## 4 Discussion
Apart from _TT_, the parameters mentioned above were computed according to traditional definitions [25] and the new adopted definitions. While formal and insubstantial diversities can be identified between \(RMS_{G\_B}\) and \(RMS_{G}\), relevant differences emerge for the smoothness and fluency parameters \(J\) and _Fl_ between the two methods. The main dissimilarity lies in the way the total time _TT_ is managed. Both methods aim to make the parameters time-independent. The traditional approach favors the ease of use of the parameters, multiplying the core element of each formula, a summation on the time of jerk or the \(a_{\text{b}}\) components, for the third and second power of the _TT_ interval, respectively, and then applying the operator of a natural logarithm; in this way, the final parameter is simplified into a (typically fairly manageable) value in meters. Such a quantity is quite straightforward to interpret: we expect that the lower the value, the better the performance since fewer nonessential movements will have been performed during the execution of the task. In this sense, Table 4 presents data that are actually in line with this expectation for longer and most complex PTs, i.e., Roll, SiSu, and SuSi. The remaining SiSt and StSi PTs reveal comparable results in terms of the mean values for healthy and pathological populations. Although it is very easy to use, this kind of approach could present a weakness in the use of _TT_ as a simplification factor, especially if involved with multiple powers, since the elapsed time may itself be a relevant indicator of the quality of a PT. The adopted new definition therefore tries to overcome this possible limitation by applying an opposite strategy, i.e., by normalizing the same core elements of the \(J\) and _Fl_ formulas with respect to the total time _TT_. This alternative definition introduces some non-negligible effects: the measurement units of the two parameters are less user-friendly, and similarly, their final values may be more difficult to handle, as the sensitivity of the clinician to these quantities could be less immediate. On the other side, though, these definitions allow obtaining parameters independent of time, which are therefore comparable across subjects, repetitions, and tasks and rigorously describe the kinematic characteristics of the performed laws of motion (variation in jerk and bodily motion component of the acceleration). Quite unexpectedly, the values obtained with the analyzed dataset reveal that the normalized smoothness and fluency \(J\) and _Fl_ are higher for healthy subjects for all the PTs. This result could simply be due to the limitations of the analyzed populations or, on the contrary, could be a hint at further functional considerations. For instance, it could be suggested that the enrolled healthy subjects are able to perform more compensatory adjustments during a PT than the patients in the pathological population. Equally, this consideration also seems to be supported by the results for the final two parameters, i.e., the jerk root mean square \(RMS_{j}\) and its maximum variation \(\Delta j\); in fact, for the current dataset, both indicators present higher values for the healthy subjects for all the PTs, and this should imply a higher activity in the variation of the jerk, both in terms of frequency and amplitude of the signal. However, the current population subsets present limitations in their composition: as Table 3 describes, the healthy sample is composed of young adults, whereas the pathological sample is more inclusive but presents a remarkably higher mean age. Kinematic differencesin movement execution are described in the literature for sit to stand due to both age [30] and gender [31]. Nevertheless, to the best of our knowledge, no studies have addressed these differences for the other PTs investigated in this study. We are aware that differences due to age may be even more pronounced if we add the presence of disease in either group.