## 2 Materials and Methods
### Data Processing  
The position data from the linear encoder and the \(GRF\) data from the force plates were acquired simultaneously at a frequency of 1000 Hz and filtered using a 50 ms moving average filter [17; 38]. The rotary encoder signals were first interpolated (1000 Hz) and then smoothed using a moving average filter with a 50 ms window; this allowed us to compare the signals between the systems. Variables from the shaft rotation were calculated from the angular frequency (\(f\)) of the shaft using basic [PERSON]'s laws (known as the inverse  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & **N** & **Age (Years)** & **Mass (kg)** & **Height (cm)** & **Body Mass (kg/m\({}^{2}\))** & **Training** & **IPAQ Score** (**MET/min/Week)** & **Knee Extension Strength** \\ \hline Male & 24 & 23.8 (2.8) & 79.3 (12.2) & 181.3 (6.3) & 24.3 (3.0) & 12.1 (3.6) & 3366.8 (1743.3) & 3.44 (0.62) \\ \hline Female & 26 & 22.2 (2.9) & 63.0 (9.1) & 168.4 (5.6) & 22.4 (2.6) & 10.5 (3.5) & 3352.8 (2093.0) & 2.88 (0.48) \\ \hline All & 50 & 23.0 (2.9) & 71.1 (13.4) & 174.8 (8.8) & 23.4 (3.0) & 11.3 (3.6) & 3359.8 (1907.7) & 3.12 (0.61) \\ \hline \hline \end{tabular} N, number of participants in the group; all, male and female; data are presented as means (standard deviations).  
\end{table}
Table 1: Main characteristics of the participants.  
dynamic approach), as described further on. Due to the analogy between angular and linear motion, the linear velocity (\(v\)) of the squat was calculated as the product of the angular velocity (\(\omega=2\pi\times f\)) and the radius of the shaft (\(r=0.015\) m). Then, the angular acceleration (\(\alpha\)) was calculated as the rate of change of \(\omega\) in each time interval of 1 ms (t) (\(\alpha=\Delta\omega/\Delta t\)). The instantaneous torque required to accelerate the FW was calculated as the product of the mass moment of inertia and the angular acceleration (\(\tau=I\times\alpha\)). Finally, the linear FW pulling force was expressed as the quotient of torque and radius of the shaft (FW pulling force \(=\tau/r\)).  
To account for the change in \(GRF\) due to acceleration of the body mass, the vertical acceleration (\(a\)) was calculated from \(\alpha\) (\(a=\alpha\times r\)). Then, \(GRF\) was calculated as the sum of the FW pulling force, the subject's weight, and the \(GRF\) due to the acceleration of the lifting body mass (\(m\))--according to the Equation (1):  
\[GRF=\text{FW pulling force}+(m\times g)+(m\times a). \tag{1}\]  
In the equation, \"\(g\)\" stands for gravitational acceleration, i.e., 9.81 m/s\({}^{2}\). Moreover, to accurately match the mean and peak values between the direct and criterion measure, the scaling factor was expressed, as a proportion of total body mass, following the Equation (2):  
\[\text{scaling factor}=(GRF\text{ from force plates}-(\text{FW pulling force}+m\times g))/(m\times a). \tag{2}\]  
Both the linear \(v\) and \(GRF\) signals were calculated for each 1 ms time segment (Figure 3) in the eccentric and concentric phase of the squat. The criterion and direct measure mean and peak values of \(v\) and \(GRF\) were calculated as the average of six consecutive squat repetitions, as previously suggested [17]. \(F\)-\(v\)-\(P\) analysis was performed using the mean concentric \(GRF\) and \(v\) variables from the criterion and direct measure variables. Based on four inertias, a linear regression model (F[v] = F0-k\(v\)) was used to determine the four outcome measures of the \(F\)-\(v\)-\(P\) relationships, where F0 represents the F-intercept and k is the _slope_ of the \(F\)-\(v\) relationship. The use of Equations (3) and (4) allowed for the calculation of V0 and P\({}_{\text{max}}\)[39]:  
\[\text{V0}=\text{F0}/\text{k} \tag{3}\]  
\[\text{P}_{\text{max}}=(\text{F0}\cdot\text{V0})/4. \tag{4}\]