## 5 Feasibility Study Based on FEA Simulation  
To simulate the possible interactions between the jaw and the environment and to evaluate the kinetostatic performance of the nanogripper, finite element simulations have been performed with the  
Figure 5: SEM image of the nano-gripper tip in contact with two particles (**a**) together with its detailed inset (**b**). Figure 6: Contact between the right-hand side jaw and one particle at 7k (**a**) and 13k (**b**) magnification. ANSYS \({}^{\copyright}\) Ver. 18 (Canonsburg, PA, USA) software [52]. The nonlinearity due to large deflections and the isotropic material formulation were considered in the analysis (polycrystalline silicon with [PERSON]'s modulus equal to 164 GPa and Poisson's ratio equal to 0.22 [53]). Figure 7 shows the mesh composed of 21,935 nodes and 17,343 elements, refined in the flexible beams and in the comb-drive fingers. The simulation setup is also illustrated in Figure 7. Two fixed supports were introduced at the flexures end-sections (labeled A), where the structure was anchored to the frame. An external force was applied to the tip considering four different directions. With reference to Figure 7, the application point is highlighted by the label B, while the four different directions correspond to the angles \(\phi=0\), \(\phi=\pi/2\), \(\phi=\pi\), and \(\phi=3\pi/2\). For each direction, four magnitudes have been considered: \(F=0\) uN, \(F=0.01\) uN, \(F=0.05\) uN, and \(F=0.1\) uN. To model the actuator action, a force was applied to each one of the 19 fingers, with the line of action perpendicular to the finger free-end section (labeled C) and magnitude equal to \(F_{\mathrm{C}}=e_{0}e_{r}hV^{2}/g\)[54]. In the previous relation, \(e_{0}\) is the vacuum permittivity (\(8.8541\times 10^{-12}\) Fm\({}^{-1}\)), \(e_{r}\) is the air relative permittivity (\(1.00058\)), \(h\) is the thickness of the finger (\(600\) nm), \(g\) is the radial distance between the movable and fixed finger (\(600\) nm), and \(V\) is the applied voltage. For each force at the tip, the simulations ran from a value of the applied tension equal to \(1\) V to the maximum tension value corresponding to the stroke of the rotary comb-drive (5 deg). In any case, the maximum voltage did not exceed \(25\) V.  
The simulation results, corresponding to the tip force directions of \(\phi=0\), \(\phi=\pi\), \(\phi=\pi/2\), and \(\phi=3\pi/2\) are reported in Figures 8-11, respectively. The results include displacements and rotations of the tip, rotations of the floating part of the comb-drive, and maximum values of the maximum principal stress. Generally, it can be noted that in the case of \(F=0\), the tip displacement, with negative components along the \(x\)- and \(y\)-axes, increases its magnitude as the actuation force (applied tension) increases. However, the application of the tip force significantly affects the kinetostatic behavior of the system. Figure 7: Generated mesh of the structure and simulation setup: fixed supports (see labels **A**), force at the tip for the case \(\phi=0\) (label **B**), and actuation force at the generic comb-drive finger (label **C**). In fact, considering the case \(\phi=0\), the force is opposite the displacement \(x\)-component. With reference to Figure 8, it can be noted that as the magnitude of \(F\) increases:  
* the tip displacement magnitude increases (Figure 8a); only for the lowest value of the force (\(F=0.01\) uN) and for high tension values (>20 V), the tip displacement magnitude is close to the case \(F=0\);
* the tip rotation (magnitude) increases (Figure 8b);
* 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 8c);
* the tip displacement shifts increasingly along the positive direction of the \(x\)-axis (Figure 8d);
* the maximum principal stress increases for all the applied tension values only for the highest value of the force magnitude (\(F=0.10\) uN).