## 2 Materials and Methods
The data was presented in such a way as to ensure its complete anonymity. The test was performed with the use of a measurement system consisting of two incremental encoders: 1 was connected with the central unit 2 transmitted by means of the micro-controlled system based on Arduino architecture, a measurement signal for the author's software (Figure 3). The measurement system used Hohner 21-122-500 encoders with the resolution of 500 impulses for determining the angular velocities of the left drive wheel \(\omega_{\mathrm{L}}\) and right drive wheel \(\omega_{\mathrm{P}}\). Then, the above was used to generate the wheelchair velocity histogram from which single propelling cycles were separated (Figure 4). Figure 4: The example of the wheelchair velocity diagram during slope climbing (**A**) and a separated single propelling cycle in the function of the percentage value of the propelling cycle completion (**B**). Figure 3: A wheelchair with the test apparatus for measuring its motion kinematics, where: 1—incremental encoder with the resolution of 500 steps, a central unit collecting a measurement signal, 2—a central unit collecting a measurement signal. Selected symbol \(\omega_{\mathrm{P}}\) is the angular velocity of the right wheel of the wheelchair. \begin{table}
\begin{tabular}{l c c c c c} \hline  & **Height** & **Weight** & **Age** & **Push Force** & **Experience** \\ \cline{2-6}  & **(cm)** & **(kg)** & **(Years)** & **(N)** & **(-)** \\ \hline Participant 1 & 170 & 96 & 33 & 282 & ******** \\ Participant 2 & 173 & 90 & 33 & 244 & **** \\ Participant 3 & 178 & 89 & 32 & 315 & **** \\ Participant 4 & 175 & 83 & 32 & 292 & **** \\ Participant 5 & 176 & 72 & 33 & 271 & **** \\ Participant 6 & 180 & 74 & 33 & 290 & **** \\ Participant 7 & 175 & 110 & 32 & 320 & **** \\ Participant 8 & 170 & 103 & 29 & 311 & **** \\ \hline \end{tabular}
\end{table} 
Table 1: Comparison of anthropometric features and the level of experience in wheelchair operation of the test subjects. The experience was assessed on the basis of the number of hours spent driving a manual wheelchair. Given the wheelchair linear velocity \(v(t)\) for a single propelling cycle, firstly, the path distance was defined \(s_{C}\) (1) and the wheelchair total acceleration \(a_{T}\) (2). Based on the defined acceleration \(a_{T}\) the propelling force \(F_{D}\) (3) of the whole wheelchair was calculated. Given the propelling force \(F_{D}\) power \(P(t)\) was calculated (4). Then, based on the above and based on the given propelling cycle duration time, total mechanical energy \(E\) generated during a single cycle was determined (5). \[s_{C}=\int\limits_{t_{start}}^{t_{start}}v(t)dt \tag{1}\]  
\[a_{T}(t)=\frac{dv(t)}{dt} \tag{2}\]  
\[F_{D}(t)=(m_{h}+m_{w})a_{T}(t)=(m_{h}+m_{w})\frac{dv(t)}{dt} \tag{3}\]  
\[P(t)=F_{D}(t)v(t)=(m_{h}+m_{w})\frac{dv(t)}{dt}v(t) \tag{4}\]  
\[E=\int\limits_{t_{start}}^{t_{end}}P(t)dt=\int\limits_{t_{start}}^{t_{end}}[F_{ D}(t)v(t)]dt \tag{5}\]  
where: \(s_{C}\) is the a path distance by the wheelchair during a single propelling cycle, \(t_{start}\) is the propelling cycle starting time, \(t_{end}\) is the propelling cycle stopping time, \(a_{T}\) is the wheelchair total acceleration considering all the enforcements and delays occurring in the propelling cycle, \(v\) is the wheelchair linear velocity measured at the constant time interval, \(F_{D}\) is the wheelchair propelling force affecting the human-wheelchair system, \(m_{h}\) is the body weight, \(m_{w}\) is the wheelchair weight, \(P\) is the power of the human-wheelchair system generated in the propelling cycle, \(E\) is the mechanical energy generated after the end of the entire propelling cycle. The muscle activity measurement enabling the estimation of the upper limb muscle activity was conducted by means of Noraxon Mini DTS apparatus for surface electromyography equipped with four measurement channels. The analysis and recording of the muscle activity signal was carried out with the use of Noraxon MR3 software.