# A Wireless Hand Grip Device for Motion and Force Analysis
## 3 Results and Validation
### Accuracy and Precision of the Force Measurements  
The analysis of the precision and accuracy of measurements was conducted with the dynamometers Takei(r) model 5101 TKK, (Figure 11a), Constant 14192-709E(r) (Figure 11b) and the Wireless Hand Grip device System of UIB (Figure 11c), the dynamometer Takei model 5101 TKK(r) has a load limit between 0 and 100 kgf (980.66 newton), digital display, minimum reading of 0.5 kgf (4.9 newton), and rectified adjustable and complacent handle. The dynamometer Constant 14192-709E(r) has a load limit of 0 to 90 kgf (882.59 newton), digital display, minimum reading of 0.2 kgf (1.96 newton), and rigid and adjustable anatomical handle. The Wireless Hand Grip device System of UIB has a load limit between 0 and 90.7 kgf (888.86 newton), and was computerized with a minimum reading of 0.2 kgf (1.96 newton) with modified rigid and adjustable handle. Figure 10: Histogram of measurements around its mean. On the left, the histogram of the measurements in the loudest direction. On the right side, the histogram of measurements in the normal direction. Each dynamometer was statically calibrated with the gradual application of factual loads (washers) in the center of their handles, as recommended by [32]. Other previous work to validate grip strength in normal population are presented in [37]. The weights pattern (average mass of 5.00 \(\pm\) 0.0153 kgf, 49.033 \(\pm\) 0.15 newton) were added one by one until they reached the final load of 60 kgf (588.39 newton), the highest force measurement limit assumed for a standard user among the three analyzed dynamometers. Figure 12 shows a scheme of the placement of the dynamometers in the cargo system, where calibration readings after the addition of each load and stabilization of the system were performed. For each load increase, the strength of the four values indicated on the dial or registration program of each dynamometer was registered. Figure 13 also shows the weights used to reach the maximum load. All weights possess the calibration certificate document that guarantees the traceability to national standards  
Figure 11: (**a**) Takei 5101 TKK, (**b**) Constant 14192-709E, (**c**) hand grip device UIB. Figure 12: Dynamometers cargo system. (**a**) Takei 5101 TKK, (**b**) Constant 14192-709E, (**c**) hand grip device UIB  
according to the International System Units (SI). Appendix A exhibits an example of the official certificate. Calibration curves were obtained based on the relationship between the application of loads and the reading of the three dynamometers. These curves were constructed using simple linear regression by the method of minimal squares and analyzed according to the following procedure: (1) scatterplots of dynamometer versus calibrator loads for each device; (2) estimation of the respective linear regression models and determination of residuals; (3) calculation of the \(\mathbf{r}^{2}\) value and verification of model's assumptions; and (4) application of a covariance analysis model (ANCOVA), since the data provides \(Y_{d}\) (load predicted value for a given dynamometer during the calibration process) and predictor x (the actual load value/washers). With this type of analysis, it was possible to model \(Y_{d}\) as a linear function of \(x\), where the coefficients of the regression line vary according to the device used. In this manner, the calibration was represented numerically by a table and graphically by a line described by the Equation (2):  
\[Y_{d}=ax+b \tag{2}\]  
where \(Y_{d}\) is the value predicted for a load for a given dynamometer, \(a\) is the angular coefficient of the equation of regression (calibration factor), \(b\) is the linear coefficient of the regression equation and \(x\) (predictor) is the factual load value (washers). Table 1 compares the measurements of the three dynamometers. The homogeneity of the variances has been analyzed using the Bartlett test, obtaining \(p\)-values of 0.9911, 0.7674 and 0.9718, respectively, for the three dynamometers.