## 3 Results  
### Strength Simulation Results  
The main results of FEM calculations are presented in Figure 21 (fifth, highest case of loading--750 N) and Table 3. The table presents the maximum values of the von Mises equivalent stress \(\sigma_{\text{eq,max}}\), the maximum deflections \(d_{\text{max}}\), and the traction forces \(F\) corresponding to different load cases. The plots in Figures 22 and 23 show the dependencies \(\sigma_{\text{eq,max}}\) vs. \(F\) and \(d_{\text{max}}\) vs. \(F\), respectively. Both diagrams allow the observation that the mechanical response of  
Figure 21: Colour map showing the distribution of the von Mises equivalent stress at the level of the entire assembly (fifth load case: traction force of 750 N). \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Load Case**} & **Traction Force** & \
\begin{tabular}{c} **Maximum Value of the** \\ **Von Mises Equivalent** \\ **Stress \(\sigma_{\text{eq,max}}\) [MPa]** \\ \end{tabular} &
\begin{tabular}{c} **Maximum Deflection** \\ \(d_{\text{max}}\) [mm] \\ \end{tabular} \\ \hline
1 & 150 & 6.48 & 2.263 \\
2 & 300 & 12.97 & 4.525 \\
3 & 450 & 19.45 & 6.788 \\
4 & 600 & 25.93 & 9.050 \\
5 & 750 & 32.42 & 11.310 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Traction force, maximum value of the von Mises equivalent stress, and maximum deflection corresponding to different load cases. the prosthesis is linear. In fact, the dependencies \(\sigma_{\text{eq,max}}\) vs. \(F\) and \(d_{\text{max}}\) vs. \(F\) are well approximated by the regressions  
\[\sigma_{\text{eq,max}}=4.323\cdot 10^{-2}\cdot F, \tag{1}\]  
and  
\[d_{\text{max}}=1.508\cdot 10^{-2}\cdot F, \tag{2}\]  
respectively (see the black lines in Figures 22 and 23). Figure 23: Dependence \(d_{\text{max}}\) vs. \(F\). Red dots—numerical results taken from Table 2. Black line—linear regression defined by Equation (2). Figure 22: Dependence \(\sigma_{\text{eq,max}}\) vs. \(F\). Red dots—numerical results taken from Table 2. Black line—linear regression defined by Equation (1). It can be easily seen in Table 2 and Figure 22 that \(\sigma_{\rm eq,max}\) equals the tensile strength of the ABS material (30 MPa--see Table 1) for a traction force 600 N \(<F_{\rm cr}<\) 750 N. This critical load results from Equation (1) as soon as the replacement \(\sigma_{\rm eq,max}\) = 30 MPa and is as follows:  
\[F_{\rm cr}=30\cdot 100/4.323=693.96\ \rm N. \tag{3}\]  
When interpreting results, two main considerations need to be taken into account:  
1. The load of 750 N is impractical and will probably never occur while using the prosthesis as intended. It would require an equivalent mass of ~75 kg to hang off the prosthesis end effector, which would be impossible to bear for the patient, and the socket would probably slide off the stump first before the prosthesis is actually damaged;
2. The simulation does not consider dependence of properties of ABS material manufactured using FDM technology on layered deposition process parameters, such as build orientation or layer thickness and many others, noted in many publications [26; 27]. The real tensile strength of ABS (as well as impact and bending strengths) would be therefore significantly lower than the declared values by the producer, depending mostly on build orientation and also other process parameters. Also, it is important to notice that only one loading scenario was considered in the analysis, with other load types and locations, and different areas of prosthesis could be in danger of breaking. Special attention should be paid to the wrist joint area, as the nut and bolt connection could be also a weak point when loading the prosthesis. As such, effective recommended load, in authors' opinion, should not exceed the third load case (450 N), and the equivalent stress in prosthesis mechanical parts made using FDM technology should not exceed 20 MPa, to avoid risk of breaking or otherwise damaging the prosthesis mid-activity. The force sensor should be able to answer what are the real loads during the prosthesis use.