## 2 Materials and Methods
### Implementation of Motion Quantitative Analysis  
During each test, a track of the wrist joint (WJ) was recorded with respect to \(x\), \(y\), and \(z\) axes (Figure 2b). The position of COM with respect to these \(x\), \(y\), and \(z\) axes was assessed by applying segmentation. Each displacement was calculated as a relation between the difference in current position and initial position divided by the maximum position estimated in the tested trial. In this study, we analyzed: (1) the \(x\)-th, \(y\)-th, and \(z\)-th displacement of the wrist joint (WJ\(x\), WJ\(y\), WJ\(z\)) and absolute displacement of the wrist joint (\(\Delta\)WJ) calculated as \(\Delta\)WJ = \(\sqrt{\left(\text{WJ}_{x}\right)^{2}+\left(\text{WJ}_{y}\right)^{2}+\left( \text{WJ}_{z}\right)^{2}}\); (2) the \(x\)-th, \(y\)-th, and \(z\)-th displacement of the upper limb COM (COM\({}_{x}\), COM\({}_{y}\), COM\({}_{z}\)) and absolute displacement of COM (\(\Delta\)COM) assessed as \(\Delta\)COM = \(\sqrt{\text{COM}_{x}{}^{2}+\text{COM}_{y}{}^{2}+\text{COM}_{z}{}^{2}}\). Each muscle activation was calculated as the difference between normalized processed EMG registered in the trial and normalized processed EMG registered at the initial stage of the trial. A piecewise linear multi-regression (the first part of approach for assessment of quality of motion) was applied to correlate muscle activations (EMG\({}_{1}\), EMG\({}_{2}\), EMG\({}_{3}\), EMG\({}_{4}\)) and the kinematic data of displacement of the wrist joint (WJ\({}_{x}\), WJ\({}_{y}\), WJ\({}_{z}\), AWJ) or upper limb COM (COM\({}_{x}\), COM\({}_{y}\), COM\({}_{z}\), \(\Delta\)COM) in each tested window that was equal to 1% of thelength of the motion fragment (composed of 10 frames). Assuming that muscle activations are independent variables (EMG\({}_{1}\), EMG\({}_{2}\), EMG\({}_{3}\), EMG\({}_{4}\)) and each kinematic datum \(y\) (WJ\({}_{x}\), WJ\({}_{y}\), WJ\({}_{z}\), \(\Delta\)WJ, COM\({}_{x}\), COM\({}_{y}\), COM\({}_{z}\) and \(\Delta\)COM) is dependent variable, the relation was formulated as:  
\[y=a_{0}+a_{1}\cdot\text{EMG}_{1}+a_{2}\cdot\text{EMG}_{2}+a_{3} \cdot\text{EMG}_{3}+a_{4}\cdot\text{EMG}_{4}=\] \[=y_{0}+y_{1}+y_{2}+y_{3}+y_{4} \tag{1}\]  
where \(y_{j}\) (for \(j=0,1,2,3,4\)) describes the \(j\)-th participation (contribution) in the value of the tested kinematic data \(y\); \(a_{0}\) describes the contribution of the motion of trunk and fingers, as well as pronation/supination of the wrist joint and/or upper limb passive structures and/or non-monitored active muscles (\(a_{0}=y_{0}\)); \(a_{i}\) (\(i=1,\ldots,4\)) describes the coefficient of the \(i\)-th muscle activation EMG\({}_{i}\) (this coefficient depends on the muscle lever arm). The product between this coefficient \(a_{i}\) and muscle activation EMG\({}_{i}\) defines the contribution of the \(i\)-th muscle to the motion performance, i.e., \(a_{1}\cdot\text{EMG}_{1}=y_{1}\), \(a_{2}\cdot\text{EMG}_{2}=y_{2}\), \(a_{3}\cdot\text{EMG}_{3}=y_{3}\), \(a_{4}\cdot\text{EMG}_{4}=y_{4}\). Linear piecewise multi-regression analysis was performed in MATLAB by using our own codes and statistics toolbox. Assuming a threshold of statistical significance in which \(p\) was equal to 0.05 (\(p\leq 0.05\)), only statistically significant results of relationships in multi-regression analysis (Equation (1)) with a coefficient of determination (R\({}^{2}\)) that was greater than 0.75 (R\({}^{2}\geq 0.75\)) were considered. Due to the fact that each muscle contribution (\(y_{1}\), \(y_{2}\), \(y_{3}\), \(y_{4}\)) (Equation (1)) can be positive (synergistic participation), negative (antagonistic), or zero, the results of multi-regression analysis were presented as: (1) distributions of synergistic and antagonistic participation at the time of the motion; (2) summarizing synergistic and antagonistic participations.