This protocol asks which club-wrench components can be identified separately for the lead and trail hands, under which measurements and assumptions. It freezes the measurement and analysis contract before a result is interpreted. The executable records are synthetic or manufactured benchtop fixtures; they are not physical-device or participant validation.
The protocol provides no muscle-force attribution and no coaching or clinical authority. A hand wrench is an interface load, not a unique tissue, muscle, neural, intentional, or causal source. Human inference remains unavailable until every governance and held-out-analysis gate is satisfied.
Primary-Source Register
| Koike (2016), Measurement of Individual Hand Forces Exerted on a Golf Club Grip (Koike 2016) |
Instrumented-grip measurement precedent |
Calibration or performance of the present manufactured fixture |
| Choi and Park (2020), Sensors 20(13):3672 (Choi and Park 2020) |
Use of measured internal grip force in upper-limb kinetics |
Validation of this device, cohort, or bilateral six-axis accuracy |
UpstreamDrift protected source 85cce4d3307bb7ad3953d9fc6e583e370803515c, bilateral-wrench structural study |
Point-force rank five and full-wrench rank six/nullity six |
Practical identifiability, anatomy, or human validation |
UpstreamDrift protected source 85cce4d3307bb7ad3953d9fc6e583e370803515c, trajectory sensor qualification |
Synthetic cross-talk, noise, contact-migration, and allocation-error controls |
Physical-device calibration or participant evidence |
The two UpstreamDrift entries are immutable executable project sources, not independent experiments. The literature entries establish relevant measurement precedent but are not treated as a governed participant-level data deposit for this protocol.
Preregistered Questions and Outcomes
The protocol revision is affinedrift.bilateral-hand-wrench/v1. It freezes the transition-to-impact window, event alignment, quantity definitions, tolerance, uncertainty method, perturbations, quality rules, exclusions, and falsifiers before evaluation.
| A total club wrench does not identify twelve bilateral wrench components |
Rank and nullity of the declared linear observation map |
Negative if a claimed unique allocation depends only on total wrench |
| Independent calibrated sensors recover the manufactured bilateral loads |
Complete component-error interval must remain inside tolerance |
Null if the interval supports no improvement; negative if it exceeds tolerance |
| The protocol transports to participant data |
Participant-held-out coverage and prediction error |
Unavailable until ethics, privacy, consent, licensing, and held-out gates exist |
Failed, excluded, negative, null, and unavailable trials stay in the disposition ledger. They are not removed when a preferred allocation or model fails.
Lead, Trail, and Club Frames
The lead and trail sensors each report a six-component wrench in a named, right-handed sensor frame. Both are transported to the declared club grip-center frame before addition. Sensor identifiers and lead/trail roles must be unique; the two transform source names must match the two sensor output-frame names exactly, and both transforms must declare one common target club frame. For sensor-to-club rotation \(R\) and the club-origin to sensor-origin vector \(r\) expressed in the club frame,
\[
F_C = R F_S,
\qquad
M_C = R M_S + r \times F_C.
\]
Lead/trail labeling, axis directions, reference points, force direction, and moment sign are data, not plotting choices. A frame transform must be proper and orthonormal. Comparing raw channels from different reference points is outside the contract.
Calibration, Cross-Talk, and Bandwidth
Each grip section requires an independently revisioned \(6\times6\) calibration matrix, traceability record, condition-number limit, sample rate, passband, and passband gain tolerance. The manufactured matrix includes declared cross-talk; solving that full-rank matrix recovers the applied fixture wrench to numerical precision. That exact recovery tests the software path, not a load cell.
The current dynamic fixture samples gain at 0, 50, 150, and 300 Hz. Its declared sample rate is 2,000 Hz, bandwidth is 300 Hz, and gain-error limit is 3%. The complete manufactured passband qualifies. Missing the bandwidth boundary, missing the 0 Hz endpoint, using a sample rate at or below twice the bandwidth, a singular calibration, or exceeding the gain tolerance fails closed. A physical device must repeat the test for every channel, direction, load combination, temperature envelope, and mounting revision used in analysis.
Synchronization and Inertial Compensation
The declared maximum absolute synchronization offset is 0.5 ms. A fixture at 0.2 ms qualifies; one at 1.2 ms does not. Future acquisition must synchronize bilateral wrenches with club motion, shaft response, and any auxiliary channels before event windows are selected.
The measured instrument/club wrench contains contact and inertial contributions. The protocol subtracts a revisioned inertial wrench computed from declared mass properties, kinematics, gravity, sensor mounting, filtering, and reference frame. If that record is missing, contact wrench is unavailable rather than silently equated with the raw signal.
Contact assumptions are explicit: each sensor is treated as reporting the complete wrench transmitted through its grip section, while pressure distribution, contact-center migration, grip compliance, and slip remain sensitivity inputs. Saturation, clipping, timestamp discontinuity, calibration expiry, and undeclared contact loss are predeclared quality failures.
Rank and Observability
Stacking lead and trail six-axis wrenches into \(w=[w_L^T,w_T^T]^T\), a single total club-wrench observation is
\[
w_C = \begin{bmatrix}I_6 & I_6\end{bmatrix} w.
\]
This \(6\times12\) map has rank six and nullity six. Infinitely many bilateral allocations therefore reproduce the same total wrench. A regularizer may choose one, but that choice is Model Estimated, not observed.
Two independent six-axis grip sensors have an identity observation map with rank twelve and nullity zero inside the declared calibration and frame model. This is structural observability, not guaranteed practical accuracy. Calibration, cross-talk, bandwidth, synchronization, inertial compensation, contact migration, shaft dynamics, and uncertainty can still make an observed component practically weak.
For the more restrictive two-point-force map, distinct contacts yield rank five and one invisible equal-and-opposite axial force mode. This reproduces the protected UpstreamDrift analytic result; it does not assert that the mode occurs in a golfer.
Measurement and Inference Tiers
| Total Measured |
Calibrated and inertially compensated total club wrench |
Bilateral allocation remains nonidentifiable |
| Bilateral Measured |
Separately calibrated lead and trail grip-section wrenches |
Practical error and contact-model uncertainty remain |
| Model Estimated |
One allocation selected by declared constraints, priors, or cost |
The selection is not a measurement or unique source |
| Unavailable |
A quantity absent from the observation map or governance record |
No value may be imputed or promoted |
Inverse dynamics can estimate net generalized loads under a declared model. It does not convert total club motion into measured bilateral loads, and neither bilateral loads nor generalized loads uniquely identify biological actuators.
Manufactured Benchtop Fixtures and Uncertainty
The deterministic fixtures exercise exact arithmetic and adverse dispositions:
| Total club-wrench closure error |
Total Measured |
0.004 |
0.002–0.008 normalized error |
Supported |
| Bilateral allocation recovery error under adverse perturbation |
Bilateral Measured |
0.025 |
0.015–0.041 normalized error |
Negative |
| Regularized allocation advantage |
Model Estimated |
0.000 |
-0.080–0.080 normalized difference |
Null |
| Individual biological actuator force |
Unavailable |
— |
— |
Unavailable |
These values are prescribed regression fixtures. They are not measured sensor performance. Future benchtop acceptance must propagate calibration residuals, cross-talk, noise, timing, inertial parameters, reference-point placement, and repeatability. Sensitivity repeats the analysis over predeclared shaft mass, inertia, compliance, grip compliance, and contact-center bounds. Conclusions must follow the complete interval, not only its center.
Negative, Null, and Unavailable Results
- Supported means the complete declared interval meets a manufactured or governed task tolerance.
- Negative means a required tolerance or hypothesis fails.
- Null means the predeclared comparison shows no supported difference.
- Unavailable means the observation, calibration, governance, or source record is absent.
A negative or null allocation result does not become evidence for a different hand strategy. An unavailable actuator force does not become an estimated value by substituting a minimum-norm solution.