## 5 Method for Designing Manipulators for Man-Portable UGVs
### Topological Optimization of the Manipulator Structure  
The forces calculated in the previous stage are used to define load cases in the topological optimization of robot components. The further optimization process will be demonstrated using the example of the manipulator joint body 3. For the selected body, an optimization space is defined in which the solution to the problem is sought as well as a passive space that is not subject to modification during optimization (Figure 7). The project space is constructed so that its volume is as small as possible but does not limit the operation of the optimization algorithm. This space is also appropriately cut out to provide space in the resulting component for gear components, cables, and electronic systems. The passive space is constructed from thin-walled primitives. This space defines  
Figure 6: Forces acting on the selected bearing surfaces of joint 3, depending on angle of maximum radial torque. Figure 7: Left side—design space (transparent) and passive space (gray) of the manipulator joint, right side—boundary conditions: red indicates the part restraint, yellow indicates the forces acting on the part surfaces. the interfaces for attaching the joint components, to which constraints and loads will also be applied. The passive space is built in such a way as to ensure tightness in the resulting structure and to guarantee the possibility of running cables between individual compartments of the body. The passive space is functionally a fully fledged model of the gear body, but it does not take into account the strength requirements. Topological optimization aims to modify the body so that it also meets the strength conditions. It should be noted that the passive space and design space models are related to a given transmission and, in accordance with the adopted methodology, are defined at the part library level. The boundary conditions are shown in the passive space (Figure 7). The part is fixed on its left surface (red marks) and the loads are applied on the surfaces which are interfaces to bearings and other components (yellow marks). The figure shows one of the load cases where the maximum radial moment is at an angle of 90\({}^{\circ}\). Firstly, calculations with a lower-resolution mesh are performed. The mass is minimized within the limits resulting from the maximum stresses. The results show that it is possible to reduce the mass of the part to 25% of the mass of the initial design space. Then, optimization on a higher-resolution mesh is performed. To reduce calculation time, settings of the optimization are changed to maximize the stiffness of the structure with the imposed mass reduction condition of 25% of the mass of the design space. The body material is EN AW-7075. The optimization result is shown in Figure 8. Calculations are performed using the SIMP method [31] implemented in nTopology software [32]. For comparison, calculations are made for a different count of load states which differ with the angle of action of the maximum radial moment in the joint. Sixteen load states are defined in which the radial moment angle changes every 22.5\({}^{\circ}\) (Table 1). The following calculation variants are considered:  
* Four load states differing in the direction of force action every 90\({}^{\circ}\) (Figure 9--left);
* Eight load states differing in the direction of force action every 45\({}^{\circ}\) (Figure 9--middle);
* Sixteen load states varying in the direction of force action every 22.5\({}^{\circ}\) (Figure 9--right). As can be seen in Figure 9, the optimization results are very similar regardless of the number of load cases considered. The analysis shows that the volumes of the resulting components overlap by 95.5% for the comparison of results 1 and 2 and by 99.6% for the comparison of results 2 and 3.