# Modeling and Design Enhancement of Electothermal Actuators for Microgripping Applications
## 1 Introduction
[29] designed and experimentally tested a microgripper equipped with piezoelectric actuators. Their developed prototype showed a capability to precisely handle and manipulate miniature parts. A PID controller was also implemented in order to achieve the stability of the microgripper operation. [PERSON] et al. [17] designed a microgripper based on a hot/cold arm micro-actuator, which is used in biomedical applications. The authors highlighted some of the failures that may occur in microgrippers, such as out-of-plane buckling, residual stresses, and stress concentration. [PERSON] et al. [18] also investigated the effect of the material (silicon type) and air gap thickness on the operation of MEMS microgrippers. Some studies available in the literature focused on observing the differences in results obtained from microgrippers by changing the fabrication process, arm widths, air gap thickness, and fabrication process. [PERSON] and [PERSON] [19] designed and analyzed a microgripper that uses comb-drive electrostatic actuation as the driving force. Another electrothermally actuated microgripper design is proposed by [PERSON] et al. [20], in which the tip is designed in a way which facilitates the grip of a bio cell. The main difference between the microgripper proposed in this study and other available microgrippers is the presence of perforations on the surface of the hot arm of the actuator. In MEMS, perforations are mainly implemented in RF MEMS switches to reduce the squeeze film damping and increase the switching speed [36]. The perforations facilitate switches which operate at low actuation voltages and power [37; 38]. Several research studies examined the impact of perforations on the dynamic response of structures at different scales [39; 40; 41]. [PERSON] et al. [39] conducted a theoretical study using the finite element method to investigate the free vibrations and forced responses of perforated multilayer beam structures. They analyzed the impact of different perforation configurations on their natural frequencies and mode shapes. [PERSON] and [PERSON] [41] develop a nonlinear mathematical model to analyze the vibrations of functionally graded piezoelectric plates under mechanical and electrical loadings for varying boundary conditions. Different types of porosity distributions are introduced by dispersing perforations (holes) over the plate. The center displacement was observed to increase when the porosity of an evenly distributed porous plate was increased. On the other hand, a decreasing trend in the center displacement was obtained when the porosity for an unevenly distributed porous plate was increased. As such, one can tune the porosity of the functionally graded as per the application of interest. As demonstrated, the distinctive merits of the inclusion of perforations in macro/ microstructures have been demonstrated over several research studies [36; 39; 40; 41]. However, there is still room for further exploitation of this kind of structural feature, especially when properly tuning its geometry and distribution to improve the operation of microgrippers comprising electrothermal actuators. Therefore, we propose, in this work, a novel design for microgrippers that benefits from the presence of perforations in order to achieve superior performance in comparison to their conventional counterparts. Previous research works have only studied other geometrical and material aspects to enhance the design of microgrippers [16; 17; 18; 24; 25; 26; 28; 31; 32; 24; 23; 22; 25; 26; 28; 31; 32; 42; 43]. In this work, we develop a computational model of a microgripper actuated via U-shaped electrothermal actuators using the finite element software tool COMSOL Multiphysics, Version 5.6. We validate the model using previously published experimental studies. We show the potential enhancement in the design of microgrippers by adding perforations of different shapes and distributions, proposed for the first time.