# Mapping of the Upper Limb Work-Space: Benchmarking Four Wrist Smoothness Metrics
## 3 Results
Finally, the NP was almost the same in all the sectors, with higher values in the up one. Smoothness differences between sectors were investigated with statistical tests for each metric and the results are reported in Figure 8.  
Figure 5: Color maps representing the level of smoothness with respect to articular angles. Results of the P2P movements (first row) and of the EXP movements (second row) are reported with respect to shoulder plane of elevation and shoulder elevation angle. The four metrics are represented in the columns. The blue areas represent the regions of the workspace in which the performed movement was smoother (lower NJ and NP, and higher SM and SAL); the yellow areas are the regions in which the movements were less smooth. In P2P movements, the NJ in the frontal and the horizontal sectors was significantly lower than the NJ in the up (\(p=0.003\), \(p=10^{-4}\)) and left sectors (\(p=0.04\), \(p=0.01\)). The SM was significantly higher in the frontal, right and horizontal sectors with respect to the up (\(p=10^{-4}\), \(p=10^{-4}\), \(p=10^{-11}\)) and left (\(p=10^{-6}\), \(p=10^{-6}\), \(p=10^{-14}\)) sectors. Moreover, the SM in the right sector was lower than in the horizontal sector (\(p=0.04\)). The SAL was significantly lower in the left (\(p=10^{-14}\)) and in the up (\(p=10^{-14}\)) sectors. Moreover, the SAL in the right sector was higher than in the right sector (\(p=0.02\)) and in the horizontal sector (\(p=10^{-4}\)). The NP, instead, was not significantly different between sectors. In EXP movements, the NJ in the left sector was significantly higher than for the right (\(p=10^{-4}\)) and horizontal (\(p=0.001\)) sectors, while the SM was lower in the left sector (\(p<10^{-3}\)) with respect to the other sectors. The SAL in the left sector was significantly lower than the other sectors (\(p<10^{-3}\)) and was lower in the up sector (\(p<10^{-3}\)) with respect to the frontal, right and horizontal sectors. Finally, the NP was higher in the up sector (\(p<0.02\)). Figure 6: 3D maps in cartesian coordinates—P2P movements. The 3D maps representing the level of smoothness are reported in cartesian coordinates referred to the shoulder. The five sectors are visualized in the 3D space with different shapes: frontal (square), up (triangle), left (bullet), right (circle) and horizontal (cross). The upper limb starting position is represented in black for a typical subject for visual reference. Each point is the average across repetitions and subjects and their colors indicate the magnitude of the metrics. The x axis points to the right of the subject, the y axis points frontally and the z axis is vertical. Correlation plots between each possible pairs of metrics are shown for each repetition and subject in Figure 9 for the P2P movements and in Figure 10 for the EXP movements. Figure 8: The statistical tests between sectors are reported for each metric (in the column). Both P2P (first row) and EXP (second row) are reported. Figure 7: 3D maps in cartesian coordinates—EXP movements. The 3D maps representing the level of smoothness are reported in cartesian coordinates referred to the shoulder. The five sectors are visualized in 3D space with different shapes: frontal (square), up (triangle), left (bullet), right (circle) and horizontal (cross). The upper limb starting position is represented in black for a typical subject for visual reference. Each point is the average across repetitions and subjects and their colors indicate the magnitude of the metrics. The x axis points to the right of the subject, the y axis points frontally and the z axis is vertical. In P2P movements, the NJ had a very high negative correlation with the SM with r coefficient \(=-0.86\) (\(p<0.001\)). The NJ had r correlation coefficient \(=-0.10\) (\(p=0.01\)) with the SAL and r \(=0.16\) (\(p=10^{-5}\)) with the NP. The correlation coefficient was \(0.23\) (\(p=10^{-10}\)) between SM and SAL, \(0.01\) (\(p=0.71\)) between SM and NP, and \(0.03\) (\(p=0.44\)) between SAL and NP.