# Modeling and Design Enhancement of Electothermal Actuators for Microgripping Applications
## 3 Results  
We examine the effect of the number, shape, and distribution of the perforations on the response of the microgripper. Four different settings are considered, as shown in Figure 7. These include single-row square, single-row circular, double-row square, and double-row circular perforations. In all of these four scenarios, the imposed boundary conditions  
Figure 14: Mesh independence results obtained for the microgripper at 5 V. The selected mesh setting for the analysis is shown. (**a**) tip displacement convergence, (**b**) tip temperature convergence. Figure 12: Schematic of the microgripper illustrating the imposed boundary conditions. Figure 13: Schematic diagram of microgripper design based on electrothermal actuator 2.  
are held constant and only the number or geometry of perforation is altered. Moreover, similar to the perforations added to micro-actuators analyzed in the previous section, the perforations on the microgripper are only added on the top surface of non-extended hot arms. In all cases, the added perforations go through the entire depth of the hot arm surface. When a voltage is applied on the microgripper, due to geometry differences in the hot and cold arms, one side will expand more than the other, causing the microgripper to open. When the voltage is disconnected, the microgripper returns to its initial state. Figure 15 shows the upper and lower tip displacements of the microgrippers. In the same figure, displacement contours for the non-perforated microgripper and double-row square-perforated microgripper are also presented. The simulation results indicate that the microgripper without perforations has the lowest tip displacement compared to perforated microgrippers in this study. Moreover, the presence of more holes on the surface of the hot arm leads to a slight increase in the tip displacement. For instance, when applying a voltage of 8 V, the microgripper with a single row of square perforations undergoes a 10.707 \(\upmu\)m tip displacement whereas the microgripper with a double row of square perforations reaches a tip displacement of 11.240 \(\upmu\)m. Similar trend is observed for the cases of single- and double-row circular perforations. Another important observation that can be made from Figure 15 is the similarity in the results obtained for the scenarios where the number of holes held constant and only the geometry of the holes has changed. Such results are expected since the radius of circular holes is intentionally selected in a way that the volume reductions caused by the added perforations in both scenarios remain unchanged. At an excitation voltage of 8 V, the single-row circular-perforated microgripper achieves a tip displacement of 10.685 \(\upmu\)m, which is 0.022 \(\upmu\)m lower than that of the single-row square-perforated microgripper at the same voltage. Similarly, the double-row circular-perforated microgripper reaches a 11.176 \(\upmu\)m tip displacement, which is 0.064 \(\upmu\)m lower than that of the double-row square-perforated microgripper. The overall trend observed in Figure 15 for the upper and lower tip displacements of microgrippers is also consistent with the results reported in the literature [16; 17; 18; 25; 26; 32]. In [18], the designed polysilicon microgripper achieved tip displacements of approximately 3.0 \(\upmu\)m when applying a voltage of 3 V, whereas, in the same study, the single crystal silicone microgripper achieved displacement of approximately 1.5 \(\upmu\)m at 14 volts. [PERSON] et al. [25] presented an electrothermally-actuated microgripper for biomedical applications and reported a tip displacement of about 2.5 \(\upmu\)m at 12 V. As shown in Figure 15, the simulation results show evidence of superior performance in the current microgripper, especially when incorporating perforations. Indeed, the application of a lower voltage of 8 V results in a tip displacement of 11.240 \(\upmu\)m for the microgripper with a double row of square perforations. Figure 16 shows the total gap opening obtained from each microgripper under study.