## 2 Materials and Methods
### Topology Optimization  
For evaluation and validation purposes, we chose a practical component called the shifting thumb (with dimensions 110 \(\times\) 55 \(\times\) 41 mm; see Figure 2), which is used as a mechanical-pneumatic power steering, on TATRA 14 TS210L manual transmissions. The original shape was topologically optimized for maximum 3D printing potential (see Figure 3). The original model was subjected to a total force of 5000 N in the normal direction of the loaded face according to Figure 4a. Considered constraints are depicted in the same picture. [PERSON]'s modulus \(E\) = 195 GPa and Poisson's ratio \(\
u\) = 0.3 were used as elastic constants of stainless steel AISI 316L in all simulations. Initially, an FE elastostatic analysis in ANSYS Workbench was performed for the original geometry. As a result, von Mises stress contours obtained in the original part are presented in Figure 3b. The keyway is not used for transferring a torque, which is why there is no hotspot of stresses. The torque is transferred by two holes with faces depicted by mark D in Figure 4a. It should be noted that the topology optimization is done to cut off the weight from the part, while ensuring that the part is functional and with comparable stiffness in comparison to its original counterpart. Specifically, in our study, we saved 63% of weight (From Figure 3a to Figure 3b, 646 g to 236 g) and obtained comparable stiffness and stresses (Figure 4b vs. Figure 6, 222 MPa vs. 232 MPa/214 MPa) after topology optimization. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Element size & 1 mm \\ Method & Inherent Strains \\ Hatch spacing & 0.11 mm \\ Scan speed & 650 mm/s \\ Laser power & 200 W \\ Preheat temperature & Ambient \\ Layer thickness & 50 μm \\ Scan strategy & Meander \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Process parameters for input data in MSC Simufact. Figure 2: Gear shift fork 14 TS210 including the previous version of the shifting thumb [17]. Topological optimization has become a powerful area of study since such algorithms can be applied to many design problems in different physical disciplines, such as solid mechanics, fluid dynamics, and thermal dynamics [18; 19; 20]. By using topological optimization methods and related algorithms, a designer can generate innovative design ideas, especially in engineering fields. Instead of using trial-and-error methods for designing engineering products, designers use different topological optimization methods to generate conceptual designs. Topological optimization methods can be distinguished by two main methods: solid isotropic material with penalization, otherwise known as SIMP, and the level-set method. Each method has unique features, although both can be used to achieve similar goals. The SIMP method is the most popular due to its conceptual simplicity and computational efficiency. However, it requires more post-processing and smoothing due to its gray elements, which produce a rough surface geometry [21]. The mathematical representation of the SIMP method is based on the heuristic relationship between the relative element density \(x_{i}\) and the element of the Young's modulus \(E_{i}\) given by  
\[E_{i}=\ E_{i}(x_{i})=\ x_{i}^{p}E_{0}\,\ \ \ x_{i}\in[0,1], \tag{1}\]  
where \(E_{0}\) is the elastic modulus of the solid material and \(p\) is the penalization power \((p>1)\). A modified SIMP approach is given by  
\[E_{i}=E_{i}(x_{i})=E_{min}+x_{i}^{p}(E_{0}-E_{min}),\ \ \ x_{i}\in[0,1], \tag{2}\]  
where \(E_{min}\) is the elastic modulus of the void material, which is non-zero to avoid a singularity of the finite element stiffness matrix. Figure 4: Boundary conditions applied to the model of the main shifting thumb (**a**) and resulting contours of von Mises stress (**b**). Figure 3: Original geometry of the main shifting thumb (**a**) and topologically smoothed shifting thumb (**b**).