2019 — Are planar simulation models affected by the assumption of coincident joint centres at the hip and shoulder?

Source: full accepted-manuscript text including both results tables, not abstract only.

This is the definitive version of the planarity question. Cite this one.

Research theme

Why do sports biomechanists use flat 2D models at all, when the movement is obviously 3D? Because of strength measurement. A torque-driven model needs to know how strong the athlete actually is at every joint angle and every joint speed, and that can only be measured in vivo on an isovelocity dynamometer — which measures one axis at a time. Nobody has established a way to measure a subject-specific 3D maximum torque profile at the hip or shoulder about all three axes. So subject-specific optimisation of maximal-effort movements is, in practice, stuck in 2D. Given that, the question becomes: how much accuracy does the 2D simplification actually cost, and can it be bought back cheaply?

Method: three variants of a 16-segment planar angle-driven forward-dynamics model of the front foot contact phase of fast bowling (Autolev), customised to one elite bowler, each independently optimised and then each evaluated on an independent fourth trial.

What they measured

Participant: one member of the England and Wales Cricket Board elite fast bowling group — age 18, mass 85.0 kg, height 1.94 m. 18 MX13 Vicon cameras at 300 Hz, 7 × 3 × 3 m volume, Kistler force platform, 50 retro-reflective markers plus a reflective patch on the ball. 12 maximal-effort stock deliveries; the 4 best (greatest ball velocity, minimal marker loss) were processed.

Score components (1° treated as equivalent to 1%):

• F1 — ground reaction force (mean of horizontal and vertical RMS differences, as % of peak vertical force)
• F2 — centre of mass velocity at ball release (%)
• F3 — trunk orientation angle (RMS difference, degrees)
• F4 — ball release velocity (%)
• F — overall objective function (%)

Model variants:

• PM — simple planar model (massless segment lengths set to zero)
• HM — non-coincident hip joint centres
• TM — non-coincident hip and shoulder joint centres + variable-length trunk+head segment (side flexion)

33 parameters (12 front-foot spring/damper, 6 wobbling-mass, 3 natural foot spring lengths, 12 trial-specific initial conditions) fitted by simulated annealing across three trials; evaluated on the fourth.

Findings

1. Full results (Table 1), four trials combined, mean ± SD:

   Component	PM (simple planar)	HM (hips free)	TM (hips + shoulders free)
   F1 force (%)	18 ± 2	12 ± 1	11 ± 1
   F2 COM velocity (%)	0.2 ± 0.2	0.2 ± 0.1	0.1 ± 0.1
   F3 trunk orientation (°)	0.9 ± 0.3	1.2 ± 0.6	0.9 ± 0.1
   F4 ball velocity (%)	3.8 ± 1.2	3.2 ± 2.6	1.5 ± 1.0
   F overall (%)	8.9 ± 0.8	6.4 ± 0.7	5.7 ± 0.3

2. Parameter-fitting vs held-out evaluation (the important robustness check): PM 9.1% fit / 8.2% evaluation; HM 6.6% / 5.7%; TM 5.8% / 5.3%. Every variant generalised to the unseen trial — the ranking is not an artefact of overfitting.

3. Ball release velocity error falls monotonically with model complexity: 3.8% → 3.2% → 1.7% (abstract quotes the parameter-determination means 3.8/3.2/1.7; the four-trial combined column gives 3.8/3.2/1.5).

4. Force: freeing the hips does the heavy lifting; freeing the shoulders helps horizontally only. Horizontal GRF: 11.4% (PM) → 10.5% (HM) → 8.6% (TM). Vertical GRF: 23.0% (PM) → 13.7% (HM) → 13.6% (TM). The authors state explicitly that the residual vertical force error is therefore not attributable to the shoulder assumption.

5. Mechanism, force: in PM the limbs attach to averaged torso positions, pulling them closer to the trunk, misplacing the mass centre and shortening the moment arm to the centre of pressure. To reproduce the same impulse and match COM velocity and trunk orientation, PM must produce a different GRF — so it cannot match the recorded one. Diagnostic evidence: PM’s fitted vertical toe stiffness came out at 94,589 N/m, roughly 3× the TM value of 33,566 N/m — the optimiser driving the centre of pressure toward the toe to lengthen the moment arm and compensate. That is a model contorting itself around a bad assumption.

6. Coefficients became more uniform across the three foot contact points as complexity increased — a sign of a better-conditioned model. No such pattern appeared in the wobbling-mass parameters.

7. The warning that matters most: COM velocity was matched to ~0.1–0.2% by all three variants, including the bad one. In other words, a model can look perfect on the kinematic outcome you happen to be checking while being 18% wrong on force. The authors extend this: previous published models using coincident joint centres “may have also been unable to accurately match the ground reaction forces… This may result in a model producing peak forces which the human body would be unable to dissipate safely.”

8. Conclusion: for maximal-effort movements with non-sagittal pelvis and torso rotation, use a planar model with non-coincident hip and shoulder joint centres — not a simple planar model, and not a full 3D model (which remains non-viable because subject-specific 3D strength parameters cannot be obtained).

Causal/methodological, established by controlled comparison. Not a claim about bowlers.

What this means for video and motion analysis

No direct coaching cue. For anyone trusting or building an analysis system:

• Quantified answer to “is side-on 2D enough?”: for angles and speeds, largely yes; for forces, no. Trunk orientation ~0.9°, COM velocity ~0.1–0.2%, ball speed 1.5–3.8% depending on how the hips and shoulders are handled — versus 11–18% on force in every case. Any product claim about load, impact or stress derived from planar kinematics is carrying at least a tenth of its magnitude as error, and up to a fifth if the geometry is naively flat.
• The single most transferable warning: matching one output well does not validate a model. All three variants nailed centre-of-mass velocity. Only the force component exposed the bad one. If you are validating a pose/biomechanics pipeline, validate against the quantity that is sensitive to your assumption, not the quantity that is easy.
• Watch for parameters going to implausible values. The 94,589 N/m toe stiffness is the tell that the fit is compensating for a structural error, not that the foot is stiff. In any fitting pipeline, a parameter pinned near a bound or 3× its physically expected value is a diagnostic signal, not a result.
• Cheap partial fix, ranked by payoff. If you can recover hip separation from the side-on view (or a second camera), you buy back most of the force error. If you can also recover shoulder separation and trunk side-flexion, you buy back most of the ball-speed error. Hips first.
• Vertical force error (~13.6%) is a floor, not a bug you can engineer away with better geometry. It comes from modelling joints as frictionless pins with no compression. This is a hard limit on any rigid-linkage system.
• Note what the input actually was. 18 cameras, 300 Hz, 50 markers, a force plate, and 95 anthropometric measurements. That is the accuracy budget these numbers were achieved with. A phone camera pipeline starts from a strictly worse position.

Caveats and limits

• n = 1. One 18-year-old elite male fast bowler, 4 trials. Every viscoelastic parameter in Table 2 is specific to him. Nothing here is a population value.
• Angle-driven, not torque-driven. The model was given the recorded joint angles. This validates representational adequacy; it does not demonstrate predictive power for a technique that was never performed.
• Front foot contact phase only (~110 ms to release).
• Simulation vs lab measurement, and the lab measurement has its own marker and force-plate error.
• The paper’s own compliance penalties were generous: front foot allowed 6 cm vertical / 9 cm horizontal displacement (against measured performance means of 3.5 cm and 5 cm), and wobbling-mass movement up to 4.5 cm shank / 7 cm thigh / 10 cm trunk. See the 2021 review, which argues these limits are probably too generous.
• Male-only, elite-only. No claim about junior, female or sub-elite bowlers.

Relationship to other Felton work

• Refines and supersedes Felton & King (2016) and Felton, Yeadon & King (2017 ISCSB). Same model, same bowler; this is the full, statistically complete version.
• TENSION with 2016: the 2016 conference paper concluded the massless-segment method “was suitable to reproduce predominately planar movements”, reporting only the best variant. This paper’s controlled comparison shows the unmodified planar assumption was substantially inadequate (8.9% overall, 18% force, 23% vertical force). The later work does not reverse the earlier conclusion, but it materially revises the impression it leaves: planarity was a real problem, not a benign simplification. Quote 2019’s numbers, not 2016’s framing.
• Enables Felton, Yeadon & King (2020) Optimising the front foot contact phase of the cricket fast bowling action (J Sports Sci 38, 2054–2062) — the optimisation study whose “optimal technique” claims all sit on top of this model.
• Reviewed and endorsed in McErlain-Naylor, King & Felton (2021) as reference [118], described as the way planar models “are likely to evolve” until 3D subject-specific strength measurement becomes possible.
• TENSION with 2021 review: this paper argues a full 3D model is “non-viable” for maximal-effort optimisation. The 2021 review, co-authored by Felton, frames the same fact as a temporary limitation and identifies 3D torque functions at the hip and shoulder as the key unlock. Same evidence, different rhetorical weight — 2019 presents planar-with-massless-segments as the solution; 2021 presents it as the stopgap.