Bilateral Hand-Wrench Identifiability and Instrumented-Grip Validation

A preregisterable, source-bounded protocol for deciding which lead- and trail-hand loads can be measured or estimated

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.

WarningScientific Authority Boundary

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

Source	What It Supports Here	What It Does Not Authorize
Koike (2016), Force and Moment Exerted by Each Hand on an Instrumented Golf Club (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.

Hypothesis	Metric and Decision Rule	Adverse Disposition
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

Tier	Permitted Label	Remaining Boundary
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:

Quantity	Tier	Result	Complete Interval	Outcome
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.

Human Tier and Promotion Gate

The current human tier is unavailable. Before collection or analysis, a future record must provide all of the following:

1. ethics approval appropriate to the protocol and jurisdiction;
2. a privacy and retention plan;
3. a revisioned informed-consent record;
4. explicit data and instrument-software licensing;
5. participant-level rather than swing-level train/test separation; and
6. a frozen participant-held-out analysis with registered exclusions, uncertainty, and falsifiers.

Promotion additionally requires traceable physical calibration, cross-talk and bandwidth qualification, independent review, uncertainty coverage, shaft/grip sensitivity, and preservation of adverse results. Even a promoted human bilateral-wrench result would remain an interface-load result with no muscle-force attribution and no coaching or clinical authority.

The executable declarations live in src/affine_control/hand_wrench_protocol.py, evidence boundaries in src/affine_control/hand_wrench_evidence.py, and exact fixtures in src/affine_control/hand_wrench_fixtures.py.

Related Articles

• Active Impedance and Co-Contraction Identification
• Equipment and Shaft Individual-Response Validation
• Force Measurement Technology
• Research Protocol and Data-Readiness Library

Cite this page

References

Choi, Hyeob, and Sukyung Park. 2020. “Three Dimensional Upper Limb Joint Kinetics of a Golf Swing with Measured Internal Grip Force.” Sensors 20 (13): 3672. https://doi.org/10.3390/s20133672.

Koike, Sekiya. 2016. “Force and Moment Exerted by Each Hand on an Instrumented Golf Club.” 34th International Conference on Biomechanics in Sports. https://ojs.ub.uni-konstanz.de/cpa/article/view/6828.