# Mapping of the Upper Limb Work-Space: Benchmarking Four Wrist Smoothness Metrics
## 3 Results  
Smoothness Maps  
The radar plot showing the smoothness metrics (NJ, SM, SAL, and NP) averaged across repetitions and subjects in each direction for all the sectors is reported in Figure 3 for P2P movements. Figure 3: Radar plot for P2P movements. The smoothness metrics are represented in separate plots. In each radar plot, the five sectors—up (purple), left (orange), frontal (green), right (blue) and horizontal (in red)—are reported and each point is the average of the metric across repetitions and subjects. In the P2P movement, the NJ was between 10 and 12.5 in all the directions and sectors, except in the horizontal sector, in which the SW, W, NW, and N directions presented the highest values (12.6, 13.4, 14.1 and 13.6), while the S, SE, and E directions showed the lowest values (6.6, 7.3, and 8.5). The SM ranged between 0.55 and 0.63 in all the directions and sectors, except in the horizontal sector in which the SM was 0.72 in the E direction. The SAL, instead, varied between sectors and the highest value was \(-\)1.70 in the E direction of the horizontal sector and the lowest one was \(-\)2.12 in the SE and S directions of the left sector. Finally, the NP was on average about 1 for all the directions and sectors. The radar plot representing the smoothness metrics (NJ, SM, SAL, and NP) averaged across repetitions and subjects in each direction for all the sectors is reported in Figure 4 for the EXP movement. In the EXP movements, the NJ was between 8 and 13, while the SM ranged between 0.57 and 0.65 in all the directions and sectors. The SAL was between \(-\)1.20 and \(-\)1.77, except for the left sector in which the SAL was between \(-\)2.30 and \(-\)2.15. Finally, the NP was on average about 1 in all the sectors and directions, except for the up sector in which the NP was higher than 1 in some directions. The color maps in Figure 5 represent the metrics with respect to the articular angles of the shoulder, plane of elevation, and elevation angle. Figure 4: Radar plot for EXP movements. The smoothness metrics are represented in separate plots. In each radar plot, the five sectors—up (purple), left (orange), frontal (green), right (blue) and horizontal (in red)—are reported and each point is the average of the metric across repetitions and subjects. In P2P movements, the color maps of NJ, SM, and SAL indicated that smoother movements were performed where both the plane of elevation and the elevation angle were low. If the angles were above 90\({}^{\circ}\), the smoothness decreased. The NP indicated almost the same smoothness for all the angles. In EXP movements, the NJ and the SM found high smoothness when both angles were high and low smoothness when angles were very small. The SAL, instead, showed that the whole region in which the plane of elevation angle was high was a low smoothness area. The NP indicated almost the same smoothness for all the angles, except with plane of elevation between 60\({}^{\circ}\) and 90\({}^{\circ}\) and elevation angle between 90\({}^{\circ}\) and 120\({}^{\circ}\). The representation of the smoothness metrics in the 3D workspace of the upper limb is reported in P2P movements in Figure 6 and in EXP movements in Figure 7.  
In P2P movements, the lowest NJ in the horizontal sector was found in the directions close to the subjects, while the highest values were in the left and up sectors and in the north-west side of the horizontal sectors. The right and the frontal sectors presented similar values of NJ. The same smoothness distribution was found with the SM. The SAL was higher in the horizontal, the right and the frontal sectors, while it was lower in the left and up sectors. Finally, the NP was almost the same in all the sectors, with higher values in the horizontal one. In EXP movements, the NJ was higher in the left sectors with respect to the others and the highest NJ was in the NE direction of the frontal sector. The same smoothness distribution was found with the SM. The SAL was higher in the left sector; the other sectors presented similar values.