# Mapping of the Upper Limb Work-Space: Benchmarking Four Wrist Smoothness Metrics
## 4 Discussion
The NP could be more suitable for more complex movements and especially for evaluating patients' performances [30; 40]. It was shown that in post-stroke patients, the number of velocity peaks may increase despite the reduced articular range of motion (due to neurological diseases) with respect to healthy people motion [30]. In a previous study [21], the NP showed to have high variability and failed to capture the trend of the performance of healthy subjects. This effect is also related to the choice of the filtering parameters; the lower the cutoff frequency of the low pass-filter, the less is the capability of NP of discriminating different levels of smoothness. While this is true for all the smoothness metrics, this is particularly crucial for NP. The areas of the workspace that presented the lowest smoothness were the up and left sectors, in which the movement execution was less comfortable and dexterous due to the high shoulder flexion angles, that require effort and coordinated control in poorly used areas of the upper limb workspace [41]. Furthermore, in P2P movements, the length of the trajectory and the execution time were higher, leading to generally less smooth movements, as already demonstrated in other studies [42; 43]. The application of different smoothness metrics on healthy subjects in a large set of upper limb movements covering the workspace provided reference values for four commonly used metrics that may be useful for the understanding of the physiological mechanisms related to smoothness and may find use when assessing motor performance of impaired patients. Since smoothness is considered as the result of a cognitive process and the improvement of motor control in patients, the use of smoothness metrics can be important for the appropriate evaluation of the motor recovery in impaired subjects [8; 20]. This work provides reference values that may be used as benchmark for the evaluation of smoothness related measurement in a clinical context, as well as deepens the relationships found between such movements. This work has some limitations. First, only movements of healthy people were considered, reducing the range of application for some of the indexes, such as the NP. However, this study is the first step towards the application of these metrics in clinical assessments and its aim is to provide reference values for future studies on specific diseases. Moreover, the use of only healthy subjects allowed us to have coherence between the smoothness metrics and to interpret the results in consistent experimental conditions. Future work may involve patients suffering from neurological and neuromuscular diseases. Second, gender differences in smoothness metrics were not investigated since the sample size of this study was limited and we could not provide statistical evidence of gender differences. Future work could include a larger cohort of subjects, with a balanced number of males and females in order to assess the smoothness differences between genders. Finally, despite us providing a quantification of smoothness computed with several metrics, covering a comprehensive set of 3D directions in the upper limb workspace, the movements we considered were all approximately rectilinear or with little curvature. Developments of this concept may include more complex movements of the activity of daily living that require more complex coordination.