The question

When can a simpler pelvis–chest model reproduce the outputs we need? A controlled computer study shows that close agreement in body rotation does not guarantee close agreement in forces at the floor.

Read final Article 2 manuscript — PDF, 27 pages

Download complete reproduction ZIP — REV2, 112.2 MB

What was compared

The same mechanical body performed a 1.5-second, standing-leg-driven task. Only its effective lower-back joint changed:

• Locked: pelvis and chest move together.

   

• Yaw only: they can rotate relative to one another around the vertical axis.

   

• Three coordinates: relative rotation, forward/backward bending and sideways bending are available.

   

These are simplified joint architectures, not three anatomical spine models.

The main result

The required model depends on what you want to predict. With strong effective stabilization of bending (1000 N·m/rad), yaw-only mobility met the stated 10% criterion for pelvis and chest rotation in 15/15 primary conditions each. Horizontal force at the floor passed in 0/15.

Matching body rotation therefore did not guarantee matching contact force.

Where the simpler model stops working

At 100 N·m/rad effective bending stabilization, all eight audited outputs failed the 10% criterion. The pelvis-rotation ratio was 30.37%; the chest-rotation ratio was 17.23%.

Adding rigid head and upper-limb mass and inertia preserved chest-rotation adequacy in 15/15 conditions, while pelvis rotation passed in 13/15. Several foot-contact and free-side outputs became less transferable.

What dancers can take from this

Pelvis–chest rotation and forces at the floor are different questions. This study helps choose and check a computer model. It does not establish a preferred dance technique or measure how real dancers move.

Scope and limitations

The primary model represents 62.790 kg and omits the head and arms. The supplementary model adds 12.615 kg of rigid head/upper-limb mass, giving 75.405 kg. It does not simulate active arm motion.

Reported joint-interface loads are net mechanical forces and moments. They do not identify individual muscle forces, tissue strain, injury risk or clinical outcomes. Human experiments remain necessary for biological validation.

Engineering method

Three effective lumbar architectures have identical segment masses, reference-pose centers of mass and inertia. The 62.790-kg primary task uses a free root, compliant load-bearing foot contact and no balance controller.

Nominal inputs are standing-ankle pitch 15 N·m and standing-hip yaw −1 N·m, with identical pulse timing over 1.5 seconds. The study includes mirrored-side checks, an analytical two-inertia benchmark, numerical refinement, 15 operating conditions, 20 lumbar-impedance sensitivity cases and a separate rigid upper-body-inertia sensitivity.

What the 10% criterion means

For each output:

η = 100 × max|yaw-only − three-coordinate| / max|locked − three-coordinate|

An output passes when η ≤ 10% over the declared analysis window. This is a locked-normalized model-reduction criterion, not 10% accuracy relative to human measurements. Numerical refinement supports the primary classification; stiffness and upper-body results remain supplementary sensitivities after their verification gates.

Completed verification and reproduction

The analytical benchmark matches the closed-form solution with maximum error 7.57 × 10⁻¹⁰ rad. Mirrored runs reproduce sign symmetry to numerical precision. Primary refinement error is orders of magnitude below architecture effects.

• Seven-check harness: 7/7 PASS.

   

• Fresh supplementary campaign: 45/45 PASS.

   

• One primary-runner smoke case: PASS.

   

• Deliberate negative control: correctly reported failure.

   

• Final manuscript consistency audit: 163/163 PASS.

   

The complete original primary campaign, including 18 refinement runs, was preserved; it was not freshly rerun in full during the publication update.

The final manuscript pass executed zero new simulations. RMS and driven-window results are post-hoc analyses of frozen trajectories. The authoritative reproduction dataset remains REV2.