## 2 Materials and Methods
### Data Analysis  
Data collected by the gyroscope and the accelerometer of the IMU sensor were extracted and imported into MATLAB(r) (MATLAB R2023b, The MathWorks, Inc., Natick, MA, USA) environment for custom data processing.  
For each repetition of each task, the total angular velocity \(\omega\) was computed as the vector sum of the triaxial components of angular velocity \(\omega_{i}\) (\(i=1\), \(2\), \(3\)) detected by the gyroscope. Likewise, the triaxial acceleration signals were combined (vector sum) into the total acceleration \(a\). The jerk signal \(j\) was computed from \(a\), applying a custom two-point derivative approximation.  
According to the literature, in the acceleration signal of a body in motion, two components can be identified: a first component due to the presence of gravity, which [PERSON] et al. [25] define as \(a_{\mathrm{g}}\), and an additional component due to bodily motion, namely \(a_{\mathrm{b}}\) in the same paper [25]. In their work from 2006 [28], [PERSON] et al. state that only the gravitational component of the acceleration signal of a body moving in space should be evaluated when aiming at measuring its postural orientation. This contribution is described by [PERSON] et al. as a trend line. The literature depicts that movements typical of the activities of daily living like gait present a frequency between 0.8 Hz (or even 0.6 Hz in some sources) and 5 Hz [13; 25; 28]. The signals were therefore low-pass-filtered with a cut-off frequency set at 5 Hz, applying a fourth-order zero-phase low-pass Butterworth filter, and then detrended. This detrended filter acceleration signal was then filtered by applying an additional fourth-order zero-phase low-pass Butterworth filter, with the cut-off frequency set at 0.6 Hz, to isolate \(a_{\mathrm{g}}\), the gravitational contribution to the signal. The acceleration due to bodily movement, \(a_{\mathrm{b}}\), was identified by the difference as the remaining part of the detrended filter acceleration signal not included in \(a_{\mathrm{g}}\).  
Subsequently, the portion of the signal corresponding to the actual movement was identified for each acquisition. The instants identifying the events of the start and end of the movement were detected in the \(a_{\mathrm{g}}\) signal, applying an improved version of the method described in [PERSON] et al. [26]. The procedure involves the implementation of a simplified version of the double window approach for the detection of the transient values in EMG signals presented in [PERSON] et al. [29]. According to this method, the signal is swept with a moving observation window (OW) of 0.2 s, which moves by 1 index step, to identify the interval presenting the minimum standard deviation. This OW corresponds to the rest condition of the subject, and the mean value OWmean of this interval is computed. The start and end of the movement are then defined as a detectable variation in the acceleration value with respect to the OWmean value. The start and stop events are in fact identified, respectively, as the first and last instants of the signal presenting a variation in the acceleration value beyond the threshold 0.003-OWmean. This threshold value was the result of a fine-tuning process of the identification algorithm and proved the most stable results in all the testing conditions.