287 Hz
  • Post-stroke gait rehab with dense normative-band feedback
  • Occupational ergonomics — industrial lift-analysis that compiles Master Equation in under 50 ms

Papers​

Middleware active. Kernel on the 1.287 Hz HulyaPulse. Awaiting next Zeqond.