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Design of a large-range rotary microgripper with freeform geometries using a genetic algorithm

Design of a large-range rotary microgripper with freeform geometries using a genetic algorithm This paper describes a novel electrostatically actuated microgripper with freeform geometries designed by a genetic algorithm. This new semiautomated design methodology is capable of designing near-optimal MEMS devices that are robust to fabrication tolerances. The use of freeform geometries designed by a genetic algorithm significantly improves the performance of the microgripper. An experiment shows that the designed microgripper has a large displacement (91.5 μm) with a low actuation voltage (47.5 V), which agrees well with the theory. The microgripper has a large actuation displacement and can handle micro-objects with a size from 10 to 100 μm. A grasping experiment on human hair with a diameter of 77 μm was performed to prove the functionality of the gripper. The result confirmed the superior performance of the new design methodology enabling freeform geometries. This design method can also be extended to the design of many other MEMS devices. Introduction ref. was based on a piezoelectric actuated microgripper. Microelectromechanical system (MEMS) microgrippers Although this design features a large displacement and are microscale grippers fabricated through a micro- bandwidth, it requires a complicated fabrication process machined process, and typically comprise actuators, and exhibits hysteresis nonlinearity, which severely limits mechanical parts for the handling and manipulation of its spatial resolution during manipulation. micro-objects (1–100 μm) and force sensors. MEMS Moreover, piezoelectric actuated microgrippers cannot microgrippers are widely used in handling cells and tis- work in a high-temperature environment. A magnetically 1 6 sues in biology and in microassembling and testing the actuated gripper was reported in ref. . This design pro- mechanical properties of micromachined devices . vides a large displacement and a quick response with MEMS microgrippers with different shapes, actuation, reasonable sensitivity, but it requires a complicated and and sensing principles have been developed in recent expensive assembly process. Alternatively, a microgripper 3,4 7 years. The designs reported in refs. were thermally based on a shape memory alloy was discussed in ref. . actuated microgrippers. These microgrippers have a large This design had excellent flexibility and large bandwidth. displacement and a low actuation voltage. However, the However, it also suffered hysteresis nonlinearity and large high working temperature of thermally actuated micro- power consumption. Electrostatically actuated micro- 8,9 grippers can be harmful to living cells and tissues in grippers were reported in refs. . In particular, for the biological manipulation. Another design described in first time, Chang et al. introduced a rotary actuation comb into an electrostatically actuated microgripper to increase the displacement range to 94 μm with an actuation vol- Correspondence: Huafeng Liu (huafengliu@hust.edu.cn) or Jian Bai (bai@zju. tage of 100 V . These designs feature a fast response edu.cn) College of Optical Science and Engineering, Zhejiang University, Hangzhou, time, low power consumption and no hysteresis. How- China ever, these designs have a relatively large dimension due Department of Electrical Engineering and Computer Science, University of to the high number of actuation comb fingers required. In Liege, Liege, Belgium Full list of author information is available at the end of the article © The Author(s) 2022 Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to theCreativeCommons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/. 1234567890():,; 1234567890():,; 1234567890():,; 1234567890():,; Wang et al. Microsystems & Nanoengineering (2022) 8:3 Page 2 of 14 addition, the maximum displacement of the electro- design of freeform geometries for MEMS sensors. Speci- statically actuated microgripper is limited by the pull-in fically, a MEMS accelerometer comprising a mechanical effect . In addition, the actuation voltage of the electro- motion amplifier was described to demonstrate the statically actuated microgrippers is relatively high, and effectiveness of the design approach . In the following, normally, a voltage larger than 80 V is required to achieve we describe a MEMS actuator (i.e., microgripper) with a displacement of 100 μm. Such a high actuation voltage is freeform geometries that are designed and optimized by not only problematic in practical applications but can also the GA-based design method. Due to the freeform geo- damage gripped samples. metries, the designed microgripper features a large dis- In the vast majority of MEMS devices, simple geome- placement with a low actuation voltage compared with trical layouts comprising only a few basic building blocks, previously described electrostatic microgrippers. Detailed such as beams, rectangular masses, and, more rarely, rings theoretical analysis and experimental validation are con- or disk-shaped structures, are used . As discussed in the ducted. A manipulation experiment using the designed following, there are cases in which such conventional, microgripper for grasping human hair is shown. More- simple designs limit the performance of MEMS devices over, the pull-in effect in electrostatically actuated and therefore may not meet the requirements for specific microgrippers is also discussed. The performances of the applications. Compared with conventional designs, geo- designed microgrippers are compared with those of metries comprising more complex geometries offer a existing microgrippers. designer more freedom. Complex geometries may result in novel designs with superior performance and over- Design of the microgripper with freeform 14–17 come the limitation of simple mechanisms . For geometries example, by using curved anti-springs, Middlemiss et al. A design methodology based on a genetic algorithm and Boom et al. developed MEMS accelerometers with The microgripper in this work was designed using a resolutions at the nano-g level. These anti-springs feature novel design method allowing freeform geometries based a low effective spring constant that cannot be achieved on a GA. The methodology comprises two parts: a para- with conventional orthogonal designs under the same metrized mechanical finite element model (FEM) with fabrication constraints. However, complex theoretical freeform geometries implemented in COMSOL and a calculations are needed to design these complex geome- GA implemented in MATLAB , illustrated by the flow tries. Such a design method requires considerable design chart in Fig. 1. The FEM model and simulation in expertise and is practically impossible to transfer to other COMSOL can be directly controlled by MATLAB devices; a case-by-case approach is required. An alter- through LiveLink for MATLAB . A GA is based on the native is topology optimization, which can be used to mechanics of natural selection and genetics, combining design MEMS devices with complex geometries. Ana- the fittest individuals in the population to search for the 16,17 18 nthasuresh et al. and Seshia et al. developed com- best solution. These evolutionary-based techniques are plex force and motion amplification mechanisms to excellent for particularly complex, multiparameter pro- increase the sensitivity of accelerometers. Cao and Zhang blems for which they are capable of finding good solutions et al. developed a module optimization method as a uni- in a short period of time. For optimization, the GA sets fied design approach for both compliant mechanisms and the parameter values of a mechanical model and simulates rigid-body mechanisms . In the module optimization each “individual” parameter set in the first generation. approach, the states of joints and links are fully para- Using a performance goal (or figure of merit (FOM)) meterized, with which a designer can obtain a rigid-body function, the GA generates a new parameter set for the mechanism, a partially compliant mechanism, or a fully compliant mechanism for a given design objective. Simulate However, in these MEMS devices, simple beam (or truss) elements are typically used as a fundamental building System Set block to form optimized topologies. Such methodology Mechanical model Performance Parameters easily results in designs that often cannot be fabricated since it is difficult to implement fabrication constraints well in the topology optimization process . In this paper, we introduce a novel electrostatically Genetic Goal(s) actuated microgripper with freeform geometries designed algorithm function / FOM by a genetic algorithm (GA) approach. The novel design approach is introduced by describing the optimization Fig. 1 Optimization system. Generic process flow of the novel process for a microgripper as a case study. In our previous designed method with freeform geometries based on a GA work, a GA was introduced for the first time for the Wang et al. Microsystems & Nanoengineering (2022) 8:3 Page 3 of 14 a b Beam end P4 Beam end ×10 μm P5 P2 P5 P2 –1 Arm tip P1 P4 P1 Gripper arm Bézier 2 ×10 μm Rotary comb Bézier 1 Bézier 2 Bézier 1 actuator P0 P3 P3 P0 Beam end Beam end Fixed comb Connecting beam Anchor Moving direction Moving comb Fig. 2 Proposed microgripper with freeform geometries and misalignment of rotary microgrippers. a Schematic view of the proposed microgripper with freeform geometries showing an arm tip, gripper arm, rotary comb actuator, connecting beam (freeform geometries), and anchor. The moving direction of the microgripper is along the direction of blue arrows. b With the use of Bezier curves, any beam can be defined with coordinates of six points. An orthogonal beam can be modified into a curved beam easily by just modifying the coordinates of P1 and P4. c Movement of a rotary comb actuator after actuation. The red line is the position of the moving comb before actuation, while the solid blue part is the position of the moving comb after actuation. The R-axis is along the radial axis of rotary comb fingers, which is the undesired displacement of comb fingers. The θ-axis is along the tangent direction of rotary comb fingers (perpendicular to the R-axis), which is the desired movement direction of comb fingers. The undesired movement along the radial axis, i.e., R , reduces the gap between the fixed and moving comb fingers next generation. After several generations, the parameter simple orthogonal structures with structures based on values converge, indicating that the mechanical model freeform geometries and explore how this can improve reaches an optimal design. The details of the design the performance of the microgripper. process are described in the following. In our design methodology, Bezier curves were used to define and parameterize the freeform geometries in the Microgripper model with freeform geometries connecting beam area. A curve can be described by a Bezier A schematic drawing of a microgripper with freeform curve with only three coordinate points. Therefore, a beam geometries is shown in Fig. 2a. It comprises rotary comb can be defined by two Bezier curves, in which 12 parameters actuators, two gripper arms, two-arm tips to grasp micro- are used to describe the (X, Y) coordinates of 6 points, as objects, and connecting beams that link the moveable showninFig. 2b. An orthogonal beam can be easily mod- structures to anchors. The gap between the two arm tips ified into a curved beam, as illustrated in Fig. 2b, in which is 100 μm. When a voltage is applied to the rotary comb only the coordinates of points P1 and P4 are modified. The actuators, due to electrostatic force, the microgripper will number of parameters is significantly reduced, which saves move in the direction of the blue arrows, as indicated in computational resources for optimization. Fig. 2a. This displacement is mechanically amplified and transferred to the arm tips through the gripper arms; this Parameter ranges and geometrical design constraints effectively functions as a mechanical lever . The critical The parameter ranges and geometrical design con- part of the microgripper is the connecting beam. It defines straints were defined based on the fabrication process the total stiffness of the structure, which influences the described in ref. and are listed in Table 1. The mini- actuation voltage, actuation displacement, bandwidth, mum width of the freeform geometries was set as 7 µm to maximum stress, etc. However, the connecting beams of prevent parts from becoming too fragile. All para- most microgrippers in the literature are based only on meterized variables have lower and upper bounds (LBs 8,10,22–25 simple orthogonal structures . Their shape is far and UBs, respectively). LBs and UBs are determined either from fully explored, and there is no evidence of achieving based on (i) practical limitations, such as fabrication tol- an optimal design. More complex, freeform geometrical erance and voltage limitation, or (ii) a qualified guess by shapes may result in a solution with superior perfor- the designer of the optimum value. It is important to mances, such as a much lower actuation voltage and a clarify that the GA was used to optimize only the con- larger displacement. Therefore, we propose replacing nected beam freeform geometry, gripper Arm geometry, Radial axis Radial axis m Wang et al. Microsystems & Nanoengineering (2022) 8:3 Page 4 of 14 Table 1 Definition, symbol, and upper and lower bounds of parameters Parameter Symbol LB UB Gripper arm length L 500 μm 1700 μm Gripper arm width W 50 μm 150 μm Arm tip length L 100 μm 200 μm Arm tip width W 40 μm 100 μm Arm tip angle A 35° 35° Finger angle A 24° 24° Finger angle offset O 4° 4° Finger length L 44 μm44 μm Finger width W 5 μm5 μm Finger gap G 3 μm3 μm Rotary actuator length L 700 μm 1000 μm Rotary actuator width W 15 μm30 μm Connecting beam length L 50 μm 300 μm Connecting beam width W 7 μm7 μm Connecting beam top length L 100 250 CT Connecting beam top width ratio WR 0.5 0.5 CT Connecting beam top ShiftX SX −150 μm 150 μm CT Connecting beam middle length ratio LR 0.1 0.9 CM Connecting beam middle width ratio WR 0.5 0.5 CM Connecting beam middle ShiftX SX −150 μm 150 μm CM Connecting beam bottom width ratio WR 0.5 0.5 CB Connecting beam bottom ShiftX SX −150 μm 150 μm CB rotary actuator length, and rotary actuator width. The GA Therefore, one important constraint during the optimi- algorithm was not applied to the other parts of the design zation process is that R needs to be less than 1.3 μm. that were related to generating electrostatic force among It is important to note that during the optimization, the the comb fingers. design space for the connecting beams is fixed (390 × The movement of a rotary comb actuator after actua- 390 μm ) for the GA; this enables objective comparison of tion can be best described by a polar coordinate system, as different designs. It could be argued that for an ortho- illustrated in Fig. 2c. The R-axis is defined along the radial gonal beam design, the actuation range can be improved direction of the rotary comb fingers; this is an undesired by simply increasing the length of the connecting beam. displacement direction of comb fingers and should be However, in a fixed design space, the two adjacent minimized . The θ-axis is along the tangential direction orthogonal connecting beams will cross each other if the of rotary comb fingers (perpendicular to the R-axis), two connecting beams are prolonged beyond a certain which is the desired movement direction of comb fingers level, which is obviously physically impossible. A serpen- and should be maximized. The displacement of the rotary tine orthogonal beam could be used to prevent this and comb actuator along the R-axis, i.e., R , reduces the gap prolong the beam length; however, this reduces the stiff- between the fixed and moving combs. As a result, the gaps ness in the radial direction and thus increases R , leading of a moving comb finger with respect to the two neigh- to a low pull-in event. Therefore, constraining the design boring fixed comb fingers are no longer equal. With any to a conventional orthogonal shape does not fully explore further increase in the actuation voltage, electrostatic the design space and does not achieve an optimal design. pull-in will thus occur if R is larger than one-third of the More complex freeform geometrical shapes may result in comb finger gap (4 μm), i.e., 1.3 μm . The pull-in effect a solution with superior performance. Thus, we propose limits the maximum displacement of the microgripper. replacing simple orthogonal structures with structures Wang et al. Microsystems & Nanoengineering (2022) 8:3 Page 5 of 14 200 μm 1st generation 2nd generation 3rd generation 4th generation 6th generation 5th generation 7th generation 8th generation Fig. 3 Optimization process. The shape of the connecting beams changes during the GA optimization based on freeform geometries. Their shapes can be opti- performed several postprocessing steps. These included mized with the GA to improve the actuation range at a picking the ten best individuals (elite preservation), low actuation voltage. deriving a certain number of new random individuals (mutation), and cross-fertilizing good individuals to create Figures of merit new offspring. This last step involved taking different In the following, we regard the sum of the displace- parameters from different good individuals and combin- ments at the two gripper arm tips as the displacement of ing them to create a new individual (child). These three the microgripper, X . Ideally, a large X with a low steps created the parameter value set for the 2nd gen- T T actuation voltage is desired for an electrostatically actu- eration. Then, the GA started the same optimization ated microgripper. Therefore, X for a fixed actuation process for the second generation as for the first gen- voltage (40 V) was used as the FOM for the design pro- eration. For each simulation, a row of values was recorded cess. The gap between the arm tips of the microgripper and displayed in the command window of MATLAB. was designed as 100 μm, which obviously defines an upper In the first generation, the FOM varied considerably, limit for X . These values were chosen because most of indicating that the algorithm still explored the design the electrostatic microgrippers described in the literature space. After the first generation, the GA already tended to require a voltage above 80 V to reach an X of 100 μm. find designs that have a large FOM. In the end, the GA Therefore, 40 V represents a typical mid-range actuation consistently settled toward designs with a higher FOM voltage, suitable for comparison. and started to converge. Consequently, the GA is programmed in such a way that Figure 3 shows a graphical illustration of the optimi- it maximizes X while maintaining R less than 1.3 μm. zation process, which went through eight generations. T m The GA considerably changed the shape of the connect- Optimization process ing beams. During the optimization, the GA attempted to In the first step of the optimization process, the GA ran make the connecting beams more compliant by bending 40 individuals (i.e., designs with a specific parameter set), them to increase X . In addition, the GA folded the which were chosen randomly within the parameter ran- connecting beams to increase their length, which further ges. For each individual, a FEM simulation was carried out reduced the stiffness and improved X . However, due to for the fully parameterized mechanical model. The FEM the rotary comb actuator, the connecting beams would simulation included a static displacement simulation for a not only move along the tangential axis but also exhibit fixed actuation voltage. For the simulation, the electro- undesired movement along the radial axis, as illustrated in mechanical multiphysics functionality in COMSOL was Fig. 2c. This increased the displacement of the micro- used, in which the electrostatic actuation force was cal- gripper in the R-axis in Fig. 2c. Thus, the GA attempted to culated based on the number and geometry of the comb reduce R by making the bends of two curved connecting fingers and the actuation voltage. The value of R > beams face each other. In that way, the undesired move- 1.3 μm or a convergence failure of the simulation indi- ment of two curved connecting beams was in opposing cated a pull-in event. The simulation result was auto- directions and canceled each other, reducing R . Finally, matically transferred to the GA in MATLAB, which the undesired movement of the rotary comb actuator was recorded and sorted the results based on the FOM and reduced. (this will be discussed in detail in Section V.C). Wang et al. Microsystems & Nanoengineering (2022) 8:3 Page 6 of 14 Table 2 Definition, symbol, and upper and lower bounds of parameters Parameter CB7-D1 CB7-D2 SB7 Gripper arm length 1520 μm 1534 μm 1545 μm Gripper arm width 78 μm88 μm88 μm Arm tip length 180 μm 210 μm 190 μm Arm tip width 79 μm85 μm90 μm Arm tip angle 35° 35° 35° Finger angle 24° 24° 24° Finger angle offset 4° 4° 4° Finger length 44 μm44 μm44 μm Finger width 5 μm5 μm5 μm Finger gap 3 μm3 μm3 μm Rotary actuator length 940 μm 949 μm 960 μm Rotary actuator width 20 μm18 μm21 μm Connecting beam length 230 μm 221 μm 200 μm Connecting beam width 7 μm7 μm7 μm Connecting beam top length 210 198 238 Connecting beam top width ratio 0.5 0.5 0.5 Connecting beam top ShiftX 5 μm4 μm0 μm Connecting beam middle length ratio 0.6 0.7 0.5 Connecting beam middle width ratio 0.5 0.5 0.5 Connecting beam middle ShiftX 25 μm30 μm0 μm Connecting beam bottom width ratio 0.5 0.5 0.5 Connecting beam bottom ShiftX 130 μm 112 μm0 μm Robustness analysis shown in Fig. 3. As mentioned before, the minimum beam The next step in the design process was a robustness width for all designs was set to 7 μm during the optimi- analysis, which started by collecting 10 individuals with the zation process. It is worth noting that the whole optimi- highest FOM; these were taken as optimal design candidates. zation process took 8 h with a 3D mechanical model and For the robustness analysis, the designer had to specify a 6 h with a 2D mechanical model using a laptop with an i7 standard deviation of each design parameter representing core of 2.5 GHz working frequency and 8 G RAM. The the fabrication tolerances. One hundred Gaussian dis- optimization was completed in 8 h, with little manual tributed parameter sets were calculated for all parameters intervention. The optimization process would take much of an individual using the mean value and designer- less time if it ran on a workstation or in a parallel supplied standard deviations. These effectively represent computation mode. the fabrication tolerances. Therefore, for each individual, Two types of freeform designs were selected as the 100 simulations were run, and the FOMs were recorded. A optimal designs, referred to as CB7-D1 (Fig. 6b (1)) and minimum threshold for the FOM was set by the designer. CB7-D2 (Fig. 6b (2)); their parameter values are listed in A yield value was calculated, representing the percentage Table 2. CB7-D1 had a larger X than CB7-D2. CB7-D2 of the simulations for each individual above the minimum had a larger R than CB7-D1. The difference between the FOM. The designer finally had to choose one as the final two designs was mainly because CB7-D1 had a more design by reviewing the yield and the FOM of the inves- compliant freeform beam than CB7-D2. tigated individuals based on the application requirement. To compare the freeform designs with a conventional orthogonal design, the same GA optimization algorithm Optimization result was also run with constraints allowing only an orthogonal The GA optimization ran continuously for eight gen- design. An identical design space (390 × 390 μm ) was erations, with one generation size of 40 individuals, as chosen for the connecting beams to allow for an objective Wang et al. Microsystems & Nanoengineering (2022) 8:3 Page 7 of 14 Table 3 The FOMs and simulated yield of microgripper design CB7-D1, CB7-D2, and SB7 Performance FOM (μm) Yield (%) CB7-D1 59 80 CB7-D2 49 79 SB7 24 87 Max stress comparison. The optimal orthogonal design was termed SB7 (Fig. 6b (3)); Table 3 also lists its FOM. Compared with CB7-D1 and CB7-D2, SB7 had the lowest FOM. 0 42 Modal von mises stress (MPa) Here, 80% of the FOM value in each optimal design was taken as the minimum threshold of acceptable FOM Fig. 4 Optimization result. A von Mises stress contour plot of the values during the robustness analysis. optimal freeform design CB7-D1 with an actuation voltage of 53 V and According to the robustness analysis, CB7-D1, CB7-D2, an X of 100 μm and SB7 had a yield of 86% (minimum FOM of 47 μm), 84% (minimum FOM of 39 μm), and 90% (minimum FOM of 19 μm), respectively. directly related to the stiffness of the connecting beams. As a freeform design has many degrees of freedom, it is The freeform design CB7-D1 is thus expected to be less necessary to disperse the parameter values during the harmful to fragile samples during manipulation compared optimization to achieve a global rather than a locally with the orthogonal design SB7. optimal solution. However, an excessively dispersed parameter space makes the optimization process com- Dynamic analysis putationally intensive. To study the convergence, the GA Given the significant influence of vibration modes and carried out ten independent optimization processes by stress on the microgripper, these parameters were ana- using different initial designs across the design space. As lyzed next. The frequencies of the first three modes of circumstantial evidence, the topologies of ten optimal freeform design CB7-D1 were 823, 10,583 and 27,932 Hz, solutions resembled each other, indicating a global con- respectively. The 2nd mode frequency is 11.86 times lar- vergence of the optimization process to a large extent. ger than the working mode (1st mode) frequency, which The FOMs of the designs obtained in 10 different opti- considerably increases the stability during actuation. The mization runs ranged from 47 to 60 μm. frequencies of the first three modes of freeform design CB7-D2 and orthogonal design SB7 are listed in Table 5; Static analysis the mode shapes of CB7-D1 were very similar. According to a FEM simulation in COMOL, the free- form design CB7-D1 had an X of 100 μm for a DC Stress analysis actuation voltage of 53 V, as shown in Fig. 4. The freeform In our design, the connecting beams are used to design CB7-D2 had an X of 100 μm for a DC actuation support the movable structures and to bend during a voltage of 57 V. The optimized orthogonal design SB7 had gripping operation. This makes the connecting beams an X of 41 μm for a DC actuation voltage of 53 V and the most fragile part of the design, and thus, they could 48 μm for a DC actuation voltage of 57 V. A DC actuation break under a large electrostatic force input. Hence, a voltage of 85 V was required for the orthogonal design stress analysis was performed to predict the stress SB7 to reach an X of 100 μm. Comparing the freeform distribution of the microgripper during actuation. design CB7-D1 with the orthogonal design SB7, X was According to a FEM simulation in COMSOL, when the increased by 144% for the same DC actuation voltage of freeform microgripper CB7-D1 reached 100 μm(its 53 V, as shown in Table 4. In addition, the actuation force maximum X ), the maximum Von Mises stress was for the freeform design CB7-D1 to reach an X of 100 μm 42MPa(as showninFig. 4), whichismuchsmaller was only 39% of that of the orthogonal design SB7, as than the yield strength of single-crystal silicon, i.e., shown in Table 4. Therefore, the stiffness of the con- 7GPa . This low-stress value is another benefitofthe necting beams in the freeform design CB7-D1 is lower freeform geometries and the GA optimization. Com- than that in the orthogonal design SB7. The output force pared with orthogonal beams, stress can be more of the gripper when grasping a micro-object is an evenly distributed by the curved shapes of freeform important parameter of the gripper performance, which is beams, and stress concentration can be prevented. Wang et al. Microsystems & Nanoengineering (2022) 8:3 Page 8 of 14 Table 4 X of microgripper design CB7-D1, CB7-D2, and Table 5 First three modes of the microgripper design SB7 under different actuation voltages CB7-D1, CB7-D2, SB7 DC actuation voltage (V) 53 57 85 Design 1st Mode (Hz) 2nd Mode (Hz) 3rd Mode (Hz) CB7-D1 X (μm) 100 / / CB7-D1 823 10583 27932 CB7-D2 X (μm) 83 100 / CB7-D2 906 11484 29365 SB7 X (μm) 41 48 100 SB7 1245 16975 48530 Additionally, the GA attempted to reduce the stress to Experiment results and discussion increase the X since a low-stress concentration leads Experiment setup to a large X .Asshown in Fig. 4, the stress was evenly As showninFig. 7a, the measurement setup included a distributed on the freeform. As will be discussed later, voltage source, a multimeter, a microscope with a camera, in the experiment, none of the microgrippers broke and an electronic circuit. The voltage source could supply a during actuation. Furthermore, the microgripper did DC voltage ranging from 0 to 60 V. The multimeter was used not break even when we manually probed the arm tips to measure the exact voltage supplied to the microgripper. A of the microgripper to release them from the actuation microscope with a camera was used to measure the dis- combs after a pull-in event. As shown in Fig. 4,the placement and gripping action of the microgripper. The maximum Von Mises stress of CB7-D1 was located at electronic circuit included some protecting resistors in case the turning point of the freeform beam. The maximum pull-in occurred and the current would become too high. Von Mises stresses of microgripper design CB7-D2 and design SB7 were 44 and 179 MPa, respectively, when Gripping range test result they reached an X of 100 μm. First, the gripping ranges were tested. Two types of freeform designs, i.e., CB7-D1 (blue line) and CB7-D2 (red Fabrication line)), and one orthogonal design, i.e., SB (black line), were Figure 5 shows the SOI-based process flow used in tested. When different voltages were applied to the microgrippers, the images of the arm tips were acquired this work, which is similar to that described in ref. . After etching a pattern of frame trenches on the handle and processed to calculate the displacement. In Fig. 7b, layer of a wafer by deep reactive-ion etching, another the experimental results of three types of microgrippers pattern of trenches and etch holes were etched on the are shown with a solid line, i.e., CB7-D1(E), CB7-D2(E), front side in a 50-μm-thick device layer. The handle and SB7(E). The experimental results indicated that the layers beneath the rotary comb actuators, gripper arms, microgripper design CB7-D1 provided a gripping range of and arm tips were removed to increase yield and 73 μm with an actuation voltage of 40 V and design CB7- reliability by offsetting the two trench patterns by D2 gripping range of 91.5 μm with an actuation voltage of 40 µm. Finally, the devices were separated from each 47.5 V. Limited by the maximum voltage of the voltage other by HF vapor phase etching without the usage of a source, microgripper design SB7 provided a gripping dicing step. range of 48.0 μm with an actuation voltage of 60 V. Since Figure 6a shows the fabricated microgripper CB7-D1 the orthogonal design SB7 is only used to evaluate the with the curved shapes of the freeform beams. For improvement of the freeform designs CB7-D1 and CB7- designs CB7-D2 and SB7, the structure was identical to D2 under the same actuation voltage, 60 V was sufficient CB7-D1, except for the connecting beams. A compar- for testing design SB7. ison of the connecting beams of CB7-D1, CB7-D2, and In Fig. 7b, the simulated results of the respective designs SB7 is shown in Fig. 6b. We fabricated 172 chips on a are also plotted (dashed lines), i.e., CB7-D1(S), CB7-D2(S), 4-in. wafer, including freeform and orthogonal designs and SB7(S). The experimental results agree well with the with achipsizeof3.7×3.7mm . Approximately, simulation results. The small discrepancy is due to fab- 90–95% of all fabricated chips had complete structures rication tolerances of the gripper parameters and the pull- and were fully functional after release, bonding, and in effect. packaging. This fabrication result indicated that the The displacements of the microgrippers were compared yield rate of the freeform MEMS devices was as good as not only at the arm tips but also in the areas of the rotary that of the orthogonal MEMS designs as long as rules comb actuators and connecting beams. A comparison of concerning minimum feature size (such as minimum the three types of microgripper designs with an actuation etching trenches, minimum widths) were followed. voltage of 40 V is shown in Fig. 6b (1)–(3), in which the Wang et al. Microsystems & Nanoengineering (2022) 8:3 Page 9 of 14 Wafer grid Process layer Sacrificial oxide layer Handle wafer trenches Device features Release holes Process layer trenches 50 mm ‘Handle wafer blocks’ iii ii iii iii Release areas Device & handle wafer block Etched oxide d Wafer grid 4.7 mm Released device from the wafer grid Released ‘handle 4.7 mm wafer blocks’ behind microlevers f Fig. 5 Fabrication process. Fabrication flow of the MEMS devices: a Backside etching using DRIE to define the backside trenches. b Front side DRIE to pattern the device features, release holes, and front side trenches. c Three release regions, namely, (i) device, (ii) handle wafer block release features, and (iii) dicing features, were etched consecutively by hydrofluoric acid in the vapor phase. d Device separation after release . e Image of the wafer grid of step (f) (the solid area resulting from a lithography fault). f Image of the released devices. (I) The front image of the released device, (II) back image of the released device, and (III) released “handle wafer blocks” highest stiffness (the smallest X red contours indicate the position of the structure before under the same actua- actuation. The X of design CB7-D1 was larger than that tion force). CB7-D2 and CB7-D1 have the second and of design CB7-D2, which, in turn, was larger than that of third lowest nonlinearities of the connection beam stiff- design SB7 in all three areas. Since CB7-D1 could not be ness under the same actuation force. Thus, the higher the actuated higher than 40 V (which is close to the pull-in connecting beam stiffness is, the lower the nonlinearity of voltage), the comparison of designs CB7-D2 and SB7 was the connecting beam stiffness under the same actuation made with an actuation voltage of 47.5 V. The X of force is. design CB7-D2 was much larger than that of the design According to the simulation, the total capacitance of the SB7 in all three comparison areas. In summary, for the rotary comb actuators in CB7-D1 changes from 2.28 to same actuation voltage, microgrippers with freeform 3.16 pF after achieving a deflection X of 72.9 μm. The geometries improved the X by 150–200% compared with total capacitance of the rotary comb actuators in CB7-D2 orthogonal geometries in the same die area. changes from 2.28 to 3.28 pF after achieving a deflection Figure 7c shows the relationships between the actuation X of 91.5 μm. The total capacitance of the rotary comb force and X for the three designs, i.e., CB7-D1, CB7-D2, actuators in S7-D2 changes from 2.28 to 3.00 pF after and SB7. Linear fittings were plotted using the least- achieving a deflection X of 54 μm. The effect of the squares method. In terms of the connecting beam stiff- fringing field does not play an important role and can be 8,10 ness, CB7-D1 has a nonlinearity of 5.5% in the worst case ignored during the actuation process . for a 51 μN actuation force range; CB7-D2 has a non- linearity of 5.6% in the worst case for a 72 μN actuation Pull-in of rotary comb drives force range; SB7 has a nonlinearity of 2.2% in the worst For design CB7-D1, an actuation voltage higher than case for a 115 μN actuation force range. CB7-D1, CB7-D2, 40 V led to the pull-in of the rotary comb actuators, as and SB7 have a nonlinearity of 5.5%, 5.2%, and 1.2% in the shown in Fig. 8a. For an actuation voltage of 40 V, the R worst case for a 51 μN actuation force range, respectively. of SB7 was not observable, whereas the R of CB7-D2 was As shown in Fig. 7c, among the three designs, SB7 has the approximately two times smaller than that of CB7-D1. In lowest nonlinearity of the connection beam stiffness addition, pull-in occurred when the gripper of design under the same actuation force range, as SB7 has the CB7-D1 moved 74 μm under an actuation voltage of 41 V. Wang et al. Microsystems & Nanoengineering (2022) 8:3 Page 10 of 14 100 um Arm tip 50 um Gripper arm 100 um 100 um Rotary comb actuator Freeform beam Anchor CB7 D1 27.1um 43.0 um 77.3 um CB7 D1 CB7 D2 SB7 (1) (2) (3) 100um 100um 100um 100um 100um 100um 11um 17um 11um 100um 100um 100um 40VDC 40VDC 40VDC Fig. 6 Fabricated microgrippers and their displacement under 40 V actuation. a Metallographic microscope image of the freeform microgripper CB7-D1. b The images of the microgripper CB7-D1, CB7-D2, and SB7 under a certain actuation voltage. Image (1)–(3). The images of the microgripper CB7-D1, CB7-D2, and SB7 under an actuation voltage of 40 V. For comparison, the red contours indicate the position of the structure before actuation. The upper images show the arm tip area, the middle shows the rotary comb actuator area, and the bottom images show the connecting beam area. (1) CB7-D1, (2) CB7-D1, and (3) SB7 for an actuation voltage of 40 V. For comparison, the red contours indicate the position of the structure before actuation. The upper images show the arm tip area. The middle images show the rotary comb actuator area. The bottom images show the connecting beam area Pull-in occurred in design CB7-D1 due to R becoming point first, as the long lever of the rotary comb actuator too large, resulting from the undesired movement of the acts as a motion amplifier. curved beam along the R-axis. As shown in Fig. 8a. (4), the The pull-in effect can easily be mitigated by increasing outermost comb fingers had the largest R value com- the stiffness of the connecting beams along the R-axis pared with other comb fingers and reached the pull-in (e.g., by increasing the beam width). However, this will Wang et al. Microsystems & Nanoengineering (2022) 8:3 Page 11 of 14 Microscope & camera 4.7 mm Multimeter Power supply Microgripper chip Electronic circuit Straight beam (SB) VS curved beam (CB) Straight beam (SB) VS curved beam (CB) with 7um minimum width with 7um minimum width CB7 D1(E) CB7D1(E) CB7 D2(E) CB7D2(E) SB7(E) SB7(E) CB7 D1(F) CB7D1(S) CB7 D2(F) CB7D2(S) SB7 (F) SB7(S) 20 20 10 10 0 0 0 10203040 50 60 020 40 60 80 100 120 Voltage (V) Force (uN) Fig. 7 Measurement setup and result. a Measurement setup. b Characterization of the simulated and measured X versus actuation voltages in two freeform designs (CB7-D1 (blue line), CB7-D2 (red line)) and one orthogonal design (SB (black line)). Simulated results (dashed lines): CB-7D1(S), CB7-D2(S), SB7(S). Measured results (solid lines): CB7-D1 (E), CB7-D2 (E), SB7 (E). c Characterization of the simulated and measured X vs. actuation force in two freeform designs (CB7-D1 (blue), CB7-D2 (red)) and one orthogonal design (SB (black)). Linear fitting lines (solid lines): CB-7D1 (F), CB7-D2 (F), SB7 (F). Measured results (dots): CB7-D1(E), CB7-D2(E), SB7(E) reduce the X for a given actuation voltage. After opti- Then, the microgripper was driven with a voltage of 31 V mization, design CB7-D2 reached a larger X (91.5 μm) and gripped the hair, as shown in Fig. 8b (2). The measured with a higher pull-in voltage (47.5 V). gap of the arm tips was 70 μm, smaller than the diameter of the hair, indicating successful gripping of the hair. In Demonstration of micro-object gripping addition, according to Fig. 7b, CB7-D2 was expected to To demonstrate the performance of the fabricated have an X of 30 μm for an actuation voltage of 31 V, microgripper, microgripper design CB7-D2 was used to matching the experimental result shown in Fig. 8b(2). grip human hair with a diameter of 77 μm. The position of the microgripper relative to the hair before the gripping Discussion test is shown in Fig. 8b (1), in which the gap of the arm For the same actuation voltage, microgrippers with tips is 100 μm. It is worth noting that the micro stick-slip freeform geometries (CB7-D1 and CB7-D2) improved X motion between the object and arm tip is mainly deter- by 150–200% compared with orthogonal geometries (SB7) mined by the friction force. In ref. , Zhang and Liu et al. for the same die area. Therefore, the use of freeform found that micro stick-slip motion could be explained by geometries has two practical advantages: (i) a lower the Stribeck model, Dahl model, and LuGre model. The actuation voltage to reach the same X and (ii) less harm LuGre model has the best accuracy. The Coulomb friction to fragile objects during gripping and releasing. model and the elastoplastic model do not work in a micro However, electrostatic rotary microgrippers exhibit an stick-slip motion system. undesired radial displacement R during actuation. This X (um) X (um) T Wang et al. Microsystems & Nanoengineering (2022) 8:3 Page 12 of 14 ab (1) Human hair 11um (1) (2) 11um 26 77 um um um Small misalignment No obvious misalignment 45 100 45 100um 0VDC 40 V SB7 40 V CB7 D2 um um um (3) (4) (2) 11um 11um 77 um 26 26 Large misalignment Pull - in um um 40 V CB7 D1 41 V CB7 D1 70 60 100um 31VDC um um um Fig. 8 Results of 47.5 V actuation experiment, pull-in experiment, and gripping experiment. a Images of designs CB7-D2 and SB7 under an actuation voltage of 47.5 V. Comparison of radial deflection R of the rotary comb actuators for different microgripper designs. (1) No apparent R in m m the microgripper design SB7 under an actuation voltage of 40 V. (2) Small R in the microgripper design CB7-D2 under an actuation voltage of 40 V. (3) Large R in the microgripper design CB7-D1 under an actuation voltage of 40 V. (4) Pull-in of the microgripper design CB7-D1 under an actuation voltage of 41 V. b Gripping a human hair with a diameter of 77 μm using microgripper design CB7-D2 (1) before gripping and (2) after gripping leads to a reduction in the gap of the comb drive elec- ability in Hao et al.’s design is due to its narrow beam- trode, potentially causing pull-in, which limits the max- width (3.6 μm). If the beamwidth of CB7-D2 was reduced imal X . With the proposed optimization method, the R from 7 to 3.6 μm, a simulation indicated that CB7-D2 T m of the rotary comb actuators is included in the FOM. The would only need 27 V to have an X of 100 μm, which is GA-based optimization concurrently maximizes X and smaller than the 31 V of Hao et al.s design. Moreover, the actuation voltage can be further reduced through an minimizes R for a given voltage. Comparing the two freeform designs, CB7-D1 has a increase in the number of rotary comb actuators, since larger X but a larger R compared with CB7-D2 for the Hao et al.’s design has six groups of rotary comb actua- T m same actuation voltage. Thus, a designer can select free- tors, while our designs only have four groups of rotary form designs according to different requirements for the comb actuators. gripping range. For example, for objects with a diameter In addition, the CB7-D1 and the CB7-D2 design were between 100 and 30 μm, design CB7-D1 is superior to developed based on Chang et al.’s design . Compared CB7-D2, as CB7-D1 can satisfy the gripping range with a with Chang et al.’s design , the CB7-D1 actuation ability lower actuation voltage. Additionally, for objects with a is 4.8 times larger, while the gripping range is 1.4 times diameter between 100 and 10 μm, CB7-D2 is better than lower, whereas the design CB7-D2 actuation ability is 4.3 CB7-D1, as CB7-D1 can offer a larger gripping range, times larger, while the gripping range is 1.1 times lower. while CB7-D1 pulls in after 74 μm. Table 6 compares the gripping range of our micro- Conclusions grippers with those of other electrostatically actuated A novel microgripper with freeform geometries microgrippers in the literature. To compare the actuation designed using a GA approach is presented. The GA- ability of different designs fairly, the maximum X is divi- based semiautomated design methodology with freeform ded by the square of the related actuation voltage, and the geometries is introduced in detail. It is capable of calculated result is taken as the actuation ability. Crescenzi designing near-optimal MEMS devices that are robust to et al.’s design have the highest actuation ability and lowest fabrication tolerances. Two types of microgrippers with actuation force but a limited gripping range. Compared freeform geometries and one microgripper with ortho- with Crescenzi et al.’s design, the CB7-D1 actuation ability gonal geometries were optimized by this method. FEA is 6 times lower, while the gripping range is 3.6 times lar- simulations were used to analyze the static and dynamic ger, whereas the design CB7-D2 actuation ability is 5 times performance as well as the stress distribution of the lower, while the gripping range is 4.6 times larger. designed microgrippers. The experiment showed that the Hao et al.’s design has the second-highest actuation microgripper with freeform geometries had a large X ability and largest gripping range. The high actuation (91.5 μm) for a low actuation voltage (47.5 V), which axis Radial Wang et al. Microsystems & Nanoengineering (2022) 8:3 Page 13 of 14 Table 6 Comparison of different gripper operating displacements Design Actuation force Actuation Actuation range Actuation ability Die area (μm ) Gripper arm (μN) voltage (V) (μm) (nm/V ) length (mm) Volland 231 80 20 3.13 1250*3300 1 Beyeler 986 150 100 4.44 7700*5600 3.3 Chen 1646 80 25 3.91 5745*3217 1 Bazaz 1181 50 17 6.80 4891*6402 2.5 Chang 297 100 94 9.40 3100*3700 1.7 Piriyanont 104 80 90 14.06 8500*5600 1.6 Xu 273 72 63 12.15 2800*3812 NA Hao 37 31.5 100 100.78 4500*4000 1.7 Crescenzi 3 11 20 165.29 2710*4417 1.4 (CB7-D1) 51 40 72.9 45.54 3700*3700 1.7 (CB7-D2) 72 47.5 91.5 40.55 3700*3700 1.7 (SB7) 115 60 54 15.00 3700*3700 1.7 From COMSOL simulation. agreed well with the theory. This made it possible to Acknowledgements This research was funded by the Science Challenge Project, grant no. manipulate a wide range of objects (size ranging from 10 TZ2016006-0502-02, and the National Key Research and Development to 100 μm). The concept was successfully demonstrated Program of China, grant no. 2021YFB3201603. by grasping a human hair with a diameter of 77 μm. A Author details detailed analysis of the pull-in effect due to the R of the College of Optical Science and Engineering, Zhejiang University, Hangzhou, actuator electrodes was conducted. Possible methods to China. Department of Electrical Engineering and Computer Science, University mitigate this effect were also discussed. of Liege, Liege, Belgium. ESAT-MNS, University of Leuven, Leuven, Belgium. PGMF and School of Physics, Huazhong University of Science and For the same actuation voltage, microgrippers with Technology, Wuhan, China freeform geometries improved X by 150–200% com- pared with orthogonal geometries in the same die area. Author contributions Thus, freeform geometries have two advantages: (i) a C.W. designed, built, and tested the MEMS microgripper. W.F. and Y.W. contributed to the design of the MEMS mechanism. X.S., S.S., and M.G. lower actuation power to reach the same X and (ii) less contributed to the MEMS fabrication. H.L. contributed to the measurement harm to fragile objects during gripping and releasing. setup. C.W., W.F., and Y.W. took the measurements. H.Z., C.W., Y.W, and A.Q. In Table 6, we briefly compare our freeform geometry performed computational analysis of the data. C.W., H.L., J.B., and M.K. led the writing of the paper, and all authors provided comments. H.L., J.B., and M.K. design with the two best electrostatic microgrippers had the initial concept of the microgripper. H.L. and J.B. oversaw the design, 8,9 described in the literature in terms of actuation range fabrication, and testing of the microgripper. and X per voltage 2 (actuation ability). Both freeform Conflict of interest geometries developed in this work have a larger gripping The authors declare that they have no conflict of interest. range compared to Crescenzi et al. . If the same number of actuation comb fingers is considered, our designs have Supplementary information The online version contains supplementary a better actuation ability compared to Hao et al. . material available at https://doi.org/10.1038/s41378-021-00336-0. The improved performance of the microgripper is mainly due to the use of GA for freeform geometric Received: 6 April 2021 Accepted: 10 November 2021 design. It is worth noting that the proposed design methodology enabling freeform geometries can be extended to a wide range of other MEMS devices. Future work will include equipping the microgripper with both References 1. Thornell, G., Bexell, M., Schweitz, J.-Å. & Johansson, S. Design and fabrication of force sensing and a feedback system. This will allow the a gripping tool for micromanipulation. Sens. Actuators A 53,428–433 (1996). gripping process to be performed with higher precision 2. Ansel, Y.,Schmitz, F., Kunz,S., Gruber,H.& Popovic, G. 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Design of a large-range rotary microgripper with freeform geometries using a genetic algorithm

Design of a large-range rotary microgripper with freeform geometries using a genetic algorithm

This paper describes a novel electrostatically actuated microgripper with freeform geometries designed by a genetic algorithm. This new semiautomated design methodology is capable of designing near-optimal MEMS devices that are robust to fabrication tolerances. The use of freeform geometries designed by a genetic algorithm significantly improves the performance of the microgripper. An experiment shows that the designed microgripper has a large displacement (91.5 μm) with a low actuation voltage (47.5 V), which agrees well with the theory. The microgripper has a large actuation displacement and can handle micro-objects with a size from 10 to 100 μm. A grasping experiment on human hair with a diameter of 77 μm was performed to prove the functionality of the gripper. The result confirmed the superior performance of the new design methodology enabling freeform geometries. This design method can also be extended to the design of many other MEMS devices. Introduction ref. was based on a piezoelectric actuated microgripper. Microelectromechanical system (MEMS) microgrippers Although this design features a large displacement and are microscale grippers fabricated through a micro- bandwidth, it requires a complicated fabrication process machined process, and typically comprise actuators, and exhibits hysteresis nonlinearity, which severely limits mechanical parts for the handling and manipulation of its spatial resolution during manipulation. micro-objects (1–100 μm) and force sensors. MEMS Moreover, piezoelectric actuated microgrippers cannot microgrippers are widely used in handling cells and tis- work in a high-temperature environment. A magnetically 1 6 sues in biology and in microassembling and testing the actuated gripper was reported in ref. . This design pro- mechanical properties of micromachined devices . vides a large displacement and a quick response with MEMS microgrippers with different shapes, actuation, reasonable sensitivity, but it requires a complicated and and sensing principles have been developed in recent expensive assembly process. Alternatively, a microgripper 3,4 7 years. The designs reported in refs. were thermally based on a shape memory alloy was discussed in ref. . actuated microgrippers. These microgrippers have a large This design had excellent flexibility and large bandwidth. displacement and a low actuation voltage. However, the However, it also suffered hysteresis nonlinearity and large high working temperature of thermally actuated micro- power consumption. Electrostatically actuated micro- 8,9 grippers can be harmful to living cells and tissues in grippers were reported in refs. . In particular, for the biological manipulation. Another design described in first time, Chang et al. introduced a rotary actuation comb into an electrostatically actuated microgripper to increase the displacement range to 94 μm with an actuation vol- Correspondence: Huafeng Liu (huafengliu@hust.edu.cn) or Jian Bai (bai@zju. tage of 100 V . These designs feature a fast response edu.cn) College of Optical Science and Engineering, Zhejiang University, Hangzhou, time, low power consumption and no hysteresis. How- China ever, these designs have a relatively large dimension due Department of Electrical Engineering and Computer Science, University of to the high number of actuation comb fingers required. In Liege, Liege, Belgium Full list of author information is available at the end of the article © The Author(s) 2022 Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to theCreativeCommons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/. 1234567890():,; 1234567890():,; 1234567890():,; 1234567890():,; Wang et al. Microsystems & Nanoengineering (2022) 8:3 Page 2 of 14 addition, the maximum displacement of the electro- design of freeform geometries for MEMS sensors. Speci- statically actuated microgripper is limited by the pull-in fically, a MEMS accelerometer comprising a mechanical effect . In addition, the actuation voltage of the electro- motion amplifier was described to demonstrate the statically actuated microgrippers is relatively high, and effectiveness of the design approach . In the following, normally, a voltage larger than 80 V is required to achieve we describe a MEMS actuator (i.e., microgripper) with a displacement of 100 μm. Such a high actuation voltage is freeform geometries that are designed and optimized by not only problematic in practical applications but can also the GA-based design method. Due to the freeform geo- damage gripped samples. metries, the designed microgripper features a large dis- In the vast majority of MEMS devices, simple geome- placement with a low actuation voltage compared with trical layouts comprising only a few basic building blocks, previously described electrostatic microgrippers. Detailed such as beams, rectangular masses, and, more rarely, rings theoretical analysis and experimental validation are con- or disk-shaped structures, are used . As discussed in the ducted. A manipulation experiment using the designed following, there are cases in which such conventional, microgripper for grasping human hair is shown. More- simple designs limit the performance of MEMS devices over, the pull-in effect in electrostatically actuated and therefore may not meet the requirements for specific microgrippers is also discussed. The performances of the applications. Compared with conventional designs, geo- designed microgrippers are compared with those of metries comprising more complex geometries offer a existing microgrippers. designer more freedom. Complex geometries may result in novel designs with superior performance and over- Design of the microgripper with freeform 14–17 come the limitation of simple mechanisms . For geometries example, by using curved anti-springs, Middlemiss et al. A design methodology based on a genetic algorithm and Boom et al. developed MEMS accelerometers with The microgripper in this work was designed using a resolutions at the nano-g level. These anti-springs feature novel design method allowing freeform geometries based a low effective spring constant that cannot be achieved on a GA. The methodology comprises two parts: a para- with conventional orthogonal designs under the same metrized mechanical finite element model (FEM) with fabrication constraints. However, complex theoretical freeform geometries implemented in COMSOL and a calculations are needed to design these complex geome- GA implemented in MATLAB , illustrated by the flow tries. Such a design method requires considerable design chart in Fig. 1. The FEM model and simulation in expertise and is practically impossible to transfer to other COMSOL can be directly controlled by MATLAB devices; a case-by-case approach is required. An alter- through LiveLink for MATLAB . A GA is based on the native is topology optimization, which can be used to mechanics of natural selection and genetics, combining design MEMS devices with complex geometries. Ana- the fittest individuals in the population to search for the 16,17 18 nthasuresh et al. and Seshia et al. developed com- best solution. These evolutionary-based techniques are plex force and motion amplification mechanisms to excellent for particularly complex, multiparameter pro- increase the sensitivity of accelerometers. Cao and Zhang blems for which they are capable of finding good solutions et al. developed a module optimization method as a uni- in a short period of time. For optimization, the GA sets fied design approach for both compliant mechanisms and the parameter values of a mechanical model and simulates rigid-body mechanisms . In the module optimization each “individual” parameter set in the first generation. approach, the states of joints and links are fully para- Using a performance goal (or figure of merit (FOM)) meterized, with which a designer can obtain a rigid-body function, the GA generates a new parameter set for the mechanism, a partially compliant mechanism, or a fully compliant mechanism for a given design objective. Simulate However, in these MEMS devices, simple beam (or truss) elements are typically used as a fundamental building System Set block to form optimized topologies. Such methodology Mechanical model Performance Parameters easily results in designs that often cannot be fabricated since it is difficult to implement fabrication constraints well in the topology optimization process . In this paper, we introduce a novel electrostatically Genetic Goal(s) actuated microgripper with freeform geometries designed algorithm function / FOM by a genetic algorithm (GA) approach. The novel design approach is introduced by describing the optimization Fig. 1 Optimization system. Generic process flow of the novel process for a microgripper as a case study. In our previous designed method with freeform geometries based on a GA work, a GA was introduced for the first time for the Wang et al. Microsystems & Nanoengineering (2022) 8:3 Page 3 of 14 a b Beam end P4 Beam end ×10 μm P5 P2 P5 P2 –1 Arm tip P1 P4 P1 Gripper arm Bézier 2 ×10 μm Rotary comb Bézier 1 Bézier 2 Bézier 1 actuator P0 P3 P3 P0 Beam end Beam end Fixed comb Connecting beam Anchor Moving direction Moving comb Fig. 2 Proposed microgripper with freeform geometries and misalignment of rotary microgrippers. a Schematic view of the proposed microgripper with freeform geometries showing an arm tip, gripper arm, rotary comb actuator, connecting beam (freeform geometries), and anchor. The moving direction of the microgripper is along the direction of blue arrows. b With the use of Bezier curves, any beam can be defined with coordinates of six points. An orthogonal beam can be modified into a curved beam easily by just modifying the coordinates of P1 and P4. c Movement of a rotary comb actuator after actuation. The red line is the position of the moving comb before actuation, while the solid blue part is the position of the moving comb after actuation. The R-axis is along the radial axis of rotary comb fingers, which is the undesired displacement of comb fingers. The θ-axis is along the tangent direction of rotary comb fingers (perpendicular to the R-axis), which is the desired movement direction of comb fingers. The undesired movement along the radial axis, i.e., R , reduces the gap between the fixed and moving comb fingers next generation. After several generations, the parameter simple orthogonal structures with structures based on values converge, indicating that the mechanical model freeform geometries and explore how this can improve reaches an optimal design. The details of the design the performance of the microgripper. process are described in the following. In our design methodology, Bezier curves were used to define and parameterize the freeform geometries in the Microgripper model with freeform geometries connecting beam area. A curve can be described by a Bezier A schematic drawing of a microgripper with freeform curve with only three coordinate points. Therefore, a beam geometries is shown in Fig. 2a. It comprises rotary comb can be defined by two Bezier curves, in which 12 parameters actuators, two gripper arms, two-arm tips to grasp micro- are used to describe the (X, Y) coordinates of 6 points, as objects, and connecting beams that link the moveable showninFig. 2b. An orthogonal beam can be easily mod- structures to anchors. The gap between the two arm tips ified into a curved beam, as illustrated in Fig. 2b, in which is 100 μm. When a voltage is applied to the rotary comb only the coordinates of points P1 and P4 are modified. The actuators, due to electrostatic force, the microgripper will number of parameters is significantly reduced, which saves move in the direction of the blue arrows, as indicated in computational resources for optimization. Fig. 2a. This displacement is mechanically amplified and transferred to the arm tips through the gripper arms; this Parameter ranges and geometrical design constraints effectively functions as a mechanical lever . The critical The parameter ranges and geometrical design con- part of the microgripper is the connecting beam. It defines straints were defined based on the fabrication process the total stiffness of the structure, which influences the described in ref. and are listed in Table 1. The mini- actuation voltage, actuation displacement, bandwidth, mum width of the freeform geometries was set as 7 µm to maximum stress, etc. However, the connecting beams of prevent parts from becoming too fragile. All para- most microgrippers in the literature are based only on meterized variables have lower and upper bounds (LBs 8,10,22–25 simple orthogonal structures . Their shape is far and UBs, respectively). LBs and UBs are determined either from fully explored, and there is no evidence of achieving based on (i) practical limitations, such as fabrication tol- an optimal design. More complex, freeform geometrical erance and voltage limitation, or (ii) a qualified guess by shapes may result in a solution with superior perfor- the designer of the optimum value. It is important to mances, such as a much lower actuation voltage and a clarify that the GA was used to optimize only the con- larger displacement. Therefore, we propose replacing nected beam freeform geometry, gripper Arm geometry, Radial axis Radial axis m Wang et al. Microsystems & Nanoengineering (2022) 8:3 Page 4 of 14 Table 1 Definition, symbol, and upper and lower bounds of parameters Parameter Symbol LB UB Gripper arm length L 500 μm 1700 μm Gripper arm width W 50 μm 150 μm Arm tip length L 100 μm 200 μm Arm tip width W 40 μm 100 μm Arm tip angle A 35° 35° Finger angle A 24° 24° Finger angle offset O 4° 4° Finger length L 44 μm44 μm Finger width W 5 μm5 μm Finger gap G 3 μm3 μm Rotary actuator length L 700 μm 1000 μm Rotary actuator width W 15 μm30 μm Connecting beam length L 50 μm 300 μm Connecting beam width W 7 μm7 μm Connecting beam top length L 100 250 CT Connecting beam top width ratio WR 0.5 0.5 CT Connecting beam top ShiftX SX −150 μm 150 μm CT Connecting beam middle length ratio LR 0.1 0.9 CM Connecting beam middle width ratio WR 0.5 0.5 CM Connecting beam middle ShiftX SX −150 μm 150 μm CM Connecting beam bottom width ratio WR 0.5 0.5 CB Connecting beam bottom ShiftX SX −150 μm 150 μm CB rotary actuator length, and rotary actuator width. The GA Therefore, one important constraint during the optimi- algorithm was not applied to the other parts of the design zation process is that R needs to be less than 1.3 μm. that were related to generating electrostatic force among It is important to note that during the optimization, the the comb fingers. design space for the connecting beams is fixed (390 × The movement of a rotary comb actuator after actua- 390 μm ) for the GA; this enables objective comparison of tion can be best described by a polar coordinate system, as different designs. It could be argued that for an ortho- illustrated in Fig. 2c. The R-axis is defined along the radial gonal beam design, the actuation range can be improved direction of the rotary comb fingers; this is an undesired by simply increasing the length of the connecting beam. displacement direction of comb fingers and should be However, in a fixed design space, the two adjacent minimized . The θ-axis is along the tangential direction orthogonal connecting beams will cross each other if the of rotary comb fingers (perpendicular to the R-axis), two connecting beams are prolonged beyond a certain which is the desired movement direction of comb fingers level, which is obviously physically impossible. A serpen- and should be maximized. The displacement of the rotary tine orthogonal beam could be used to prevent this and comb actuator along the R-axis, i.e., R , reduces the gap prolong the beam length; however, this reduces the stiff- between the fixed and moving combs. As a result, the gaps ness in the radial direction and thus increases R , leading of a moving comb finger with respect to the two neigh- to a low pull-in event. Therefore, constraining the design boring fixed comb fingers are no longer equal. With any to a conventional orthogonal shape does not fully explore further increase in the actuation voltage, electrostatic the design space and does not achieve an optimal design. pull-in will thus occur if R is larger than one-third of the More complex freeform geometrical shapes may result in comb finger gap (4 μm), i.e., 1.3 μm . The pull-in effect a solution with superior performance. Thus, we propose limits the maximum displacement of the microgripper. replacing simple orthogonal structures with structures Wang et al. Microsystems & Nanoengineering (2022) 8:3 Page 5 of 14 200 μm 1st generation 2nd generation 3rd generation 4th generation 6th generation 5th generation 7th generation 8th generation Fig. 3 Optimization process. The shape of the connecting beams changes during the GA optimization based on freeform geometries. Their shapes can be opti- performed several postprocessing steps. These included mized with the GA to improve the actuation range at a picking the ten best individuals (elite preservation), low actuation voltage. deriving a certain number of new random individuals (mutation), and cross-fertilizing good individuals to create Figures of merit new offspring. This last step involved taking different In the following, we regard the sum of the displace- parameters from different good individuals and combin- ments at the two gripper arm tips as the displacement of ing them to create a new individual (child). These three the microgripper, X . Ideally, a large X with a low steps created the parameter value set for the 2nd gen- T T actuation voltage is desired for an electrostatically actu- eration. Then, the GA started the same optimization ated microgripper. Therefore, X for a fixed actuation process for the second generation as for the first gen- voltage (40 V) was used as the FOM for the design pro- eration. For each simulation, a row of values was recorded cess. The gap between the arm tips of the microgripper and displayed in the command window of MATLAB. was designed as 100 μm, which obviously defines an upper In the first generation, the FOM varied considerably, limit for X . These values were chosen because most of indicating that the algorithm still explored the design the electrostatic microgrippers described in the literature space. After the first generation, the GA already tended to require a voltage above 80 V to reach an X of 100 μm. find designs that have a large FOM. In the end, the GA Therefore, 40 V represents a typical mid-range actuation consistently settled toward designs with a higher FOM voltage, suitable for comparison. and started to converge. Consequently, the GA is programmed in such a way that Figure 3 shows a graphical illustration of the optimi- it maximizes X while maintaining R less than 1.3 μm. zation process, which went through eight generations. T m The GA considerably changed the shape of the connect- Optimization process ing beams. During the optimization, the GA attempted to In the first step of the optimization process, the GA ran make the connecting beams more compliant by bending 40 individuals (i.e., designs with a specific parameter set), them to increase X . In addition, the GA folded the which were chosen randomly within the parameter ran- connecting beams to increase their length, which further ges. For each individual, a FEM simulation was carried out reduced the stiffness and improved X . However, due to for the fully parameterized mechanical model. The FEM the rotary comb actuator, the connecting beams would simulation included a static displacement simulation for a not only move along the tangential axis but also exhibit fixed actuation voltage. For the simulation, the electro- undesired movement along the radial axis, as illustrated in mechanical multiphysics functionality in COMSOL was Fig. 2c. This increased the displacement of the micro- used, in which the electrostatic actuation force was cal- gripper in the R-axis in Fig. 2c. Thus, the GA attempted to culated based on the number and geometry of the comb reduce R by making the bends of two curved connecting fingers and the actuation voltage. The value of R > beams face each other. In that way, the undesired move- 1.3 μm or a convergence failure of the simulation indi- ment of two curved connecting beams was in opposing cated a pull-in event. The simulation result was auto- directions and canceled each other, reducing R . Finally, matically transferred to the GA in MATLAB, which the undesired movement of the rotary comb actuator was recorded and sorted the results based on the FOM and reduced. (this will be discussed in detail in Section V.C). Wang et al. Microsystems & Nanoengineering (2022) 8:3 Page 6 of 14 Table 2 Definition, symbol, and upper and lower bounds of parameters Parameter CB7-D1 CB7-D2 SB7 Gripper arm length 1520 μm 1534 μm 1545 μm Gripper arm width 78 μm88 μm88 μm Arm tip length 180 μm 210 μm 190 μm Arm tip width 79 μm85 μm90 μm Arm tip angle 35° 35° 35° Finger angle 24° 24° 24° Finger angle offset 4° 4° 4° Finger length 44 μm44 μm44 μm Finger width 5 μm5 μm5 μm Finger gap 3 μm3 μm3 μm Rotary actuator length 940 μm 949 μm 960 μm Rotary actuator width 20 μm18 μm21 μm Connecting beam length 230 μm 221 μm 200 μm Connecting beam width 7 μm7 μm7 μm Connecting beam top length 210 198 238 Connecting beam top width ratio 0.5 0.5 0.5 Connecting beam top ShiftX 5 μm4 μm0 μm Connecting beam middle length ratio 0.6 0.7 0.5 Connecting beam middle width ratio 0.5 0.5 0.5 Connecting beam middle ShiftX 25 μm30 μm0 μm Connecting beam bottom width ratio 0.5 0.5 0.5 Connecting beam bottom ShiftX 130 μm 112 μm0 μm Robustness analysis shown in Fig. 3. As mentioned before, the minimum beam The next step in the design process was a robustness width for all designs was set to 7 μm during the optimi- analysis, which started by collecting 10 individuals with the zation process. It is worth noting that the whole optimi- highest FOM; these were taken as optimal design candidates. zation process took 8 h with a 3D mechanical model and For the robustness analysis, the designer had to specify a 6 h with a 2D mechanical model using a laptop with an i7 standard deviation of each design parameter representing core of 2.5 GHz working frequency and 8 G RAM. The the fabrication tolerances. One hundred Gaussian dis- optimization was completed in 8 h, with little manual tributed parameter sets were calculated for all parameters intervention. The optimization process would take much of an individual using the mean value and designer- less time if it ran on a workstation or in a parallel supplied standard deviations. These effectively represent computation mode. the fabrication tolerances. Therefore, for each individual, Two types of freeform designs were selected as the 100 simulations were run, and the FOMs were recorded. A optimal designs, referred to as CB7-D1 (Fig. 6b (1)) and minimum threshold for the FOM was set by the designer. CB7-D2 (Fig. 6b (2)); their parameter values are listed in A yield value was calculated, representing the percentage Table 2. CB7-D1 had a larger X than CB7-D2. CB7-D2 of the simulations for each individual above the minimum had a larger R than CB7-D1. The difference between the FOM. The designer finally had to choose one as the final two designs was mainly because CB7-D1 had a more design by reviewing the yield and the FOM of the inves- compliant freeform beam than CB7-D2. tigated individuals based on the application requirement. To compare the freeform designs with a conventional orthogonal design, the same GA optimization algorithm Optimization result was also run with constraints allowing only an orthogonal The GA optimization ran continuously for eight gen- design. An identical design space (390 × 390 μm ) was erations, with one generation size of 40 individuals, as chosen for the connecting beams to allow for an objective Wang et al. Microsystems & Nanoengineering (2022) 8:3 Page 7 of 14 Table 3 The FOMs and simulated yield of microgripper design CB7-D1, CB7-D2, and SB7 Performance FOM (μm) Yield (%) CB7-D1 59 80 CB7-D2 49 79 SB7 24 87 Max stress comparison. The optimal orthogonal design was termed SB7 (Fig. 6b (3)); Table 3 also lists its FOM. Compared with CB7-D1 and CB7-D2, SB7 had the lowest FOM. 0 42 Modal von mises stress (MPa) Here, 80% of the FOM value in each optimal design was taken as the minimum threshold of acceptable FOM Fig. 4 Optimization result. A von Mises stress contour plot of the values during the robustness analysis. optimal freeform design CB7-D1 with an actuation voltage of 53 V and According to the robustness analysis, CB7-D1, CB7-D2, an X of 100 μm and SB7 had a yield of 86% (minimum FOM of 47 μm), 84% (minimum FOM of 39 μm), and 90% (minimum FOM of 19 μm), respectively. directly related to the stiffness of the connecting beams. As a freeform design has many degrees of freedom, it is The freeform design CB7-D1 is thus expected to be less necessary to disperse the parameter values during the harmful to fragile samples during manipulation compared optimization to achieve a global rather than a locally with the orthogonal design SB7. optimal solution. However, an excessively dispersed parameter space makes the optimization process com- Dynamic analysis putationally intensive. To study the convergence, the GA Given the significant influence of vibration modes and carried out ten independent optimization processes by stress on the microgripper, these parameters were ana- using different initial designs across the design space. As lyzed next. The frequencies of the first three modes of circumstantial evidence, the topologies of ten optimal freeform design CB7-D1 were 823, 10,583 and 27,932 Hz, solutions resembled each other, indicating a global con- respectively. The 2nd mode frequency is 11.86 times lar- vergence of the optimization process to a large extent. ger than the working mode (1st mode) frequency, which The FOMs of the designs obtained in 10 different opti- considerably increases the stability during actuation. The mization runs ranged from 47 to 60 μm. frequencies of the first three modes of freeform design CB7-D2 and orthogonal design SB7 are listed in Table 5; Static analysis the mode shapes of CB7-D1 were very similar. According to a FEM simulation in COMOL, the free- form design CB7-D1 had an X of 100 μm for a DC Stress analysis actuation voltage of 53 V, as shown in Fig. 4. The freeform In our design, the connecting beams are used to design CB7-D2 had an X of 100 μm for a DC actuation support the movable structures and to bend during a voltage of 57 V. The optimized orthogonal design SB7 had gripping operation. This makes the connecting beams an X of 41 μm for a DC actuation voltage of 53 V and the most fragile part of the design, and thus, they could 48 μm for a DC actuation voltage of 57 V. A DC actuation break under a large electrostatic force input. Hence, a voltage of 85 V was required for the orthogonal design stress analysis was performed to predict the stress SB7 to reach an X of 100 μm. Comparing the freeform distribution of the microgripper during actuation. design CB7-D1 with the orthogonal design SB7, X was According to a FEM simulation in COMSOL, when the increased by 144% for the same DC actuation voltage of freeform microgripper CB7-D1 reached 100 μm(its 53 V, as shown in Table 4. In addition, the actuation force maximum X ), the maximum Von Mises stress was for the freeform design CB7-D1 to reach an X of 100 μm 42MPa(as showninFig. 4), whichismuchsmaller was only 39% of that of the orthogonal design SB7, as than the yield strength of single-crystal silicon, i.e., shown in Table 4. Therefore, the stiffness of the con- 7GPa . This low-stress value is another benefitofthe necting beams in the freeform design CB7-D1 is lower freeform geometries and the GA optimization. Com- than that in the orthogonal design SB7. The output force pared with orthogonal beams, stress can be more of the gripper when grasping a micro-object is an evenly distributed by the curved shapes of freeform important parameter of the gripper performance, which is beams, and stress concentration can be prevented. Wang et al. Microsystems & Nanoengineering (2022) 8:3 Page 8 of 14 Table 4 X of microgripper design CB7-D1, CB7-D2, and Table 5 First three modes of the microgripper design SB7 under different actuation voltages CB7-D1, CB7-D2, SB7 DC actuation voltage (V) 53 57 85 Design 1st Mode (Hz) 2nd Mode (Hz) 3rd Mode (Hz) CB7-D1 X (μm) 100 / / CB7-D1 823 10583 27932 CB7-D2 X (μm) 83 100 / CB7-D2 906 11484 29365 SB7 X (μm) 41 48 100 SB7 1245 16975 48530 Additionally, the GA attempted to reduce the stress to Experiment results and discussion increase the X since a low-stress concentration leads Experiment setup to a large X .Asshown in Fig. 4, the stress was evenly As showninFig. 7a, the measurement setup included a distributed on the freeform. As will be discussed later, voltage source, a multimeter, a microscope with a camera, in the experiment, none of the microgrippers broke and an electronic circuit. The voltage source could supply a during actuation. Furthermore, the microgripper did DC voltage ranging from 0 to 60 V. The multimeter was used not break even when we manually probed the arm tips to measure the exact voltage supplied to the microgripper. A of the microgripper to release them from the actuation microscope with a camera was used to measure the dis- combs after a pull-in event. As shown in Fig. 4,the placement and gripping action of the microgripper. The maximum Von Mises stress of CB7-D1 was located at electronic circuit included some protecting resistors in case the turning point of the freeform beam. The maximum pull-in occurred and the current would become too high. Von Mises stresses of microgripper design CB7-D2 and design SB7 were 44 and 179 MPa, respectively, when Gripping range test result they reached an X of 100 μm. First, the gripping ranges were tested. Two types of freeform designs, i.e., CB7-D1 (blue line) and CB7-D2 (red Fabrication line)), and one orthogonal design, i.e., SB (black line), were Figure 5 shows the SOI-based process flow used in tested. When different voltages were applied to the microgrippers, the images of the arm tips were acquired this work, which is similar to that described in ref. . After etching a pattern of frame trenches on the handle and processed to calculate the displacement. In Fig. 7b, layer of a wafer by deep reactive-ion etching, another the experimental results of three types of microgrippers pattern of trenches and etch holes were etched on the are shown with a solid line, i.e., CB7-D1(E), CB7-D2(E), front side in a 50-μm-thick device layer. The handle and SB7(E). The experimental results indicated that the layers beneath the rotary comb actuators, gripper arms, microgripper design CB7-D1 provided a gripping range of and arm tips were removed to increase yield and 73 μm with an actuation voltage of 40 V and design CB7- reliability by offsetting the two trench patterns by D2 gripping range of 91.5 μm with an actuation voltage of 40 µm. Finally, the devices were separated from each 47.5 V. Limited by the maximum voltage of the voltage other by HF vapor phase etching without the usage of a source, microgripper design SB7 provided a gripping dicing step. range of 48.0 μm with an actuation voltage of 60 V. Since Figure 6a shows the fabricated microgripper CB7-D1 the orthogonal design SB7 is only used to evaluate the with the curved shapes of the freeform beams. For improvement of the freeform designs CB7-D1 and CB7- designs CB7-D2 and SB7, the structure was identical to D2 under the same actuation voltage, 60 V was sufficient CB7-D1, except for the connecting beams. A compar- for testing design SB7. ison of the connecting beams of CB7-D1, CB7-D2, and In Fig. 7b, the simulated results of the respective designs SB7 is shown in Fig. 6b. We fabricated 172 chips on a are also plotted (dashed lines), i.e., CB7-D1(S), CB7-D2(S), 4-in. wafer, including freeform and orthogonal designs and SB7(S). The experimental results agree well with the with achipsizeof3.7×3.7mm . Approximately, simulation results. The small discrepancy is due to fab- 90–95% of all fabricated chips had complete structures rication tolerances of the gripper parameters and the pull- and were fully functional after release, bonding, and in effect. packaging. This fabrication result indicated that the The displacements of the microgrippers were compared yield rate of the freeform MEMS devices was as good as not only at the arm tips but also in the areas of the rotary that of the orthogonal MEMS designs as long as rules comb actuators and connecting beams. A comparison of concerning minimum feature size (such as minimum the three types of microgripper designs with an actuation etching trenches, minimum widths) were followed. voltage of 40 V is shown in Fig. 6b (1)–(3), in which the Wang et al. Microsystems & Nanoengineering (2022) 8:3 Page 9 of 14 Wafer grid Process layer Sacrificial oxide layer Handle wafer trenches Device features Release holes Process layer trenches 50 mm ‘Handle wafer blocks’ iii ii iii iii Release areas Device & handle wafer block Etched oxide d Wafer grid 4.7 mm Released device from the wafer grid Released ‘handle 4.7 mm wafer blocks’ behind microlevers f Fig. 5 Fabrication process. Fabrication flow of the MEMS devices: a Backside etching using DRIE to define the backside trenches. b Front side DRIE to pattern the device features, release holes, and front side trenches. c Three release regions, namely, (i) device, (ii) handle wafer block release features, and (iii) dicing features, were etched consecutively by hydrofluoric acid in the vapor phase. d Device separation after release . e Image of the wafer grid of step (f) (the solid area resulting from a lithography fault). f Image of the released devices. (I) The front image of the released device, (II) back image of the released device, and (III) released “handle wafer blocks” highest stiffness (the smallest X red contours indicate the position of the structure before under the same actua- actuation. The X of design CB7-D1 was larger than that tion force). CB7-D2 and CB7-D1 have the second and of design CB7-D2, which, in turn, was larger than that of third lowest nonlinearities of the connection beam stiff- design SB7 in all three areas. Since CB7-D1 could not be ness under the same actuation force. Thus, the higher the actuated higher than 40 V (which is close to the pull-in connecting beam stiffness is, the lower the nonlinearity of voltage), the comparison of designs CB7-D2 and SB7 was the connecting beam stiffness under the same actuation made with an actuation voltage of 47.5 V. The X of force is. design CB7-D2 was much larger than that of the design According to the simulation, the total capacitance of the SB7 in all three comparison areas. In summary, for the rotary comb actuators in CB7-D1 changes from 2.28 to same actuation voltage, microgrippers with freeform 3.16 pF after achieving a deflection X of 72.9 μm. The geometries improved the X by 150–200% compared with total capacitance of the rotary comb actuators in CB7-D2 orthogonal geometries in the same die area. changes from 2.28 to 3.28 pF after achieving a deflection Figure 7c shows the relationships between the actuation X of 91.5 μm. The total capacitance of the rotary comb force and X for the three designs, i.e., CB7-D1, CB7-D2, actuators in S7-D2 changes from 2.28 to 3.00 pF after and SB7. Linear fittings were plotted using the least- achieving a deflection X of 54 μm. The effect of the squares method. In terms of the connecting beam stiff- fringing field does not play an important role and can be 8,10 ness, CB7-D1 has a nonlinearity of 5.5% in the worst case ignored during the actuation process . for a 51 μN actuation force range; CB7-D2 has a non- linearity of 5.6% in the worst case for a 72 μN actuation Pull-in of rotary comb drives force range; SB7 has a nonlinearity of 2.2% in the worst For design CB7-D1, an actuation voltage higher than case for a 115 μN actuation force range. CB7-D1, CB7-D2, 40 V led to the pull-in of the rotary comb actuators, as and SB7 have a nonlinearity of 5.5%, 5.2%, and 1.2% in the shown in Fig. 8a. For an actuation voltage of 40 V, the R worst case for a 51 μN actuation force range, respectively. of SB7 was not observable, whereas the R of CB7-D2 was As shown in Fig. 7c, among the three designs, SB7 has the approximately two times smaller than that of CB7-D1. In lowest nonlinearity of the connection beam stiffness addition, pull-in occurred when the gripper of design under the same actuation force range, as SB7 has the CB7-D1 moved 74 μm under an actuation voltage of 41 V. Wang et al. Microsystems & Nanoengineering (2022) 8:3 Page 10 of 14 100 um Arm tip 50 um Gripper arm 100 um 100 um Rotary comb actuator Freeform beam Anchor CB7 D1 27.1um 43.0 um 77.3 um CB7 D1 CB7 D2 SB7 (1) (2) (3) 100um 100um 100um 100um 100um 100um 11um 17um 11um 100um 100um 100um 40VDC 40VDC 40VDC Fig. 6 Fabricated microgrippers and their displacement under 40 V actuation. a Metallographic microscope image of the freeform microgripper CB7-D1. b The images of the microgripper CB7-D1, CB7-D2, and SB7 under a certain actuation voltage. Image (1)–(3). The images of the microgripper CB7-D1, CB7-D2, and SB7 under an actuation voltage of 40 V. For comparison, the red contours indicate the position of the structure before actuation. The upper images show the arm tip area, the middle shows the rotary comb actuator area, and the bottom images show the connecting beam area. (1) CB7-D1, (2) CB7-D1, and (3) SB7 for an actuation voltage of 40 V. For comparison, the red contours indicate the position of the structure before actuation. The upper images show the arm tip area. The middle images show the rotary comb actuator area. The bottom images show the connecting beam area Pull-in occurred in design CB7-D1 due to R becoming point first, as the long lever of the rotary comb actuator too large, resulting from the undesired movement of the acts as a motion amplifier. curved beam along the R-axis. As shown in Fig. 8a. (4), the The pull-in effect can easily be mitigated by increasing outermost comb fingers had the largest R value com- the stiffness of the connecting beams along the R-axis pared with other comb fingers and reached the pull-in (e.g., by increasing the beam width). However, this will Wang et al. Microsystems & Nanoengineering (2022) 8:3 Page 11 of 14 Microscope & camera 4.7 mm Multimeter Power supply Microgripper chip Electronic circuit Straight beam (SB) VS curved beam (CB) Straight beam (SB) VS curved beam (CB) with 7um minimum width with 7um minimum width CB7 D1(E) CB7D1(E) CB7 D2(E) CB7D2(E) SB7(E) SB7(E) CB7 D1(F) CB7D1(S) CB7 D2(F) CB7D2(S) SB7 (F) SB7(S) 20 20 10 10 0 0 0 10203040 50 60 020 40 60 80 100 120 Voltage (V) Force (uN) Fig. 7 Measurement setup and result. a Measurement setup. b Characterization of the simulated and measured X versus actuation voltages in two freeform designs (CB7-D1 (blue line), CB7-D2 (red line)) and one orthogonal design (SB (black line)). Simulated results (dashed lines): CB-7D1(S), CB7-D2(S), SB7(S). Measured results (solid lines): CB7-D1 (E), CB7-D2 (E), SB7 (E). c Characterization of the simulated and measured X vs. actuation force in two freeform designs (CB7-D1 (blue), CB7-D2 (red)) and one orthogonal design (SB (black)). Linear fitting lines (solid lines): CB-7D1 (F), CB7-D2 (F), SB7 (F). Measured results (dots): CB7-D1(E), CB7-D2(E), SB7(E) reduce the X for a given actuation voltage. After opti- Then, the microgripper was driven with a voltage of 31 V mization, design CB7-D2 reached a larger X (91.5 μm) and gripped the hair, as shown in Fig. 8b (2). The measured with a higher pull-in voltage (47.5 V). gap of the arm tips was 70 μm, smaller than the diameter of the hair, indicating successful gripping of the hair. In Demonstration of micro-object gripping addition, according to Fig. 7b, CB7-D2 was expected to To demonstrate the performance of the fabricated have an X of 30 μm for an actuation voltage of 31 V, microgripper, microgripper design CB7-D2 was used to matching the experimental result shown in Fig. 8b(2). grip human hair with a diameter of 77 μm. The position of the microgripper relative to the hair before the gripping Discussion test is shown in Fig. 8b (1), in which the gap of the arm For the same actuation voltage, microgrippers with tips is 100 μm. It is worth noting that the micro stick-slip freeform geometries (CB7-D1 and CB7-D2) improved X motion between the object and arm tip is mainly deter- by 150–200% compared with orthogonal geometries (SB7) mined by the friction force. In ref. , Zhang and Liu et al. for the same die area. Therefore, the use of freeform found that micro stick-slip motion could be explained by geometries has two practical advantages: (i) a lower the Stribeck model, Dahl model, and LuGre model. The actuation voltage to reach the same X and (ii) less harm LuGre model has the best accuracy. The Coulomb friction to fragile objects during gripping and releasing. model and the elastoplastic model do not work in a micro However, electrostatic rotary microgrippers exhibit an stick-slip motion system. undesired radial displacement R during actuation. This X (um) X (um) T Wang et al. Microsystems & Nanoengineering (2022) 8:3 Page 12 of 14 ab (1) Human hair 11um (1) (2) 11um 26 77 um um um Small misalignment No obvious misalignment 45 100 45 100um 0VDC 40 V SB7 40 V CB7 D2 um um um (3) (4) (2) 11um 11um 77 um 26 26 Large misalignment Pull - in um um 40 V CB7 D1 41 V CB7 D1 70 60 100um 31VDC um um um Fig. 8 Results of 47.5 V actuation experiment, pull-in experiment, and gripping experiment. a Images of designs CB7-D2 and SB7 under an actuation voltage of 47.5 V. Comparison of radial deflection R of the rotary comb actuators for different microgripper designs. (1) No apparent R in m m the microgripper design SB7 under an actuation voltage of 40 V. (2) Small R in the microgripper design CB7-D2 under an actuation voltage of 40 V. (3) Large R in the microgripper design CB7-D1 under an actuation voltage of 40 V. (4) Pull-in of the microgripper design CB7-D1 under an actuation voltage of 41 V. b Gripping a human hair with a diameter of 77 μm using microgripper design CB7-D2 (1) before gripping and (2) after gripping leads to a reduction in the gap of the comb drive elec- ability in Hao et al.’s design is due to its narrow beam- trode, potentially causing pull-in, which limits the max- width (3.6 μm). If the beamwidth of CB7-D2 was reduced imal X . With the proposed optimization method, the R from 7 to 3.6 μm, a simulation indicated that CB7-D2 T m of the rotary comb actuators is included in the FOM. The would only need 27 V to have an X of 100 μm, which is GA-based optimization concurrently maximizes X and smaller than the 31 V of Hao et al.s design. Moreover, the actuation voltage can be further reduced through an minimizes R for a given voltage. Comparing the two freeform designs, CB7-D1 has a increase in the number of rotary comb actuators, since larger X but a larger R compared with CB7-D2 for the Hao et al.’s design has six groups of rotary comb actua- T m same actuation voltage. Thus, a designer can select free- tors, while our designs only have four groups of rotary form designs according to different requirements for the comb actuators. gripping range. For example, for objects with a diameter In addition, the CB7-D1 and the CB7-D2 design were between 100 and 30 μm, design CB7-D1 is superior to developed based on Chang et al.’s design . Compared CB7-D2, as CB7-D1 can satisfy the gripping range with a with Chang et al.’s design , the CB7-D1 actuation ability lower actuation voltage. Additionally, for objects with a is 4.8 times larger, while the gripping range is 1.4 times diameter between 100 and 10 μm, CB7-D2 is better than lower, whereas the design CB7-D2 actuation ability is 4.3 CB7-D1, as CB7-D1 can offer a larger gripping range, times larger, while the gripping range is 1.1 times lower. while CB7-D1 pulls in after 74 μm. Table 6 compares the gripping range of our micro- Conclusions grippers with those of other electrostatically actuated A novel microgripper with freeform geometries microgrippers in the literature. To compare the actuation designed using a GA approach is presented. The GA- ability of different designs fairly, the maximum X is divi- based semiautomated design methodology with freeform ded by the square of the related actuation voltage, and the geometries is introduced in detail. It is capable of calculated result is taken as the actuation ability. Crescenzi designing near-optimal MEMS devices that are robust to et al.’s design have the highest actuation ability and lowest fabrication tolerances. Two types of microgrippers with actuation force but a limited gripping range. Compared freeform geometries and one microgripper with ortho- with Crescenzi et al.’s design, the CB7-D1 actuation ability gonal geometries were optimized by this method. FEA is 6 times lower, while the gripping range is 3.6 times lar- simulations were used to analyze the static and dynamic ger, whereas the design CB7-D2 actuation ability is 5 times performance as well as the stress distribution of the lower, while the gripping range is 4.6 times larger. designed microgrippers. The experiment showed that the Hao et al.’s design has the second-highest actuation microgripper with freeform geometries had a large X ability and largest gripping range. The high actuation (91.5 μm) for a low actuation voltage (47.5 V), which axis Radial Wang et al. Microsystems & Nanoengineering (2022) 8:3 Page 13 of 14 Table 6 Comparison of different gripper operating displacements Design Actuation force Actuation Actuation range Actuation ability Die area (μm ) Gripper arm (μN) voltage (V) (μm) (nm/V ) length (mm) Volland 231 80 20 3.13 1250*3300 1 Beyeler 986 150 100 4.44 7700*5600 3.3 Chen 1646 80 25 3.91 5745*3217 1 Bazaz 1181 50 17 6.80 4891*6402 2.5 Chang 297 100 94 9.40 3100*3700 1.7 Piriyanont 104 80 90 14.06 8500*5600 1.6 Xu 273 72 63 12.15 2800*3812 NA Hao 37 31.5 100 100.78 4500*4000 1.7 Crescenzi 3 11 20 165.29 2710*4417 1.4 (CB7-D1) 51 40 72.9 45.54 3700*3700 1.7 (CB7-D2) 72 47.5 91.5 40.55 3700*3700 1.7 (SB7) 115 60 54 15.00 3700*3700 1.7 From COMSOL simulation. agreed well with the theory. This made it possible to Acknowledgements This research was funded by the Science Challenge Project, grant no. manipulate a wide range of objects (size ranging from 10 TZ2016006-0502-02, and the National Key Research and Development to 100 μm). The concept was successfully demonstrated Program of China, grant no. 2021YFB3201603. by grasping a human hair with a diameter of 77 μm. A Author details detailed analysis of the pull-in effect due to the R of the College of Optical Science and Engineering, Zhejiang University, Hangzhou, actuator electrodes was conducted. Possible methods to China. Department of Electrical Engineering and Computer Science, University mitigate this effect were also discussed. of Liege, Liege, Belgium. ESAT-MNS, University of Leuven, Leuven, Belgium. PGMF and School of Physics, Huazhong University of Science and For the same actuation voltage, microgrippers with Technology, Wuhan, China freeform geometries improved X by 150–200% com- pared with orthogonal geometries in the same die area. Author contributions Thus, freeform geometries have two advantages: (i) a C.W. designed, built, and tested the MEMS microgripper. W.F. and Y.W. contributed to the design of the MEMS mechanism. X.S., S.S., and M.G. lower actuation power to reach the same X and (ii) less contributed to the MEMS fabrication. H.L. contributed to the measurement harm to fragile objects during gripping and releasing. setup. C.W., W.F., and Y.W. took the measurements. H.Z., C.W., Y.W, and A.Q. In Table 6, we briefly compare our freeform geometry performed computational analysis of the data. C.W., H.L., J.B., and M.K. led the writing of the paper, and all authors provided comments. H.L., J.B., and M.K. design with the two best electrostatic microgrippers had the initial concept of the microgripper. H.L. and J.B. oversaw the design, 8,9 described in the literature in terms of actuation range fabrication, and testing of the microgripper. and X per voltage 2 (actuation ability). Both freeform Conflict of interest geometries developed in this work have a larger gripping The authors declare that they have no conflict of interest. range compared to Crescenzi et al. . If the same number of actuation comb fingers is considered, our designs have Supplementary information The online version contains supplementary a better actuation ability compared to Hao et al. . material available at https://doi.org/10.1038/s41378-021-00336-0. The improved performance of the microgripper is mainly due to the use of GA for freeform geometric Received: 6 April 2021 Accepted: 10 November 2021 design. It is worth noting that the proposed design methodology enabling freeform geometries can be extended to a wide range of other MEMS devices. Future work will include equipping the microgripper with both References 1. Thornell, G., Bexell, M., Schweitz, J.-Å. & Johansson, S. Design and fabrication of force sensing and a feedback system. This will allow the a gripping tool for micromanipulation. Sens. Actuators A 53,428–433 (1996). gripping process to be performed with higher precision 2. Ansel, Y.,Schmitz, F., Kunz,S., Gruber,H.& Popovic, G. 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Precision position/force interaction control of a piezoelectric multi- isms: module optimization. J. Mech. Des. 137, 122301 (2015). morph microgripper for microassembly. IEEE Trans. Autom. Sci. Eng. 10, 20. Wang, C. et al. Design of freeform geometries in a MEMS accelerometer with a 503–514 (2013). mechanical motion preamplifier based on a genetic algorithm. Microsyst. 6. Kim, D.-H., Lee, M. G., Kim, B. & Sun, Y. A superelastic alloy microgripper with Nanoeng. 6,1–15 (2020). embedded electromagnetic actuators and piezoelectric force sensors: a 21. COMSOL, https://www.comsol.com/. Accessed 23 May 2020. numerical and experimental study. Smart Mater. Struct. 14, 1265 (2005). 22. Beyeler, F. et al. Monolithically fabricated microgripper with integrated force 7. AbuZaiter, A., Nafea, M. & Ali, M. S. M. Development of a shape-memory-alloy sensor for manipulating microobjects and biological cells aligned in an micromanipulator based on integrated bimorph microactuators. 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10.1038/s41378-021-00336-0
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Abstract

This paper describes a novel electrostatically actuated microgripper with freeform geometries designed by a genetic algorithm. This new semiautomated design methodology is capable of designing near-optimal MEMS devices that are robust to fabrication tolerances. The use of freeform geometries designed by a genetic algorithm significantly improves the performance of the microgripper. An experiment shows that the designed microgripper has a large displacement (91.5 μm) with a low actuation voltage (47.5 V), which agrees well with the theory. The microgripper has a large actuation displacement and can handle micro-objects with a size from 10 to 100 μm. A grasping experiment on human hair with a diameter of 77 μm was performed to prove the functionality of the gripper. The result confirmed the superior performance of the new design methodology enabling freeform geometries. This design method can also be extended to the design of many other MEMS devices. Introduction ref. was based on a piezoelectric actuated microgripper. Microelectromechanical system (MEMS) microgrippers Although this design features a large displacement and are microscale grippers fabricated through a micro- bandwidth, it requires a complicated fabrication process machined process, and typically comprise actuators, and exhibits hysteresis nonlinearity, which severely limits mechanical parts for the handling and manipulation of its spatial resolution during manipulation. micro-objects (1–100 μm) and force sensors. MEMS Moreover, piezoelectric actuated microgrippers cannot microgrippers are widely used in handling cells and tis- work in a high-temperature environment. A magnetically 1 6 sues in biology and in microassembling and testing the actuated gripper was reported in ref. . This design pro- mechanical properties of micromachined devices . vides a large displacement and a quick response with MEMS microgrippers with different shapes, actuation, reasonable sensitivity, but it requires a complicated and and sensing principles have been developed in recent expensive assembly process. Alternatively, a microgripper 3,4 7 years. The designs reported in refs. were thermally based on a shape memory alloy was discussed in ref. . actuated microgrippers. These microgrippers have a large This design had excellent flexibility and large bandwidth. displacement and a low actuation voltage. However, the However, it also suffered hysteresis nonlinearity and large high working temperature of thermally actuated micro- power consumption. Electrostatically actuated micro- 8,9 grippers can be harmful to living cells and tissues in grippers were reported in refs. . In particular, for the biological manipulation. Another design described in first time, Chang et al. introduced a rotary actuation comb into an electrostatically actuated microgripper to increase the displacement range to 94 μm with an actuation vol- Correspondence: Huafeng Liu (huafengliu@hust.edu.cn) or Jian Bai (bai@zju. tage of 100 V . These designs feature a fast response edu.cn) College of Optical Science and Engineering, Zhejiang University, Hangzhou, time, low power consumption and no hysteresis. How- China ever, these designs have a relatively large dimension due Department of Electrical Engineering and Computer Science, University of to the high number of actuation comb fingers required. In Liege, Liege, Belgium Full list of author information is available at the end of the article © The Author(s) 2022 Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to theCreativeCommons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/. 1234567890():,; 1234567890():,; 1234567890():,; 1234567890():,; Wang et al. Microsystems & Nanoengineering (2022) 8:3 Page 2 of 14 addition, the maximum displacement of the electro- design of freeform geometries for MEMS sensors. Speci- statically actuated microgripper is limited by the pull-in fically, a MEMS accelerometer comprising a mechanical effect . In addition, the actuation voltage of the electro- motion amplifier was described to demonstrate the statically actuated microgrippers is relatively high, and effectiveness of the design approach . In the following, normally, a voltage larger than 80 V is required to achieve we describe a MEMS actuator (i.e., microgripper) with a displacement of 100 μm. Such a high actuation voltage is freeform geometries that are designed and optimized by not only problematic in practical applications but can also the GA-based design method. Due to the freeform geo- damage gripped samples. metries, the designed microgripper features a large dis- In the vast majority of MEMS devices, simple geome- placement with a low actuation voltage compared with trical layouts comprising only a few basic building blocks, previously described electrostatic microgrippers. Detailed such as beams, rectangular masses, and, more rarely, rings theoretical analysis and experimental validation are con- or disk-shaped structures, are used . As discussed in the ducted. A manipulation experiment using the designed following, there are cases in which such conventional, microgripper for grasping human hair is shown. More- simple designs limit the performance of MEMS devices over, the pull-in effect in electrostatically actuated and therefore may not meet the requirements for specific microgrippers is also discussed. The performances of the applications. Compared with conventional designs, geo- designed microgrippers are compared with those of metries comprising more complex geometries offer a existing microgrippers. designer more freedom. Complex geometries may result in novel designs with superior performance and over- Design of the microgripper with freeform 14–17 come the limitation of simple mechanisms . For geometries example, by using curved anti-springs, Middlemiss et al. A design methodology based on a genetic algorithm and Boom et al. developed MEMS accelerometers with The microgripper in this work was designed using a resolutions at the nano-g level. These anti-springs feature novel design method allowing freeform geometries based a low effective spring constant that cannot be achieved on a GA. The methodology comprises two parts: a para- with conventional orthogonal designs under the same metrized mechanical finite element model (FEM) with fabrication constraints. However, complex theoretical freeform geometries implemented in COMSOL and a calculations are needed to design these complex geome- GA implemented in MATLAB , illustrated by the flow tries. Such a design method requires considerable design chart in Fig. 1. The FEM model and simulation in expertise and is practically impossible to transfer to other COMSOL can be directly controlled by MATLAB devices; a case-by-case approach is required. An alter- through LiveLink for MATLAB . A GA is based on the native is topology optimization, which can be used to mechanics of natural selection and genetics, combining design MEMS devices with complex geometries. Ana- the fittest individuals in the population to search for the 16,17 18 nthasuresh et al. and Seshia et al. developed com- best solution. These evolutionary-based techniques are plex force and motion amplification mechanisms to excellent for particularly complex, multiparameter pro- increase the sensitivity of accelerometers. Cao and Zhang blems for which they are capable of finding good solutions et al. developed a module optimization method as a uni- in a short period of time. For optimization, the GA sets fied design approach for both compliant mechanisms and the parameter values of a mechanical model and simulates rigid-body mechanisms . In the module optimization each “individual” parameter set in the first generation. approach, the states of joints and links are fully para- Using a performance goal (or figure of merit (FOM)) meterized, with which a designer can obtain a rigid-body function, the GA generates a new parameter set for the mechanism, a partially compliant mechanism, or a fully compliant mechanism for a given design objective. Simulate However, in these MEMS devices, simple beam (or truss) elements are typically used as a fundamental building System Set block to form optimized topologies. Such methodology Mechanical model Performance Parameters easily results in designs that often cannot be fabricated since it is difficult to implement fabrication constraints well in the topology optimization process . In this paper, we introduce a novel electrostatically Genetic Goal(s) actuated microgripper with freeform geometries designed algorithm function / FOM by a genetic algorithm (GA) approach. The novel design approach is introduced by describing the optimization Fig. 1 Optimization system. Generic process flow of the novel process for a microgripper as a case study. In our previous designed method with freeform geometries based on a GA work, a GA was introduced for the first time for the Wang et al. Microsystems & Nanoengineering (2022) 8:3 Page 3 of 14 a b Beam end P4 Beam end ×10 μm P5 P2 P5 P2 –1 Arm tip P1 P4 P1 Gripper arm Bézier 2 ×10 μm Rotary comb Bézier 1 Bézier 2 Bézier 1 actuator P0 P3 P3 P0 Beam end Beam end Fixed comb Connecting beam Anchor Moving direction Moving comb Fig. 2 Proposed microgripper with freeform geometries and misalignment of rotary microgrippers. a Schematic view of the proposed microgripper with freeform geometries showing an arm tip, gripper arm, rotary comb actuator, connecting beam (freeform geometries), and anchor. The moving direction of the microgripper is along the direction of blue arrows. b With the use of Bezier curves, any beam can be defined with coordinates of six points. An orthogonal beam can be modified into a curved beam easily by just modifying the coordinates of P1 and P4. c Movement of a rotary comb actuator after actuation. The red line is the position of the moving comb before actuation, while the solid blue part is the position of the moving comb after actuation. The R-axis is along the radial axis of rotary comb fingers, which is the undesired displacement of comb fingers. The θ-axis is along the tangent direction of rotary comb fingers (perpendicular to the R-axis), which is the desired movement direction of comb fingers. The undesired movement along the radial axis, i.e., R , reduces the gap between the fixed and moving comb fingers next generation. After several generations, the parameter simple orthogonal structures with structures based on values converge, indicating that the mechanical model freeform geometries and explore how this can improve reaches an optimal design. The details of the design the performance of the microgripper. process are described in the following. In our design methodology, Bezier curves were used to define and parameterize the freeform geometries in the Microgripper model with freeform geometries connecting beam area. A curve can be described by a Bezier A schematic drawing of a microgripper with freeform curve with only three coordinate points. Therefore, a beam geometries is shown in Fig. 2a. It comprises rotary comb can be defined by two Bezier curves, in which 12 parameters actuators, two gripper arms, two-arm tips to grasp micro- are used to describe the (X, Y) coordinates of 6 points, as objects, and connecting beams that link the moveable showninFig. 2b. An orthogonal beam can be easily mod- structures to anchors. The gap between the two arm tips ified into a curved beam, as illustrated in Fig. 2b, in which is 100 μm. When a voltage is applied to the rotary comb only the coordinates of points P1 and P4 are modified. The actuators, due to electrostatic force, the microgripper will number of parameters is significantly reduced, which saves move in the direction of the blue arrows, as indicated in computational resources for optimization. Fig. 2a. This displacement is mechanically amplified and transferred to the arm tips through the gripper arms; this Parameter ranges and geometrical design constraints effectively functions as a mechanical lever . The critical The parameter ranges and geometrical design con- part of the microgripper is the connecting beam. It defines straints were defined based on the fabrication process the total stiffness of the structure, which influences the described in ref. and are listed in Table 1. The mini- actuation voltage, actuation displacement, bandwidth, mum width of the freeform geometries was set as 7 µm to maximum stress, etc. However, the connecting beams of prevent parts from becoming too fragile. All para- most microgrippers in the literature are based only on meterized variables have lower and upper bounds (LBs 8,10,22–25 simple orthogonal structures . Their shape is far and UBs, respectively). LBs and UBs are determined either from fully explored, and there is no evidence of achieving based on (i) practical limitations, such as fabrication tol- an optimal design. More complex, freeform geometrical erance and voltage limitation, or (ii) a qualified guess by shapes may result in a solution with superior perfor- the designer of the optimum value. It is important to mances, such as a much lower actuation voltage and a clarify that the GA was used to optimize only the con- larger displacement. Therefore, we propose replacing nected beam freeform geometry, gripper Arm geometry, Radial axis Radial axis m Wang et al. Microsystems & Nanoengineering (2022) 8:3 Page 4 of 14 Table 1 Definition, symbol, and upper and lower bounds of parameters Parameter Symbol LB UB Gripper arm length L 500 μm 1700 μm Gripper arm width W 50 μm 150 μm Arm tip length L 100 μm 200 μm Arm tip width W 40 μm 100 μm Arm tip angle A 35° 35° Finger angle A 24° 24° Finger angle offset O 4° 4° Finger length L 44 μm44 μm Finger width W 5 μm5 μm Finger gap G 3 μm3 μm Rotary actuator length L 700 μm 1000 μm Rotary actuator width W 15 μm30 μm Connecting beam length L 50 μm 300 μm Connecting beam width W 7 μm7 μm Connecting beam top length L 100 250 CT Connecting beam top width ratio WR 0.5 0.5 CT Connecting beam top ShiftX SX −150 μm 150 μm CT Connecting beam middle length ratio LR 0.1 0.9 CM Connecting beam middle width ratio WR 0.5 0.5 CM Connecting beam middle ShiftX SX −150 μm 150 μm CM Connecting beam bottom width ratio WR 0.5 0.5 CB Connecting beam bottom ShiftX SX −150 μm 150 μm CB rotary actuator length, and rotary actuator width. The GA Therefore, one important constraint during the optimi- algorithm was not applied to the other parts of the design zation process is that R needs to be less than 1.3 μm. that were related to generating electrostatic force among It is important to note that during the optimization, the the comb fingers. design space for the connecting beams is fixed (390 × The movement of a rotary comb actuator after actua- 390 μm ) for the GA; this enables objective comparison of tion can be best described by a polar coordinate system, as different designs. It could be argued that for an ortho- illustrated in Fig. 2c. The R-axis is defined along the radial gonal beam design, the actuation range can be improved direction of the rotary comb fingers; this is an undesired by simply increasing the length of the connecting beam. displacement direction of comb fingers and should be However, in a fixed design space, the two adjacent minimized . The θ-axis is along the tangential direction orthogonal connecting beams will cross each other if the of rotary comb fingers (perpendicular to the R-axis), two connecting beams are prolonged beyond a certain which is the desired movement direction of comb fingers level, which is obviously physically impossible. A serpen- and should be maximized. The displacement of the rotary tine orthogonal beam could be used to prevent this and comb actuator along the R-axis, i.e., R , reduces the gap prolong the beam length; however, this reduces the stiff- between the fixed and moving combs. As a result, the gaps ness in the radial direction and thus increases R , leading of a moving comb finger with respect to the two neigh- to a low pull-in event. Therefore, constraining the design boring fixed comb fingers are no longer equal. With any to a conventional orthogonal shape does not fully explore further increase in the actuation voltage, electrostatic the design space and does not achieve an optimal design. pull-in will thus occur if R is larger than one-third of the More complex freeform geometrical shapes may result in comb finger gap (4 μm), i.e., 1.3 μm . The pull-in effect a solution with superior performance. Thus, we propose limits the maximum displacement of the microgripper. replacing simple orthogonal structures with structures Wang et al. Microsystems & Nanoengineering (2022) 8:3 Page 5 of 14 200 μm 1st generation 2nd generation 3rd generation 4th generation 6th generation 5th generation 7th generation 8th generation Fig. 3 Optimization process. The shape of the connecting beams changes during the GA optimization based on freeform geometries. Their shapes can be opti- performed several postprocessing steps. These included mized with the GA to improve the actuation range at a picking the ten best individuals (elite preservation), low actuation voltage. deriving a certain number of new random individuals (mutation), and cross-fertilizing good individuals to create Figures of merit new offspring. This last step involved taking different In the following, we regard the sum of the displace- parameters from different good individuals and combin- ments at the two gripper arm tips as the displacement of ing them to create a new individual (child). These three the microgripper, X . Ideally, a large X with a low steps created the parameter value set for the 2nd gen- T T actuation voltage is desired for an electrostatically actu- eration. Then, the GA started the same optimization ated microgripper. Therefore, X for a fixed actuation process for the second generation as for the first gen- voltage (40 V) was used as the FOM for the design pro- eration. For each simulation, a row of values was recorded cess. The gap between the arm tips of the microgripper and displayed in the command window of MATLAB. was designed as 100 μm, which obviously defines an upper In the first generation, the FOM varied considerably, limit for X . These values were chosen because most of indicating that the algorithm still explored the design the electrostatic microgrippers described in the literature space. After the first generation, the GA already tended to require a voltage above 80 V to reach an X of 100 μm. find designs that have a large FOM. In the end, the GA Therefore, 40 V represents a typical mid-range actuation consistently settled toward designs with a higher FOM voltage, suitable for comparison. and started to converge. Consequently, the GA is programmed in such a way that Figure 3 shows a graphical illustration of the optimi- it maximizes X while maintaining R less than 1.3 μm. zation process, which went through eight generations. T m The GA considerably changed the shape of the connect- Optimization process ing beams. During the optimization, the GA attempted to In the first step of the optimization process, the GA ran make the connecting beams more compliant by bending 40 individuals (i.e., designs with a specific parameter set), them to increase X . In addition, the GA folded the which were chosen randomly within the parameter ran- connecting beams to increase their length, which further ges. For each individual, a FEM simulation was carried out reduced the stiffness and improved X . However, due to for the fully parameterized mechanical model. The FEM the rotary comb actuator, the connecting beams would simulation included a static displacement simulation for a not only move along the tangential axis but also exhibit fixed actuation voltage. For the simulation, the electro- undesired movement along the radial axis, as illustrated in mechanical multiphysics functionality in COMSOL was Fig. 2c. This increased the displacement of the micro- used, in which the electrostatic actuation force was cal- gripper in the R-axis in Fig. 2c. Thus, the GA attempted to culated based on the number and geometry of the comb reduce R by making the bends of two curved connecting fingers and the actuation voltage. The value of R > beams face each other. In that way, the undesired move- 1.3 μm or a convergence failure of the simulation indi- ment of two curved connecting beams was in opposing cated a pull-in event. The simulation result was auto- directions and canceled each other, reducing R . Finally, matically transferred to the GA in MATLAB, which the undesired movement of the rotary comb actuator was recorded and sorted the results based on the FOM and reduced. (this will be discussed in detail in Section V.C). Wang et al. Microsystems & Nanoengineering (2022) 8:3 Page 6 of 14 Table 2 Definition, symbol, and upper and lower bounds of parameters Parameter CB7-D1 CB7-D2 SB7 Gripper arm length 1520 μm 1534 μm 1545 μm Gripper arm width 78 μm88 μm88 μm Arm tip length 180 μm 210 μm 190 μm Arm tip width 79 μm85 μm90 μm Arm tip angle 35° 35° 35° Finger angle 24° 24° 24° Finger angle offset 4° 4° 4° Finger length 44 μm44 μm44 μm Finger width 5 μm5 μm5 μm Finger gap 3 μm3 μm3 μm Rotary actuator length 940 μm 949 μm 960 μm Rotary actuator width 20 μm18 μm21 μm Connecting beam length 230 μm 221 μm 200 μm Connecting beam width 7 μm7 μm7 μm Connecting beam top length 210 198 238 Connecting beam top width ratio 0.5 0.5 0.5 Connecting beam top ShiftX 5 μm4 μm0 μm Connecting beam middle length ratio 0.6 0.7 0.5 Connecting beam middle width ratio 0.5 0.5 0.5 Connecting beam middle ShiftX 25 μm30 μm0 μm Connecting beam bottom width ratio 0.5 0.5 0.5 Connecting beam bottom ShiftX 130 μm 112 μm0 μm Robustness analysis shown in Fig. 3. As mentioned before, the minimum beam The next step in the design process was a robustness width for all designs was set to 7 μm during the optimi- analysis, which started by collecting 10 individuals with the zation process. It is worth noting that the whole optimi- highest FOM; these were taken as optimal design candidates. zation process took 8 h with a 3D mechanical model and For the robustness analysis, the designer had to specify a 6 h with a 2D mechanical model using a laptop with an i7 standard deviation of each design parameter representing core of 2.5 GHz working frequency and 8 G RAM. The the fabrication tolerances. One hundred Gaussian dis- optimization was completed in 8 h, with little manual tributed parameter sets were calculated for all parameters intervention. The optimization process would take much of an individual using the mean value and designer- less time if it ran on a workstation or in a parallel supplied standard deviations. These effectively represent computation mode. the fabrication tolerances. Therefore, for each individual, Two types of freeform designs were selected as the 100 simulations were run, and the FOMs were recorded. A optimal designs, referred to as CB7-D1 (Fig. 6b (1)) and minimum threshold for the FOM was set by the designer. CB7-D2 (Fig. 6b (2)); their parameter values are listed in A yield value was calculated, representing the percentage Table 2. CB7-D1 had a larger X than CB7-D2. CB7-D2 of the simulations for each individual above the minimum had a larger R than CB7-D1. The difference between the FOM. The designer finally had to choose one as the final two designs was mainly because CB7-D1 had a more design by reviewing the yield and the FOM of the inves- compliant freeform beam than CB7-D2. tigated individuals based on the application requirement. To compare the freeform designs with a conventional orthogonal design, the same GA optimization algorithm Optimization result was also run with constraints allowing only an orthogonal The GA optimization ran continuously for eight gen- design. An identical design space (390 × 390 μm ) was erations, with one generation size of 40 individuals, as chosen for the connecting beams to allow for an objective Wang et al. Microsystems & Nanoengineering (2022) 8:3 Page 7 of 14 Table 3 The FOMs and simulated yield of microgripper design CB7-D1, CB7-D2, and SB7 Performance FOM (μm) Yield (%) CB7-D1 59 80 CB7-D2 49 79 SB7 24 87 Max stress comparison. The optimal orthogonal design was termed SB7 (Fig. 6b (3)); Table 3 also lists its FOM. Compared with CB7-D1 and CB7-D2, SB7 had the lowest FOM. 0 42 Modal von mises stress (MPa) Here, 80% of the FOM value in each optimal design was taken as the minimum threshold of acceptable FOM Fig. 4 Optimization result. A von Mises stress contour plot of the values during the robustness analysis. optimal freeform design CB7-D1 with an actuation voltage of 53 V and According to the robustness analysis, CB7-D1, CB7-D2, an X of 100 μm and SB7 had a yield of 86% (minimum FOM of 47 μm), 84% (minimum FOM of 39 μm), and 90% (minimum FOM of 19 μm), respectively. directly related to the stiffness of the connecting beams. As a freeform design has many degrees of freedom, it is The freeform design CB7-D1 is thus expected to be less necessary to disperse the parameter values during the harmful to fragile samples during manipulation compared optimization to achieve a global rather than a locally with the orthogonal design SB7. optimal solution. However, an excessively dispersed parameter space makes the optimization process com- Dynamic analysis putationally intensive. To study the convergence, the GA Given the significant influence of vibration modes and carried out ten independent optimization processes by stress on the microgripper, these parameters were ana- using different initial designs across the design space. As lyzed next. The frequencies of the first three modes of circumstantial evidence, the topologies of ten optimal freeform design CB7-D1 were 823, 10,583 and 27,932 Hz, solutions resembled each other, indicating a global con- respectively. The 2nd mode frequency is 11.86 times lar- vergence of the optimization process to a large extent. ger than the working mode (1st mode) frequency, which The FOMs of the designs obtained in 10 different opti- considerably increases the stability during actuation. The mization runs ranged from 47 to 60 μm. frequencies of the first three modes of freeform design CB7-D2 and orthogonal design SB7 are listed in Table 5; Static analysis the mode shapes of CB7-D1 were very similar. According to a FEM simulation in COMOL, the free- form design CB7-D1 had an X of 100 μm for a DC Stress analysis actuation voltage of 53 V, as shown in Fig. 4. The freeform In our design, the connecting beams are used to design CB7-D2 had an X of 100 μm for a DC actuation support the movable structures and to bend during a voltage of 57 V. The optimized orthogonal design SB7 had gripping operation. This makes the connecting beams an X of 41 μm for a DC actuation voltage of 53 V and the most fragile part of the design, and thus, they could 48 μm for a DC actuation voltage of 57 V. A DC actuation break under a large electrostatic force input. Hence, a voltage of 85 V was required for the orthogonal design stress analysis was performed to predict the stress SB7 to reach an X of 100 μm. Comparing the freeform distribution of the microgripper during actuation. design CB7-D1 with the orthogonal design SB7, X was According to a FEM simulation in COMSOL, when the increased by 144% for the same DC actuation voltage of freeform microgripper CB7-D1 reached 100 μm(its 53 V, as shown in Table 4. In addition, the actuation force maximum X ), the maximum Von Mises stress was for the freeform design CB7-D1 to reach an X of 100 μm 42MPa(as showninFig. 4), whichismuchsmaller was only 39% of that of the orthogonal design SB7, as than the yield strength of single-crystal silicon, i.e., shown in Table 4. Therefore, the stiffness of the con- 7GPa . This low-stress value is another benefitofthe necting beams in the freeform design CB7-D1 is lower freeform geometries and the GA optimization. Com- than that in the orthogonal design SB7. The output force pared with orthogonal beams, stress can be more of the gripper when grasping a micro-object is an evenly distributed by the curved shapes of freeform important parameter of the gripper performance, which is beams, and stress concentration can be prevented. Wang et al. Microsystems & Nanoengineering (2022) 8:3 Page 8 of 14 Table 4 X of microgripper design CB7-D1, CB7-D2, and Table 5 First three modes of the microgripper design SB7 under different actuation voltages CB7-D1, CB7-D2, SB7 DC actuation voltage (V) 53 57 85 Design 1st Mode (Hz) 2nd Mode (Hz) 3rd Mode (Hz) CB7-D1 X (μm) 100 / / CB7-D1 823 10583 27932 CB7-D2 X (μm) 83 100 / CB7-D2 906 11484 29365 SB7 X (μm) 41 48 100 SB7 1245 16975 48530 Additionally, the GA attempted to reduce the stress to Experiment results and discussion increase the X since a low-stress concentration leads Experiment setup to a large X .Asshown in Fig. 4, the stress was evenly As showninFig. 7a, the measurement setup included a distributed on the freeform. As will be discussed later, voltage source, a multimeter, a microscope with a camera, in the experiment, none of the microgrippers broke and an electronic circuit. The voltage source could supply a during actuation. Furthermore, the microgripper did DC voltage ranging from 0 to 60 V. The multimeter was used not break even when we manually probed the arm tips to measure the exact voltage supplied to the microgripper. A of the microgripper to release them from the actuation microscope with a camera was used to measure the dis- combs after a pull-in event. As shown in Fig. 4,the placement and gripping action of the microgripper. The maximum Von Mises stress of CB7-D1 was located at electronic circuit included some protecting resistors in case the turning point of the freeform beam. The maximum pull-in occurred and the current would become too high. Von Mises stresses of microgripper design CB7-D2 and design SB7 were 44 and 179 MPa, respectively, when Gripping range test result they reached an X of 100 μm. First, the gripping ranges were tested. Two types of freeform designs, i.e., CB7-D1 (blue line) and CB7-D2 (red Fabrication line)), and one orthogonal design, i.e., SB (black line), were Figure 5 shows the SOI-based process flow used in tested. When different voltages were applied to the microgrippers, the images of the arm tips were acquired this work, which is similar to that described in ref. . After etching a pattern of frame trenches on the handle and processed to calculate the displacement. In Fig. 7b, layer of a wafer by deep reactive-ion etching, another the experimental results of three types of microgrippers pattern of trenches and etch holes were etched on the are shown with a solid line, i.e., CB7-D1(E), CB7-D2(E), front side in a 50-μm-thick device layer. The handle and SB7(E). The experimental results indicated that the layers beneath the rotary comb actuators, gripper arms, microgripper design CB7-D1 provided a gripping range of and arm tips were removed to increase yield and 73 μm with an actuation voltage of 40 V and design CB7- reliability by offsetting the two trench patterns by D2 gripping range of 91.5 μm with an actuation voltage of 40 µm. Finally, the devices were separated from each 47.5 V. Limited by the maximum voltage of the voltage other by HF vapor phase etching without the usage of a source, microgripper design SB7 provided a gripping dicing step. range of 48.0 μm with an actuation voltage of 60 V. Since Figure 6a shows the fabricated microgripper CB7-D1 the orthogonal design SB7 is only used to evaluate the with the curved shapes of the freeform beams. For improvement of the freeform designs CB7-D1 and CB7- designs CB7-D2 and SB7, the structure was identical to D2 under the same actuation voltage, 60 V was sufficient CB7-D1, except for the connecting beams. A compar- for testing design SB7. ison of the connecting beams of CB7-D1, CB7-D2, and In Fig. 7b, the simulated results of the respective designs SB7 is shown in Fig. 6b. We fabricated 172 chips on a are also plotted (dashed lines), i.e., CB7-D1(S), CB7-D2(S), 4-in. wafer, including freeform and orthogonal designs and SB7(S). The experimental results agree well with the with achipsizeof3.7×3.7mm . Approximately, simulation results. The small discrepancy is due to fab- 90–95% of all fabricated chips had complete structures rication tolerances of the gripper parameters and the pull- and were fully functional after release, bonding, and in effect. packaging. This fabrication result indicated that the The displacements of the microgrippers were compared yield rate of the freeform MEMS devices was as good as not only at the arm tips but also in the areas of the rotary that of the orthogonal MEMS designs as long as rules comb actuators and connecting beams. A comparison of concerning minimum feature size (such as minimum the three types of microgripper designs with an actuation etching trenches, minimum widths) were followed. voltage of 40 V is shown in Fig. 6b (1)–(3), in which the Wang et al. Microsystems & Nanoengineering (2022) 8:3 Page 9 of 14 Wafer grid Process layer Sacrificial oxide layer Handle wafer trenches Device features Release holes Process layer trenches 50 mm ‘Handle wafer blocks’ iii ii iii iii Release areas Device & handle wafer block Etched oxide d Wafer grid 4.7 mm Released device from the wafer grid Released ‘handle 4.7 mm wafer blocks’ behind microlevers f Fig. 5 Fabrication process. Fabrication flow of the MEMS devices: a Backside etching using DRIE to define the backside trenches. b Front side DRIE to pattern the device features, release holes, and front side trenches. c Three release regions, namely, (i) device, (ii) handle wafer block release features, and (iii) dicing features, were etched consecutively by hydrofluoric acid in the vapor phase. d Device separation after release . e Image of the wafer grid of step (f) (the solid area resulting from a lithography fault). f Image of the released devices. (I) The front image of the released device, (II) back image of the released device, and (III) released “handle wafer blocks” highest stiffness (the smallest X red contours indicate the position of the structure before under the same actua- actuation. The X of design CB7-D1 was larger than that tion force). CB7-D2 and CB7-D1 have the second and of design CB7-D2, which, in turn, was larger than that of third lowest nonlinearities of the connection beam stiff- design SB7 in all three areas. Since CB7-D1 could not be ness under the same actuation force. Thus, the higher the actuated higher than 40 V (which is close to the pull-in connecting beam stiffness is, the lower the nonlinearity of voltage), the comparison of designs CB7-D2 and SB7 was the connecting beam stiffness under the same actuation made with an actuation voltage of 47.5 V. The X of force is. design CB7-D2 was much larger than that of the design According to the simulation, the total capacitance of the SB7 in all three comparison areas. In summary, for the rotary comb actuators in CB7-D1 changes from 2.28 to same actuation voltage, microgrippers with freeform 3.16 pF after achieving a deflection X of 72.9 μm. The geometries improved the X by 150–200% compared with total capacitance of the rotary comb actuators in CB7-D2 orthogonal geometries in the same die area. changes from 2.28 to 3.28 pF after achieving a deflection Figure 7c shows the relationships between the actuation X of 91.5 μm. The total capacitance of the rotary comb force and X for the three designs, i.e., CB7-D1, CB7-D2, actuators in S7-D2 changes from 2.28 to 3.00 pF after and SB7. Linear fittings were plotted using the least- achieving a deflection X of 54 μm. The effect of the squares method. In terms of the connecting beam stiff- fringing field does not play an important role and can be 8,10 ness, CB7-D1 has a nonlinearity of 5.5% in the worst case ignored during the actuation process . for a 51 μN actuation force range; CB7-D2 has a non- linearity of 5.6% in the worst case for a 72 μN actuation Pull-in of rotary comb drives force range; SB7 has a nonlinearity of 2.2% in the worst For design CB7-D1, an actuation voltage higher than case for a 115 μN actuation force range. CB7-D1, CB7-D2, 40 V led to the pull-in of the rotary comb actuators, as and SB7 have a nonlinearity of 5.5%, 5.2%, and 1.2% in the shown in Fig. 8a. For an actuation voltage of 40 V, the R worst case for a 51 μN actuation force range, respectively. of SB7 was not observable, whereas the R of CB7-D2 was As shown in Fig. 7c, among the three designs, SB7 has the approximately two times smaller than that of CB7-D1. In lowest nonlinearity of the connection beam stiffness addition, pull-in occurred when the gripper of design under the same actuation force range, as SB7 has the CB7-D1 moved 74 μm under an actuation voltage of 41 V. Wang et al. Microsystems & Nanoengineering (2022) 8:3 Page 10 of 14 100 um Arm tip 50 um Gripper arm 100 um 100 um Rotary comb actuator Freeform beam Anchor CB7 D1 27.1um 43.0 um 77.3 um CB7 D1 CB7 D2 SB7 (1) (2) (3) 100um 100um 100um 100um 100um 100um 11um 17um 11um 100um 100um 100um 40VDC 40VDC 40VDC Fig. 6 Fabricated microgrippers and their displacement under 40 V actuation. a Metallographic microscope image of the freeform microgripper CB7-D1. b The images of the microgripper CB7-D1, CB7-D2, and SB7 under a certain actuation voltage. Image (1)–(3). The images of the microgripper CB7-D1, CB7-D2, and SB7 under an actuation voltage of 40 V. For comparison, the red contours indicate the position of the structure before actuation. The upper images show the arm tip area, the middle shows the rotary comb actuator area, and the bottom images show the connecting beam area. (1) CB7-D1, (2) CB7-D1, and (3) SB7 for an actuation voltage of 40 V. For comparison, the red contours indicate the position of the structure before actuation. The upper images show the arm tip area. The middle images show the rotary comb actuator area. The bottom images show the connecting beam area Pull-in occurred in design CB7-D1 due to R becoming point first, as the long lever of the rotary comb actuator too large, resulting from the undesired movement of the acts as a motion amplifier. curved beam along the R-axis. As shown in Fig. 8a. (4), the The pull-in effect can easily be mitigated by increasing outermost comb fingers had the largest R value com- the stiffness of the connecting beams along the R-axis pared with other comb fingers and reached the pull-in (e.g., by increasing the beam width). However, this will Wang et al. Microsystems & Nanoengineering (2022) 8:3 Page 11 of 14 Microscope & camera 4.7 mm Multimeter Power supply Microgripper chip Electronic circuit Straight beam (SB) VS curved beam (CB) Straight beam (SB) VS curved beam (CB) with 7um minimum width with 7um minimum width CB7 D1(E) CB7D1(E) CB7 D2(E) CB7D2(E) SB7(E) SB7(E) CB7 D1(F) CB7D1(S) CB7 D2(F) CB7D2(S) SB7 (F) SB7(S) 20 20 10 10 0 0 0 10203040 50 60 020 40 60 80 100 120 Voltage (V) Force (uN) Fig. 7 Measurement setup and result. a Measurement setup. b Characterization of the simulated and measured X versus actuation voltages in two freeform designs (CB7-D1 (blue line), CB7-D2 (red line)) and one orthogonal design (SB (black line)). Simulated results (dashed lines): CB-7D1(S), CB7-D2(S), SB7(S). Measured results (solid lines): CB7-D1 (E), CB7-D2 (E), SB7 (E). c Characterization of the simulated and measured X vs. actuation force in two freeform designs (CB7-D1 (blue), CB7-D2 (red)) and one orthogonal design (SB (black)). Linear fitting lines (solid lines): CB-7D1 (F), CB7-D2 (F), SB7 (F). Measured results (dots): CB7-D1(E), CB7-D2(E), SB7(E) reduce the X for a given actuation voltage. After opti- Then, the microgripper was driven with a voltage of 31 V mization, design CB7-D2 reached a larger X (91.5 μm) and gripped the hair, as shown in Fig. 8b (2). The measured with a higher pull-in voltage (47.5 V). gap of the arm tips was 70 μm, smaller than the diameter of the hair, indicating successful gripping of the hair. In Demonstration of micro-object gripping addition, according to Fig. 7b, CB7-D2 was expected to To demonstrate the performance of the fabricated have an X of 30 μm for an actuation voltage of 31 V, microgripper, microgripper design CB7-D2 was used to matching the experimental result shown in Fig. 8b(2). grip human hair with a diameter of 77 μm. The position of the microgripper relative to the hair before the gripping Discussion test is shown in Fig. 8b (1), in which the gap of the arm For the same actuation voltage, microgrippers with tips is 100 μm. It is worth noting that the micro stick-slip freeform geometries (CB7-D1 and CB7-D2) improved X motion between the object and arm tip is mainly deter- by 150–200% compared with orthogonal geometries (SB7) mined by the friction force. In ref. , Zhang and Liu et al. for the same die area. Therefore, the use of freeform found that micro stick-slip motion could be explained by geometries has two practical advantages: (i) a lower the Stribeck model, Dahl model, and LuGre model. The actuation voltage to reach the same X and (ii) less harm LuGre model has the best accuracy. The Coulomb friction to fragile objects during gripping and releasing. model and the elastoplastic model do not work in a micro However, electrostatic rotary microgrippers exhibit an stick-slip motion system. undesired radial displacement R during actuation. This X (um) X (um) T Wang et al. Microsystems & Nanoengineering (2022) 8:3 Page 12 of 14 ab (1) Human hair 11um (1) (2) 11um 26 77 um um um Small misalignment No obvious misalignment 45 100 45 100um 0VDC 40 V SB7 40 V CB7 D2 um um um (3) (4) (2) 11um 11um 77 um 26 26 Large misalignment Pull - in um um 40 V CB7 D1 41 V CB7 D1 70 60 100um 31VDC um um um Fig. 8 Results of 47.5 V actuation experiment, pull-in experiment, and gripping experiment. a Images of designs CB7-D2 and SB7 under an actuation voltage of 47.5 V. Comparison of radial deflection R of the rotary comb actuators for different microgripper designs. (1) No apparent R in m m the microgripper design SB7 under an actuation voltage of 40 V. (2) Small R in the microgripper design CB7-D2 under an actuation voltage of 40 V. (3) Large R in the microgripper design CB7-D1 under an actuation voltage of 40 V. (4) Pull-in of the microgripper design CB7-D1 under an actuation voltage of 41 V. b Gripping a human hair with a diameter of 77 μm using microgripper design CB7-D2 (1) before gripping and (2) after gripping leads to a reduction in the gap of the comb drive elec- ability in Hao et al.’s design is due to its narrow beam- trode, potentially causing pull-in, which limits the max- width (3.6 μm). If the beamwidth of CB7-D2 was reduced imal X . With the proposed optimization method, the R from 7 to 3.6 μm, a simulation indicated that CB7-D2 T m of the rotary comb actuators is included in the FOM. The would only need 27 V to have an X of 100 μm, which is GA-based optimization concurrently maximizes X and smaller than the 31 V of Hao et al.s design. Moreover, the actuation voltage can be further reduced through an minimizes R for a given voltage. Comparing the two freeform designs, CB7-D1 has a increase in the number of rotary comb actuators, since larger X but a larger R compared with CB7-D2 for the Hao et al.’s design has six groups of rotary comb actua- T m same actuation voltage. Thus, a designer can select free- tors, while our designs only have four groups of rotary form designs according to different requirements for the comb actuators. gripping range. For example, for objects with a diameter In addition, the CB7-D1 and the CB7-D2 design were between 100 and 30 μm, design CB7-D1 is superior to developed based on Chang et al.’s design . Compared CB7-D2, as CB7-D1 can satisfy the gripping range with a with Chang et al.’s design , the CB7-D1 actuation ability lower actuation voltage. Additionally, for objects with a is 4.8 times larger, while the gripping range is 1.4 times diameter between 100 and 10 μm, CB7-D2 is better than lower, whereas the design CB7-D2 actuation ability is 4.3 CB7-D1, as CB7-D1 can offer a larger gripping range, times larger, while the gripping range is 1.1 times lower. while CB7-D1 pulls in after 74 μm. Table 6 compares the gripping range of our micro- Conclusions grippers with those of other electrostatically actuated A novel microgripper with freeform geometries microgrippers in the literature. To compare the actuation designed using a GA approach is presented. The GA- ability of different designs fairly, the maximum X is divi- based semiautomated design methodology with freeform ded by the square of the related actuation voltage, and the geometries is introduced in detail. It is capable of calculated result is taken as the actuation ability. Crescenzi designing near-optimal MEMS devices that are robust to et al.’s design have the highest actuation ability and lowest fabrication tolerances. Two types of microgrippers with actuation force but a limited gripping range. Compared freeform geometries and one microgripper with ortho- with Crescenzi et al.’s design, the CB7-D1 actuation ability gonal geometries were optimized by this method. FEA is 6 times lower, while the gripping range is 3.6 times lar- simulations were used to analyze the static and dynamic ger, whereas the design CB7-D2 actuation ability is 5 times performance as well as the stress distribution of the lower, while the gripping range is 4.6 times larger. designed microgrippers. The experiment showed that the Hao et al.’s design has the second-highest actuation microgripper with freeform geometries had a large X ability and largest gripping range. The high actuation (91.5 μm) for a low actuation voltage (47.5 V), which axis Radial Wang et al. Microsystems & Nanoengineering (2022) 8:3 Page 13 of 14 Table 6 Comparison of different gripper operating displacements Design Actuation force Actuation Actuation range Actuation ability Die area (μm ) Gripper arm (μN) voltage (V) (μm) (nm/V ) length (mm) Volland 231 80 20 3.13 1250*3300 1 Beyeler 986 150 100 4.44 7700*5600 3.3 Chen 1646 80 25 3.91 5745*3217 1 Bazaz 1181 50 17 6.80 4891*6402 2.5 Chang 297 100 94 9.40 3100*3700 1.7 Piriyanont 104 80 90 14.06 8500*5600 1.6 Xu 273 72 63 12.15 2800*3812 NA Hao 37 31.5 100 100.78 4500*4000 1.7 Crescenzi 3 11 20 165.29 2710*4417 1.4 (CB7-D1) 51 40 72.9 45.54 3700*3700 1.7 (CB7-D2) 72 47.5 91.5 40.55 3700*3700 1.7 (SB7) 115 60 54 15.00 3700*3700 1.7 From COMSOL simulation. agreed well with the theory. This made it possible to Acknowledgements This research was funded by the Science Challenge Project, grant no. manipulate a wide range of objects (size ranging from 10 TZ2016006-0502-02, and the National Key Research and Development to 100 μm). The concept was successfully demonstrated Program of China, grant no. 2021YFB3201603. by grasping a human hair with a diameter of 77 μm. A Author details detailed analysis of the pull-in effect due to the R of the College of Optical Science and Engineering, Zhejiang University, Hangzhou, actuator electrodes was conducted. Possible methods to China. Department of Electrical Engineering and Computer Science, University mitigate this effect were also discussed. of Liege, Liege, Belgium. ESAT-MNS, University of Leuven, Leuven, Belgium. PGMF and School of Physics, Huazhong University of Science and For the same actuation voltage, microgrippers with Technology, Wuhan, China freeform geometries improved X by 150–200% com- pared with orthogonal geometries in the same die area. Author contributions Thus, freeform geometries have two advantages: (i) a C.W. designed, built, and tested the MEMS microgripper. W.F. and Y.W. contributed to the design of the MEMS mechanism. X.S., S.S., and M.G. lower actuation power to reach the same X and (ii) less contributed to the MEMS fabrication. H.L. contributed to the measurement harm to fragile objects during gripping and releasing. setup. C.W., W.F., and Y.W. took the measurements. H.Z., C.W., Y.W, and A.Q. In Table 6, we briefly compare our freeform geometry performed computational analysis of the data. C.W., H.L., J.B., and M.K. led the writing of the paper, and all authors provided comments. H.L., J.B., and M.K. design with the two best electrostatic microgrippers had the initial concept of the microgripper. H.L. and J.B. oversaw the design, 8,9 described in the literature in terms of actuation range fabrication, and testing of the microgripper. and X per voltage 2 (actuation ability). Both freeform Conflict of interest geometries developed in this work have a larger gripping The authors declare that they have no conflict of interest. range compared to Crescenzi et al. . If the same number of actuation comb fingers is considered, our designs have Supplementary information The online version contains supplementary a better actuation ability compared to Hao et al. . material available at https://doi.org/10.1038/s41378-021-00336-0. The improved performance of the microgripper is mainly due to the use of GA for freeform geometric Received: 6 April 2021 Accepted: 10 November 2021 design. It is worth noting that the proposed design methodology enabling freeform geometries can be extended to a wide range of other MEMS devices. Future work will include equipping the microgripper with both References 1. Thornell, G., Bexell, M., Schweitz, J.-Å. & Johansson, S. Design and fabrication of force sensing and a feedback system. This will allow the a gripping tool for micromanipulation. Sens. Actuators A 53,428–433 (1996). gripping process to be performed with higher precision 2. Ansel, Y.,Schmitz, F., Kunz,S., Gruber,H.& Popovic, G. 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Published: Jan 6, 2022

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