# Z-Shaped Electrothermal Microgripper Based on Novel Asymmetric Actuator

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Design Concept and Simulation

#### 2.2. Modelling of the Asymmetric Actuator

#### 2.2.1. Displacement of the V-Shaped Actuator

_{c}is its cross-section area. The component of F

_{b}in the Y-axis is

#### 2.2.2. Displacement of the Asymmetric Actuator

^{3}), m = (6 E/L

^{2}), n = (4 EI/L) y r = (2 EI/L), where A is the corresponding cross-section area of the corresponding beam, c = cosθ, and s = sinθ, with θ in grades.

_{x}= 0, i.e., there is no displacement in the X-axis, U

_{y}≠ 0, meaning there is displacement in the Y-axis and R

_{y}= R

_{x}= 0, and M

_{3}= 0, meaning there are no reactions or moments. The only displacement that will be generated is in DOF 5, in the Y-axis, since DOFs 2 and 8 are embedded to the anchors and the displacement matrix is given by

_{5}= U

_{y}, and the corresponding subindexes 1 and 2, for the case of the geometrical characteristics of beam 1 and 2, respectively, U

_{y}is obtained as

_{1}and A

_{2}are the cross-section areas, L

_{1}and L

_{2}the beam lengths, I

_{1}and I

_{2}are the inertia moments in (m

^{4}) of beams 1 and 2, respectively. ${I}_{1}=\frac{t{w}_{1}^{3}}{12}$, and ${I}_{2}=\frac{t{w}_{2}^{3}}{12}$.

#### 2.2.3. Force of V-Shaped Actuator

_{y}= kU

_{y}, with k and U

_{y}given by Equation (12), with N = 1, and Equation (3), respectively.

#### 2.2.4. Force of Asymmetric Actuator

_{1}and A

_{2}) and lengths (L

_{1}and L

_{2}) of beams, the equivalent stiffness coefficient can be given by:

_{1}and k

_{2}were obtained from Equation (12). The force in the Y direction can be calculated as F

_{y}= kU

_{y}, with k and U

_{y}given by Equations (11) and (13), respectively.

#### 2.2.5. Electric Modelling of the Asymmetrical Microactuator

_{a}and A

_{a}are the length and cross-section area of the anchor, respectively, and ${L}_{2}=2{L}_{1}$. Electric current can be calculated from Equation (6), as I = V/R

_{e}.

_{e}= 248.57 Ω is obtained by Expression (6), considering ρ = 1.5 × 10

^{−4}Ω × m.

#### 2.3. Electrical Modeling of Microgripper

_{1}to R

_{13}are calculated by the well-known relation $R=\rho \frac{L}{A}$, where ρ is the resistivity, L and A are the length and the corresponding cross-section of the beam, respectively. The geometric sizes of the elements with R

_{1}to R

_{13}are given in Table 5. We considered ρ = 1.5 × 10

^{−4}Ω*m, and t = 70 µm.

_{h}, is obtained by performing the corresponding simplifications of the resistive circuit shown in Figure 5a, considering two transformations, the first one from delta to star, and the second one from star to delta. Therefore, the total resistance, R

_{T}, of the microgripper is calculated as the parallel of the two resistances R

_{h}as follows:

^{−4}Ω × m, Re = 41.74 Ω.

## 3. Results

#### 3.1. Multiphysics FEM Model of Asymmetric Microactuator

_{a}= 22 °C. As part of the device operating conditions, the pads were fixed. The left pad was set to a temperature of 22 °C, and its electric potential was set to 0 V. The right pad was set to 2 V. It should be noted that the simulations of microactuators 1 and 2 were performed with the same boundary conditions.

_{y}= 17.3 mN with an error of 28% and the the stiffness calculated using Equation (13) was 5250 N/m, with an error of 0.05%. It is necessary to mention that in simulation, thermal convection was used, which could increase the errors. Similar errors were observed for the case of the V-shaped actuator, where displacement has an error of 29%. In addition, in this first approach to the displacement calculation of the asymmetric actuator, no moments or reactions were considered.

#### 3.2. Multiphysics FEM Model of Microgripper

_{z}= 0.023 µm for the microgripper with damping elements, and without them, U

_{z}= 0.022 µm. In both cases, these values are small compared to the displacement in the other axis.

## 4. Discussion

_{2}= 2 L

_{1}, and W

_{2}= 5 W

_{1}), and applying 2 V, the temperature increases nonlinearly until approximately 100 °C in the short beam at ≈350 µm, and after, the growth is slower with a tendency to remain constant, in the range between ≈105 °C and 120 °C (Figure 7a). This actuator was compared with actuator 1 (L

_{2}= 2 L

_{1}, and W

_{2}= W

_{1}) and the V-shaped actuator (L = 3 L

_{1}/2, W = W

_{1}). In all cases, the temperature in the short beam of microactuator 2 was higher, which is a disadvantage.

_{n}= 37.994 kHz. Its maximum equivalent von Mises stress was 68.65 MPa, a lower value than the ultimate stress for Si (Table 11). The performance parameters of MWD also have larger values than the case of MWoutD (Table 10 and Table 11).

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Pistorio, F.; Saleem, M.M.; Somà, A. A dual-mass resonant MEMS gyroscope design with electrostatic tuning for frequency mismatch compensation. Appl. Sci.
**2021**, 11, 1129. [Google Scholar] [CrossRef] - Rasras, M.; Elfadel, I.A.; Ngo, H.D. Editorial for the special issue on MEMS accelerometers. Micromachines
**2019**, 10, 290. [Google Scholar] [CrossRef] [PubMed] - Zhang, Z.; Yu, Y.; Zhang, X. Vibration modes and parameter analysis of V-shaped electrothermal microactuators. Shock Vib.
**2018**, 2018, 1080652. [Google Scholar] [CrossRef] - Li, X.-C.; Li, Y.; Ding, B.-X.; Xu, H.-Y. An investigation on kinematics and dynamics performance of a novel 3-PRC-compliant parallel micromanipulator. Adv. Mech. Eng.
**2018**, 10, 168781401878980. [Google Scholar] [CrossRef] - Wang, S.; Yuan, X. The designing of magnetic-driven micromirror for portable ftirs. J. Sens.
**2018**, 2018, 1460582. [Google Scholar] [CrossRef] - Samaali, H.; Najar, F.; Choura, S. Dynamic Study of a capacitive MEMS switch with double clamped-clamped Microbeams. Shock Vib.
**2014**, 2014, 807489. [Google Scholar] [CrossRef] - Roy, A.; Nabi, M.; Rahman, N. Finite element compatible matrix interpolation for parametric model order reduction of electrothermal microgripper. J. Comput. Des. Eng.
**2021**, 8, 1622–1635. [Google Scholar] [CrossRef] - Farokhi, H.; Ghayesh, M.H.; Hussain, S. Large-amplitude dynamical behaviour of microcantilevers. Int. J. Eng. Sci.
**2016**, 106, 29–41. [Google Scholar] [CrossRef] - Arya, S.; Khan, S.; Lehana, P. Analytic model of Microcantilevers as low frequency generator. Modell. Simul. Eng.
**2014**, 2014, 38. [Google Scholar] [CrossRef] - Ruiz-Díez, V.; Hernando-García, J.; Toledo, J.; Ababneh, A.; Seidel, H.; Sánchez-Rojas, J.L. Piezoelectric MEMS linear motor for nanopositioning applications. Actuators
**2021**, 10, 36. [Google Scholar] [CrossRef] - Sriramdas, R.; Pratap, R. Scaling and performance analysis of MEMS Piezoelectric Energy Harvesters. J Microelectromech Syst
**2017**, 26, 679–690. [Google Scholar] [CrossRef] - Steiner, H.; Stifter, M.; Hortschitz, W.; Keplinger, F. Planar magnetostrictive micromechanical actuator. IEEE Trans. Magn.
**2015**, 51, 4700104. [Google Scholar] [CrossRef] - Tao, K.; Miao, J.; Lye, S.W.; Hu, X. Sandwich-structured two-dimensional MEMS electret power generator for low-level ambient vibrational energy harvesting. Sens Actuators A Phys.
**2015**, 228, 95–103. [Google Scholar] [CrossRef] - Fu, Q.; Suzuki, Y. A design method of in-plane MEMS Electret Energy Harvester with comb drives. J. Phys. Conf. Ser.
**2014**, 557, 012011. [Google Scholar] [CrossRef] - Tian, W.; Ling, Z.; Yu, W.; Shi, J. A review of MEMS scale Piezoelectric Energy Harvester. Appl. Sci.
**2018**, 8, 645. [Google Scholar] [CrossRef] - Bußmann, A.; Leistner, H.; Zhou, D.; Wackerle, M.; Congar, Y.; Richter, M.; Hubbuch, J. Piezoelectric silicon micropump for drug delivery applications. Appl. Sci.
**2021**, 11, 8008. [Google Scholar] [CrossRef] - Iannacci, J.; Tagliapietra, G. Getting Ready for Beyond-5G, Super-IoT and 6G at Hardware Passive Components Level—A Multi-State RF-MEMS Monolithic Step Attenuator Analyzed up to 60 GHz. Springer Link
**2022**, 28, 1235–1240. [Google Scholar] [CrossRef] - Yadav, R.; Yadav, R.; Nehra, V.; Rangara, K.J. RF MEMS Switches: Fabrication, Key Features, Application & Design Tools. Int. J. Electron. Eng.
**2011**, 3, 179–183. [Google Scholar] - Comtois, J.H.; Bright, V.M. Applications for surface-micromachined polysilicon thermal actuators and arrays. Sens. Actuators
**1997**, 58, 19–25. [Google Scholar] [CrossRef] - Varona, J.; Tecpoyotl-Torres, M.; Velazquez, R. Micro sensor-actuador térmico sin baterias para aplicaciones en microelectrónica de ultra-bajo consumo de potencia. Rev. Mex. De Fis.
**2013**, 59, 26–38. [Google Scholar] - Li, L.; Begbie, M.; Brown, G.; Uttamchandani, D. Design, simulation and characterization of a MEMS Optical Scanner. J. Micromech. Microeng.
**2007**, 17, 1781–1787. [Google Scholar] [CrossRef] - Yahya, Z.; Johar, M.A. Comparative performance study of smart structure for thermal microactuators. AIP Conf. Proc.
**2017**, 1931, 020041. [Google Scholar] - Wang, S.; Chun, Q.; You, Q.; Wang, Y.; Zhang, H. Dynamic modelling and experimental study of asymmetric optothermal microactuator. Opt. Commun.
**2017**, 383, 566–570. [Google Scholar] [CrossRef] - Thangavel, A.; Rengaswamy, R.; Sukumar, P.K.; Sekar, R. Modelling of chevron electrothermal actuator and its performance analysis. Microsyst. Technol.
**2018**, 24, 1767–1774. [Google Scholar] [CrossRef] - Hoang, K.T.; Nguyen, D.T.; Pham, P.H. Impact of design parameters on working stability of the electrothermal V-shaped actuator. Microsyst. Technol.
**2019**, 26, 1479–1487. [Google Scholar] [CrossRef] - Zhao, L.F.; Zhou, Z.F.; Meng, M.Z.; Li, M.J.; Huang, Q.A. An efficient electro-thermo-mechanical model for the analysis of V-shaped thermal actuator connected with driven structures. Int. J. Numer. Model. Electron. Netw. Devices Fields
**2020**, 34, e2843. [Google Scholar] [CrossRef] - Tecpoyotl Torres, M.; Cabello-Ruiz, R.; Vera-Dimas, J.G. Diseño y Simulación de un Microactuador Electrotérmico Optimizado con Brazos en Forma Z. Acta Univ.
**2015**, 25, 19–24. [Google Scholar] [CrossRef] - Zhang, Z.; Yu, Y.; Liu, X.; Zhang, X. A comparison model of V- and Z-shaped electrothermal microactuators. In Proceedings of the 2015 IEEE International Conference on Mechatronics and Automation (ICMA), Beijing, China, 2–5 August 2015. [Google Scholar]
- Zhang, Z.; Zhang, W.; Wu, Q.; Yu, Y.; Liu, X.; Zhang, X. Closed-form modelling and design analysis of V- and Z-shaped electrothermal microactuators. J. Micromech. Microeng.
**2016**, 27, 015023. [Google Scholar] [CrossRef] - Enikov, E.T.; Kedar, S.S.; Lazarov, K.V. Analytical model for analysis and design of V-shaped thermal microactuators. J Microelectromech Syst
**2005**, 14, 788–798. [Google Scholar] [CrossRef] - Guan, C.; Zhu, Y. An electrothermal microactuator with Z-shaped beams. J. Micromech. Microeng.
**2010**, 20, 085014. [Google Scholar] [CrossRef] - Ma, F.; Chen, G. Modeling V-shape thermal in-plane microactuator using chained beam-constraint-model. In Proceedings of the 2014 International Conference on Manipulation, Manufacturing and Measurement on the Nanoscale (3M-NANO), Taipei, Taiwan, 27–31 October 2014. [Google Scholar]
- Alamin Dow, A.B.; Jazizadeh, B.; Kherani, N.P.; Rangelow, I. Development and modeling of an electrothermally MEMS microactuator with an integrated microgripper. J. Micromech. Microeng.
**2011**, 21, 125026. [Google Scholar] [CrossRef] - Rezaei Kivi, A.; Azizi, S. On the dynamics of a micro-gripper subjected to electrostatic and piezoelectric excitations. Int. J. Non-Linear Mech.
**2015**, 77, 183–192. [Google Scholar] [CrossRef] - Shivhare, P.; Uma, G.; Umapathy, M. Design enhancement of a chevron electrothermally actuated microgripper for improved gripping performance. Microsyst. Technol.
**2015**, 22, 2623–2631. [Google Scholar] [CrossRef] - Yang, S.; Xu, Q. Design of a microelectromechanical systems microgripper with integrated electrothermal actuator and Force Sensor. Int. J. Adv. Robot. Syst.
**2016**, 13, 172988141666337. [Google Scholar] [CrossRef] - Wang, Z.; Shen, X.; Chen, X. Design, modeling, and characterization of a MEMS electrothermal microgripper. Microsyst. Technol.
**2015**, 21, 2307–2314. [Google Scholar] [CrossRef] - Cauchi, M.; Grech, I.; Mallia, B.; Mollicone, P.; Portelli, B.; Sammut, N. Essential design and fabrication considerations for the reliable performance of an electrothermal MEMS microgripper. Microsyst. Technol.
**2019**, 28, 1435–1450. [Google Scholar] [CrossRef] - Masood, M.U.; Saleem, M.M.; Khan, U.S.; Hamza, A. Design, closed-form modeling and analysis of su-8 based electrothermal microgripper for biomedical applications. Microsyst. Technol.
**2018**, 25, 1171–1184. [Google Scholar] [CrossRef] - Potekhina, A.; Voicu, R.-C.; Muller, R.; Al-Zandi, M.H.; Wang, C. Design and characterization of a polymer electrothermal microgripper with a polynomial flexure for efficient operation and studies of moisture effect on negative deflection. Microsyst. Technol.
**2020**, 27, 2723–2731. [Google Scholar] [CrossRef] - Zhu, Y.; Corigliano, A.; Espinosa, H. A thermal actuator for nanoscale in situ microscopy testing: Design and characterization. J. Micromech. Microeng.
**2006**, 16, 242–253. [Google Scholar] [CrossRef] - Li, M.; Zhou, Z.; Yi, L.; Wang, X.; Adnan, S. Design of a test structure based on chevron-shaped thermal actuator for in-situ measurement of the fracture strength of MEMS thin films. Nanotechnol. Precis. Eng.
**2019**, 2, 163–168. [Google Scholar] [CrossRef] - Novely, B. Análisis Matricial de estructuras por el método de la rigidez. In Problemas Resueltos e Introducción a los Elementos Finitos; Editor Independiente: Pamplona, Colombia, 2015. [Google Scholar]

**Figure 1.**(

**a**) Elements and geometric sizes, and (

**b**) operating conditions of the asymmetric microactuator.

**Figure 5.**(

**a**) Resistive equivalent circuit of one half of the microgripper with damping elements. (

**b**) Equivalent resistance.

**Figure 6.**Simulation results of (

**a**) deformation and (

**b**) equivalent von Mises stress of microactuator 1. (

**c**) Deformation and (

**d**) equivalent von Mises stress of microactuator 2. (

**e**) Deformation and (

**f**) equivalent von Mises stress of V-shaped microactuator.

**Figure 8.**(

**a**) Force, and (

**b**) 2D and (

**c**) 3D graph of equivalent von Mises stress microactuators 1, 2, and V-shaped.

**Figure 9.**Results of equivalent von Mises stress for the microactuators considered. A represents the pad fed with 0 V, B corresponds to the shuttle location of each actuator. C indicates the pad fed at 2 V. In A, B and C the von Mises stress values are shown.

**Figure 10.**Displacement of microgripper (

**a**) with and (

**b**) without damping elements. (

**c**) Displacement of microgripper with a V-shaped actuator.

**Figure 11.**(

**a**) Temperature distribution vs. length, (

**b**) force vs. applied voltage, and (

**c**) displacement vs. jaw length for the micro gripper with actuator 2, with and without damping elements, and with the V-shaped actuator.

**Figure 12.**Equivalent von Mises stress distribution for MWD, and MWoutD. A, D, G, and J represent the pad fed with 0 V. B, E, H, and K correspond to the shuttle location of each actuator. C, F, I, and L indicate the pad fed at 2 V.

**Table 1.**State of the art of recent V- and Z-shaped beam microactuators, and some of their fundamental parameters.

Ref. | Microactuator Type | Structural Material | Number of Pair of Beams | Inclination Angle | Dimensions (µm) | Software for Simulation | Displacement (µm) | Force (µN) | Stiffness (N/m) |
---|---|---|---|---|---|---|---|---|---|

[3] | V-shaped | Poly-Si | 1 | NA | 600 × 100 × 20 | Ansys™ | NA | NA | NA |

[12] | Planar magnetostrictive | Ni | 6 | 4° | 4 × 2 × 0.4 | Comsol™ | 10.2 | NA | 5.56 |

[24] | Chevron thermal | Al | 4 | 10° | 510 × 335 × 10 | Comsol™ | 10.94 | NA | NA |

[25] | V-shaped | Si | 10 | 2° | ≈1500 × 300 × 30 | Ansys™ | 70 | NA | NA |

[26] | V-shaped | Poly-Si | 10 | 10° | ≈600 × 400 × 10 | Comsol™ | 0.6 | NA | NA |

[28] | Z-shaped | Si | 2 | NA | 412 × 60 × 10 | Ansys™ | 0.2107 | NA | NA |

[30] | V-shaped | Ni | 1 | 0.5° | ≈1.5 × 12 × 21 | Ansys™ | ≈50 | 1000 | NA |

[31] | Z-shaped | Si | 2 | 10° | ≈176 × 88 × 10 | Ansys™ | 0.750 | 30–40 | NA |

[32] | V-shaped | Poly-Si | 3 | NA | ≈600 × 4 × 6.95 | Abaqus™ | ≈5 | ≈400 | NA |

Ref. | Microgripper Type | Microactuator Type | Structural Material | Simulated or Fabricated | Dimensions (µm) | Displacement of Tips (µm) | Initial Gap (µm) | Stress Max (kPa) | Force on Tips (µN) | Stiffness (N/m) |
---|---|---|---|---|---|---|---|---|---|---|

[33] | Electrothermal | U-beam | Si | Fabricated | ≈375 × 200 × 60 | ≈11 at 9 V | ≈15 | NA | NA | NA |

[34] | Electrostatic and piezoelectric | Two fully clamped symmetrically microbeams | Si and PZT | Simulated | ≈600 × 600 × NA | 2 at 18 V | ≈2 | ≈0.156 | NA | NA |

[35] | Electrothermal | Chevron | Poly-Si | Simulated | ≈1000 × 900 × 10 | 19.2 at 1 V | 100 | 470 | 0–17,000 | NA |

[36] | Electrothermal | Z-shaped | Poly-Si | Simulated | ≈2680 × 2750 × 50 | 80 at 6 V | 100 | Na | 6575 | 263 × 10^{−6} |

[37] | Electrothermal | U-shaped | Poly-Si | Fabricated | ≈280 × 100 × NA | 9.1 at 14 V | 20 | 104 | 36 to 14 V | 4.05 |

[38] | Electrothermal | U-shaped | Poly-Si | Fabricated | ≈1000 × 210 × 2 | 19.6 at 5 V | 5 | ND | 0.011 | NA |

[39] | Electrothermal | V-shaped | SU-8 | Simulated | ≈1650 × 800 × 9.85 | 11 at 80 mV | ND | 22 | 231 | NA |

[40] | Electrothermal | Z-shaped | SU-8 | Fabricated | ≈1300 × 500 × 20 | 80 at 0.4 V | 203.8 | NA | 26.3 | NA |

Parameters | Silicon Values |
---|---|

Density $\rho $ (kg/m^{3}) | 2329 |

Thermal expansion coefficient, α (C^{−1}) | 2.568 × 10^{−6} |

Young’s modulus, E (GPa) | 130.1 |

Poisson’s ratio, ν | 0.33 |

Isotropic thermal conductivity, κ (W/m °C) | 148 |

Isotropic resistivity, ${\rho}_{0}$ (Ω × m) | 0.00015 |

Average heat transfer coefficient, h (W/m^{2}K) | 25 |

Ultimate strength, (MPa) | 250 |

Convection coefficient (W/m^{2} °C) | 25 |

Element Description | Dimensions (µm) | Element Description | Dimensions (µm) |
---|---|---|---|

Length of the short and thin beam of the microactuator (L_{1}) | 400 | Gripper length from shaft to damping elements 1 (L_{g}_{1}) | 631 |

Length of long and thick beam length of the microactuator (L_{2} = 2 × L_{1}) | 800 | Gripper length from damping elements to jaw 2 (L_{g}_{2}) | 770 |

Width of the short and thin beam of the microactuator (w_{1}) | 5 | Width of the base beam of gripper 1 (w_{g}_{1}) | 25 |

Width of long and thick beam length of the microactuator (w_{2}) | 25 | Width of the Z section of gripper 2 (w_{g}_{2}) | 50 |

Length of shuttle (Ls) | 192.5 | Width of the base of jaw 3 (w_{g}_{3}) | 25 |

Width of shuttle (Ws) | 60 | Thickness of the structure (t) | 70 |

Length of damping beam 1 (L_{3}) | 154.5 | Gap (initial aperture between jaws) | 50 |

Length of damping beam 2 (L_{4}) | 301 | Pre-bending angle of the microactuator beams (θ) | 91° |

Length of damping beam 3 (L_{5}) | 170.5 | Pre-bending angle of the damping beam 2 (θ_{2}) | 22° |

Width of upper gap between gripper arms (w_{3}) | 78.5 | Pre-bending angle of the damping beam 3 (θ_{3}) | 31° |

Width of damping beams (w_{4}) | 9.5 | Pre-bending angle between the beam base of the gripper and the pad (θ_{4}) | 80° |

Resistance | Length (µm) | Width (µm) | Resistance | Length (µm) | Width (µm) |
---|---|---|---|---|---|

R_{1} | 200 | 263.72 | R_{8} | 192 | 25 |

R_{2} | 400 | 25 | R_{9} | 154.6 | 3.5 |

R_{3} | 400 | 5 | R_{10} | 293.56 | 25 |

R_{4} | 232.5 | 60 | R_{11} | 170.44 | 3.57 |

R_{5} | 400 | 25 | R_{12} | 300 | 25 |

R_{6} | 240.92 | 50 | R_{13} | 200 | 100 |

R_{7} | 300.7 | 1.75 |

**Table 6.**Technical details about FEA in Ansys Workbench for microactuators 1 and 2, and the V-shaped microactuator.

Device | Solver Target | Element Type/Mesh/Number of DOF | Face Sizing with Element Size | Inflation | Convergence | Total Mass (kg) | |||
---|---|---|---|---|---|---|---|---|---|

Transition Ratio | Max. Layers | Growth Rate | No. of Total Nodes | No. of Total Elements | |||||

Microactuator 1 | Mechanical APDL | SOLID 187/refinement controlled program | Default | 0.272 | 5 | 1.2 | 3941 | 1749 | 0.7776 × 10^{−8} |

Microactuator 2 | 3003 | 1324 | 1.176 × 10^{−8} | ||||||

V-shaped microactuator | 26,237 | 12507 | 7.77 × 10^{−9} |

**Table 7.**Comparison of performance parameters of microactuators 1 and 2, and the V-shaped microactuator obtained by simulation in ANSYS™.

Device | Displacement @ 2 V (µm) | Force at 2 V (mN) | Stiffness (N/m) |
---|---|---|---|

Microactuator 1 | 6.69 | 5.4 | 807.17 |

Microactuator 2 | 4.8 | 24 | 5000 |

V-shaped actuator | 6.23 | 5.1 | 818.620 |

Device | Maximum Von Misses Stress (MPa) | ||
---|---|---|---|

Point A | Point B | Point C | |

Microactuator 1 | 29.8 | 11.5 | 163.8 |

Microactuator 2 | 53.3 | 57.3 | 74.2 |

V-shaped actuator | 34.4 | 14.4 | 161.8 |

Device | Solver Target | Physics Type and Analysis Type | Element Type/Mesh/Number of DOF | Inflation | Convergence | Total Mass (kg) | |||
---|---|---|---|---|---|---|---|---|---|

Transition Ratio | Max. Layers | Growth Rate | No. of Total Nodes | No. of Total Elements | |||||

*MWD | Mechanical APDL | Electric -> steady-state Thermal-electric conduction (1) | Solid187/refinement/39356 | 0.272 | 5 | 1.2 | 20,223 | 10877 | 0.551 × 10^{−7} |

*MWoutD | Solid187/refinement/36432 | 12,834 | 5685 | 0.545 × 10^{−7} | |||||

*MWVS | Structural -> static structural (2) | Solid187/refinement/38304 | 13,478 | 5930 | 0.534 × 10^{−7} |

Actuator | Displacement (µm) at 2 V | Force (mN) at 2 V | ∆T at 2 V | Natural Frequency (kHz) |
---|---|---|---|---|

MWoutD | 1.830 | 70.151 | 111.53 | 14.899 |

MWD | 2.426 | 73.61 | 111.52 | 37.994 |

MWVS | 0.426 | 42.11 | 111.09 | 11.361 |

Von Misses Stress (MPa) | |||||
---|---|---|---|---|---|

MWD | |||||

A | B | C | D | E | F |

24.2 | 34.8 | 68.65 | 18.0 | 37.93 | 57.26 |

MWoutD | |||||

G | H | I | J | K | L |

33.98 | 35.13 | 71.74 | 27.8 | 42.1 | 72.19 |

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**MDPI and ACS Style**

Tecpoyotl-Torres, M.; Vargas-Chable, P.; Escobedo-Alatorre, J.; Cisneros-Villalobos, L.; Sarabia-Vergara, J.
Z-Shaped Electrothermal Microgripper Based on Novel Asymmetric Actuator. *Micromachines* **2022**, *13*, 1460.
https://doi.org/10.3390/mi13091460

**AMA Style**

Tecpoyotl-Torres M, Vargas-Chable P, Escobedo-Alatorre J, Cisneros-Villalobos L, Sarabia-Vergara J.
Z-Shaped Electrothermal Microgripper Based on Novel Asymmetric Actuator. *Micromachines*. 2022; 13(9):1460.
https://doi.org/10.3390/mi13091460

**Chicago/Turabian Style**

Tecpoyotl-Torres, Margarita, Pedro Vargas-Chable, Jesus Escobedo-Alatorre, Luis Cisneros-Villalobos, and Josahandy Sarabia-Vergara.
2022. "Z-Shaped Electrothermal Microgripper Based on Novel Asymmetric Actuator" *Micromachines* 13, no. 9: 1460.
https://doi.org/10.3390/mi13091460