Both reciprocal effects were smaller than the corresponding estimated expanded engineering uncertainties. The experiment used reference masses, rigid targets and an instrumented frame; it included no human participants and did not assess stature, clinical utility or legal-metrology conformity. The custom wheeled platform integrated four nominal 40-kg load-cell elements, a load-cell balancing and amplification stage, an ESP32 controller, an optical distance sensor, a USB hub, a tablet interface and a pass-through power bank.

The mass measurand was the total applied working-reference load transferred through the seated frame. The distance measurand was the separation between the sensor reference plane and a rigid target along the optical axis, used here as a bench surrogate for a possible knee-height sensing path rather than as a direct measurement of human stature. Because the mass and distance subsystems shared the frame, sensing arm, wiring environment, embedded controller and power architecture, the study tested loading and geometry effects in both directions rather than treating the sensors as isolated components.

Reference masses of 0, 20, 40, 60, 80 and 100 kg were applied, while rigid-target separations ranged from 300 to 600 mm. Across the 15 nonzero observations from three ascending linearity runs, the mass pathway had a mean signed error of 0.065 kg, a mean absolute error of 0.071 kg and a root-mean-square error of 0.081 kg. The maximum absolute error was 0.150 kg.

Linear regression returned an intercept of 0.010 kg, a slope of 1.00092 and an R-squared of 0.999998, indicating close agreement with the platform’s in-house working references over 20 to 100 kg. However, the archive did not preserve the reference instrument’s identity, external verification certificate or the derivation of its internal allowance, so these results characterize agreement with the working-reference system rather than traceable calibration accuracy. Path-dependent and geometry-dependent mass effects were larger than the pathway’s average bias.

Repeatability standard deviations were 0.032, 0.057 and 0.080 kg at reference loads of 20, 60 and 100 kg, respectively. The maximum paired hysteresis reached 0.240 kg during complete loading and unloading sequences, while the largest center-referenced shift under eccentric loading was 0.144 kg. A centered 60-kg load produced a maximum change of 0.190 kg during a 30-minute creep session.

The initial-zero indication remained small, reaching 0.010 kg. These observations show why a near-unity regression line alone was insufficient to characterize the system: loading history, load position and time under load introduced measurable effects. They are also consistent with the broader force-transducer literature cited by the study, in which creep, loading mode, calibration conditions and temperature can affect sensor performance.

Across 21 observations from three runs at seven target positions, the mean signed error and mean absolute error were both 0.952 mm, the root-mean-square error was 1.039 mm and the maximum absolute error was 1.8 mm. The fitted slope was 1.00119, the intercept was 0.417 mm and the R-squared was 0.999984. Repeatability standard deviations at target separations of 350, 450 and 550 mm were 0.408, 0.471 and 0.578 mm.

By comparison, changing the nominal angle setting produced a maximum contrast of 2.5 mm, mean readings for rigid matte white, gray and black targets differed by as much as 2.2 mm, and the recorded 30-minute temporal trend amounted to 1.3 mm. Those optical contrasts require careful interpretation. Pivot geometry and the complete test order were not retained, so the nominal angle result could not be isolated as a pure angular-sensor coefficient.

Material reflectance was not independently quantified, and the finish experiment was not fully documented as randomized or counterbalanced. The 2.2-mm difference therefore applies only to the three tested finishes and may include time or order effects; it is not a calibrated response across colors or surface properties. Ambient temperature, relative humidity, illuminance, supply voltage, warm-up duration, sampling frequency and filter settings were also not logged contemporaneously.

The 1.3-mm temporal change is consequently best described as system-plus-environment drift under the recorded bench conditions, not as drift attributable solely to the optical sensor. For the mass-to-distance experiment, the target was held at a 450-mm reference separation while the six mass levels were applied sequentially. Five readings at each level were averaged because they represented repeated observations of one mechanical state, avoiding the treatment of consecutive sensor readings as independent experiments.

The resulting run-level regression slopes were 0.0097, 0.0103 and 0.0094 mm per kilogram, giving a mean of 0.0098 mm per kilogram and a between-run standard deviation of 0.0005 mm per kilogram. Within-run R-squared values of 0.9995 to 0.9996 described the fit to six ordered design points rather than external reproducibility. The largest projected change over the full 0-to-100-kg range was 1.026 mm.

Adding a quadratic mass term did not materially improve the six-point fits. In the opposite direction, the sensing arm was placed in marked Home, Mid and Full states while a centered 60-kg load remained applied. Ten readings per state were averaged within each of three runs, and the primary result was the Full-minus-Home difference.

Those differences were 0.105, 0.105 and 0.120 kg, producing a mean of 0.110 kg, a sample standard deviation of 0.0087 kg and an observed range of 0.105 to 0.120 kg. The state analysis was restricted to three independent experimental blocks, and the archive contained no numerical arm angle or tip displacement. The result consequently applies to the physical configurations tested and cannot be converted into a universal geometric sensitivity coefficient.

A continuous arm-position metric would allow such a coefficient to be evaluated in a subsequent, independently replicated campaign with fully recorded mechanical conditions. The researchers supplemented the bench observations with a GUM-informed engineering uncertainty analysis. Type A repeatability terms came from repeated measurements, resolution terms used rectangular rounding models, and bounded zero, hysteresis, eccentricity, alignment, target-finish, creep and drift terms were represented by rectangular distributions.

The calculation used a root-sum-of-squares approximation with zero covariance. Under those assumptions, the combined standard uncertainty was 0.177 kg for the mass pathway and 1.269 mm for the distance pathway. These corresponded to expanded engineering values of 0.354 kg and 2.538 mm at a coverage factor of two.

The figures are illustrative engineering estimates, not certificate-derived uncertainties or exact 95-percent coverage intervals, because the internal reference allowances could not be reconstructed and covariance information was unavailable. Both observed reciprocal effects fell below their pathway’s expanded value, limiting claims about their significance for an individual reading. Taken together, the bench campaign supports continued engineering development of the integrated platform while defining what remains unresolved.

The mass system was close to the working references over its tested range, and the optical system tracked rigid targets with a maximum absolute linearity error of 1.8 mm, yet hysteresis, eccentric loading, creep, angle setting, target finish and temporal drift were all measurable. The shared frame also produced reciprocal trends relevant to future versions in which mounting stiffness, sensor alignment, zeroing or filtering might change. Exact component replication remains limited because load-cell and amplifier models, gain, sampling rate, firmware build, filter window, warm-up rules, optical field of view and display rounding were absent from the retained archive.

A confirmatory campaign would require traceable references, complete hardware and software documentation, logged environmental and power conditions, randomized or counterbalanced optical tests, more independently re-established runs and separate validation before any inference involving human anthropometry.

Subject of Research: Bench characterization and reciprocal cross-sensitivity of mass and optical-distance sensing in a shared seated measurement frame

Article Title: Engineering bench characterization and reciprocal cross-sensitivity of a sensor-integrated seated measurement platform

Article References: Widiyanto, W. W., Kuntoadi, G. B., & Ismawatie, E. (2026). Engineering bench characterization and reciprocal cross-sensitivity of a sensor-integrated seated measurement platform. Results in Engineering, 32, Article 113615. https://doi.org/10.1016/j.rineng.2026.113615

Image Credits: AI Generated

DOI: 10.1016/j.rineng.2026.113615

Keywords: sensor cross-sensitivity, seated measurement platform, load-cell testing, optical distance sensing, bench validation, measurement uncertainty, sensor integration, creep, hysteresis, Engineering, bench, characterization