## 5 Feasibility Study Based on FEA Simulation
The force magnitudes \(F=0.05\) uN and \(F=0.01\) uN give the predominant contribution to the MPSuntil the applied tension does not exceed about 20 V and 9 V, respectively (Figure 8e). Figure 8: _Cont._  
In the case \(\phi=\pi/2\), the force \(F\) is opposite the displacement \(y\)-component (Figure 9). As the magnitude of \(F\) increases:  
* the tip displacement magnitude increases (Figure 9a); however, with respect to the case \(\phi=0\) (Figure 8a), it is also affected by high values of the applied tension;
* the tip rotation increases (Figure 9b);
* the applied tension required to achieve the maximum rotation of the comb-drive increases (from 22 V for \(F=0\) to 25 V for \(F=0.10\) uN, Figure 9c);
* the tip displacement shifts increasingly along the negative direction of the \(x\)-axis (Figure 9d);
* the maximum principal stress generally increases, but depends on the applied tension values (Figure 9e). Figure 8: Simulation results for the force direction \(\phi=0\) and applied tension from 1 V-25 V: tip displacement magnitude (**a**), tip rotation (**b**), comb-drive rotation (**c**), tip displacement in the \(x\)-\(y\) plane (**d**), and maximum value of the maximum principal stress (**e**). In the case \(\phi=\pi\), the force \(F\) has the same direction of the displacement \(x\)-component (Figure 10). As the magnitude of \(F\) increases:  
* the tip displacement magnitude increases (Figure 10a);
* the tip rotation increases (Figure 10b);
* the applied tension required to achieve the maximum rotation of the comb-drive decreases (from 22 V for \(F=0\) to 19 V for \(F=0.10\) uN, Figure 10c);
* the tip displacement shifts increasingly along the negative direction of the \(x-\)axis (Figure 10d);
* the maximum principal stress increases (for \(F=0.10\) uN and for \(F=0.05\) uN). The force magnitude \(F=0.01\) uN gives the predominant contribution to the MPS until the applied tension does not exceed about 8 V (Figure 10e). Figure 9: Simulation results for the force direction \(\phi=\pi/2\) and applied tension from 1 V–25 V: tip displacement magnitude (**a**), tip rotation (**b**), comb-drive rotation (**c**), tip displacement in the \(x\)-\(y\) plane (**d**), and maximum value of the maximum principal stress (**e**). In the case \(\phi=3\pi/2\), the force \(F\) has the same direction of the displacement \(y\)-component (Figure 11). As the magnitude of \(F\) increases:  
* the tip displacement magnitude increases (Figure 11a);
* the tip rotation (magnitude) increases (Figure 11b);
* the applied tension required to achieve the maximum rotation of the comb-drive decreases (from 22 V for \(F=0\) to 15 V for \(F=0.10\) uN, Figure 11c);  
Figure 10: Simulation results for the force direction \(\phi=\pi\) and applied tension from 1 V-22 V: tip displacement magnitude (**a**), tip rotation (**b**), comb-drive rotation (**c**), tip displacement in the \(x\)-\(y\) plane (**d**), and maximum value of the maximum principal stress (**e**). * the tip displacement shifts increasingly along the positive direction of the \(x\)-axis (Figure 11d);
* the maximum principal stress increases (Figure 11e). The results of the simulations performed show that the possible interactions between the gripper jaw and the environment, modeled as a set of forces applied at the tip, affect the tip pose and, through the deformation of the gripper compliant structure, the rotation of the comb-drive actuator. As a  
Figure 11: Simulation results for the force direction \(\phi=3\pi/2\) and applied tension from 1 V–22 V: tip displacement magnitude (**a**), tip rotation (**b**), comb-drive rotation (**c**), tip displacement in the \(x\)-\(y\) plane (**d**), and maximum value of the maximum principal stress (**e**). consequence, the required voltage to reach the end of the stroke position depends on the tip force magnitude and direction. For all the considered load conditions, the maximum principal stress value is below 150 MPa, less than the yield strength of silicon, i.e., 7 GPa [55].