# Modeling and Design Enhancement of Electothermal Actuators for Microgripping Applications
## 1 Introduction  
Micro-Electro-Mechanical-Systems (MEMS) are devices that are widely used across different industries. MEMS can serve in several engineering applications, including sensing, actuation, and signal conditioning. For instance, MEMS accelerometers can be used for structural health monitoring applications. [PERSON] et al. [1] developed and deployed a data acquisition system equipped with MEMS accelerometers to measure and analyze the vibrations of reinforced concrete beams when subjected to different damage levels. [PERSON] et al. [2] acquired vibration data from MEMS accelerometers to investigate the dynamic response of modular steel frames and the impact of gypsum partition walls on their dynamic characteristics. MEMS strain sensors have also been deployed in the design of crackmeters used for measuring cracks in structures [3, 4]. Another use of MEMS technology includes the measurement of envelope air leakage in buildings using a networkof MEMS pressure sensors [5]. There are multiple actuation methods that MEMS devices can deploy for operation, such as electrostatic [6; 7; 8], piezoelectric [9], electromagnetic, and electrothermal [10; 11]. Electrostatic and electrothermal actuations are two that are commonly used due to their simple operating principle, high energy density, and compatibility with other electronics. Electrostatic actuation is characterized by a fast response, low power requirement, and well controlled force [12]. However, the associated nonlinearity limits the travel range of the actuated microstructure and can lead to its collapse due to pull-in instability and the failure of the MEMS device. On the other hand, electrothermal actuation relies on the Joule effect by heating a microstructure by means of passing a current through it in order to achieve large deflection of flexible elements, as required in several MEMS applications [13]. There are three main mechanisms of electrothermal actuation, namely the hot/cold arm actuator, the chevron, and the bimorph [10; 12; 13; 14; 15]. The operation of the hot/cold arm actuator is based on two arms of different thermal expansions leading to more generation of heat in one arm, which results in the deflection of the supporting microstructure. The chevron actuator also relies on the thermal expansion of the material, but it is only restricted to move in one direction. Lastly, the bimorph actuator is made of two materials with different thermal expansion coefficients that result in one material expanding more than the other and hence deflecting the actuator [13]. The most well-known design for a hot/cold arm actuator is the U-shaped actuator. This actuator has the capability to achieve wider ranges of displacement compared to other actuators [13; 14]. In other words, large output forces can be produced by applying relatively low voltages (below 10 V) [13; 14]. Electrothermal actuators have been widely deployed for microgripping applications [16; 17; 18; 19; 20; 21; 22; 23; 24; 25; 26; 27; 28]. Microgrippers are expected to finely grab and handle small-sized objects, such as microchips in electronics and cells in the biomedical field, without any damage. They include actuators and gripping arms made of thin silicon or stainless sheets, which are used to produce sufficient strength. Several research studies have reported on the design and performance analysis of microgrippers [16; 17; 18; 19; 20; 21; 22; 23; 24; 25; 26; 27; 28; 29; 30; 31; 32; 33; 34; 35]. The design aspects of these microstructures include the kinematic structure [18; 24], the material selection [21; 24], the actuation mechanism [16], the fabrication process [17; 20], and the impact of the surrounding environment on their operation [21; 22]. For instance, [PERSON] et al. [16] designed an unconventional micropgripper comprising hot and cold arms of varying area instead of uniform area. This modification resulted in an increase in the deformation of the arms and lower power requirements for actuation. [PERSON] et al.