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.


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Moreover, piezoelectric actuated microgrippers cannot work in a high temperature environment. A magnetically 38 actuated gripper was reported in [6]. This design provides a large displacement and a quick response with a reasonable 39 sensitivity, but it requires a complicated and expensive assembly process. Alternatively, a microgripper based on shape 40 memory alloy was discussed in [7]. This design had excellent flexibility and a large bandwidth. However, it also 41 suffered hysteresis nonlinearity and a large power consumption. Electrostatically actuated microgrippers were reported 42 in [8,9]. Especially, for the first time, Chang et al. introduced a rotary actuation comb into an electrostatically actuated 43 microgripper to increase the displacement range to 94 μm with an actuation voltage of 100 V [10]. These designs 44 feature a fast response time, low power consumption as well as no hysteresis. However, these designs have a relatively 45 large dimension due to the high number of actuation comb fingers required. Besides, the maximum displacement of 46 the electrostatically actuated microgripper is limited by the pull-in effect [11]. Also, the actuation voltage of the electrostatically actuated microgrippers is relatively high and normally, a voltage larger than 80 V is required to achieve 48 a displacement of 100 μm. Such a high actuation voltage is not only problematic in practical applications but also can 49 damage gripped samples.

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In the vast majority of MEMS devices, simple geometrical layouts comprising only a few simple building blocks, 51 such as beams, rectangular masses and, more rarely, rings or disk-shaped structures are used [12]. As discussed in the 52 following, there are cases in which such conventional, simple designs limit the performance of MEMS devices and 53 therefore may not meet the requirements for specific applications. Compared with conventional designs, geometries 54 comprising more complex geometries offer the designer more freedom. Complex geometries may result in novel 55 designs with superior performance [13] and overcome the limitation of simple mechanisms [14][15][16][17]. For example, by 2 using curved anti-springs, Middlemiss      LG 500 µm 1700 µm The movement of a rotary comb actuator after actuation can be best described by a polar coordinate system, as

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It is important to note that during the optimization, the design space for the connecting beams is fixed (390ⅹ390 159 μm2) for the GA; this enables objective comparison of different designs. It could be argued that for an orthogonal beam 160 design, the actuation range can be improved by simply increasing the length of the connecting beam. However, in a 161 fixed design space, the two adjacent orthogonal connecting beams will cross each other if the two connecting beams 162 are prolonged beyond a certain level, which is physical obviously impossible. A serpentine orthogonal beam could be 163 used to prevent this and prolong the beam length, however, this reduces the stiffness in the radial direction and thus 164 increases Rm, leading to a low pull-in event. Therefore, constraining the design to a conventional orthogonal shape does 165 not fully explore the design space and does not achieve an optimal design. More complex freeform geometrical shapes 166 may result in a solution with superior performance. Thus, we propose to replace simple orthogonal structures with 167 structures based on freeform geometries. Their shapes can be optimized with the GA to improve the actuation range at 168 a low actuation voltage.

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In the following, we regard the sum of the displacements at the two gripper arm tips as the displacement of the 171 microgripper, XT. Ideally, a large XT with a low actuation voltage is desired for an electrostatically actuated 172 microgripper. Therefore, XT for a fixed actuation voltage (40 V) was used as the FOM for the design process. The gap 173 between the arm tips of the microgripper was designed as 100 μm, which obviously defines an upper limit for XT.

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These values were chosen as most of the electrostatic microgrippers described in the literature require a voltage above 175 80 V to reach a XT of 100 μm. Therefore, 40 V represents a typical mid-range actuation voltage, suitable for comparison.

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Consequently, the GA is programmed in such a way that it maximizes XT while maintaining Rm less than 1.3 μm.

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CB7-D2 had a larger Rm than CB7-D1. The difference between the two designs was mainly due to that CB7-D1 had a 225 more compliant freeform beam than CB7-D2.

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To compare the freeform designs with a conventional orthogonal design, the same GA optimization algorithm was 229 also run with constraints allowing only an orthogonal design. An identical design space (390ⅹ390 μm2) for chosen for 230 the connecting beams to allow an objective comparison. The optimal orthogonal design was termed SB7 (( Fig. 6b (3)); 231

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As a freeform design has many degrees of freedom, it is necessary to disperse the parameter values during the 239 optimization to achieve a global rather than a locally optimal solution. However, a too dispersed parameter space makes 240 the optimization process computationally intensive. To study the convergence, the GA carried out 10 independent 241 optimization processes by using different initial designs across the design space. As circumstantial evidence, the 242 topologies of 10 optimal solutions resembled each other, indicating a global convergence of the optimization process 243 to a large extent. The FOMs of the designs obtained in 10 different optimization runs ranged from 47 μm to 60 μm.   Table 4. Besides, the actuation force for the freeform design CB7-254 D1 to reach a XT of 100 μm was only 39% of that of the orthogonal design SB7, as shown in Table 4. Therefore, the 255 stiffness of the connecting beams in the freeform design CB7-D1 is lower than that in the orthogonal design SB7. The 256 output force of the gripper when grasping a micro-object is an important parameter of the gripper performance, which 257 is directly related to the stiffness of the connecting beams. The freeform design CB7-D1 is thus expected to be less 258 harmful to fragile samples during manipulation compared with the orthogonal design SB7.

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Given the significant influence of vibration modes and stress on the microgripper, these parameters were analyzed 262 next. The frequencies of the first three modes of the freeform design CB7-D1 were 823 Hz, 10583 Hz and 27932 Hz, 263 respectively. The 2nd mode frequency is 11.86 times larger than the working mode (1st mode) frequency, which 264 dramatically increased the stability during actuation. The frequencies of the first three modes of the freeform design 265 CB7-D2 and the orthogonal design SB7 are listed in Table 5; the mode shapes of CB7-D1 were very similar. to increase the XT, since a low stress concentration leads to a large XT. As shown in Fig. 4, the stress was evenly 277 distributed on the freeform. As will be discussed later, in the experiment, none of the microgrippers broke during 278 actuation. Furthermore, the microgripper did not break even when we manually probed the arm tips of the microgripper 279 to release them from the actuation combs after a pull-in event. As shown in Fig. 4

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The displacements of the microgrippers were compared not only at the arm tips but also in the areas of the rotary 338 comb actuators and connecting beams. A comparison of the three types of microgripper designs with an actuation 339 voltage of 40 V is shown in Fig. 6b (1), (2), (3), in which the red contours indicate the position of the structure before 11 actuation. The XT of design CB7-D1 was larger than that of design CB7-D2, which, in turn, was larger than that of 341 design SB7 in all three areas. Since CB7-D1 could not be actuated higher than 40 V (which is close to the pull-in

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To demonstrate the performance of the fabricated microgripper, microgripper design CB7-D2 was used to grip a 381 human hair with a diameter of 77 μm. The position of the microgripper relative to the hair before the gripping test is 382 shown in Fig. 8b (1

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The Coulomb friction model and the elastoplastic model do not work in a micro stick-slip motion system.

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Then, the microgripper was driven with a voltage of 31 V and gripped the hair, as shown in Fig. 8b (2). The measured 387 gap of the arm tips was 70 μm, smaller than the diameter of the hair, indicating the successful gripping of the hair.

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Also, according to Fig. 7b, CB7-D2 was expected to have a XT of 30 μm for an actuation voltage of 31 V, matching 389 the experimental result shown in Fig. 8b (2 A novel microgripper with freeform geometries designed using a GA approach is presented. The GA based semi-424 automated design methodology with freeform geometries is introduced in detail. It is capable of designing near-optimal 425 MEMS devices that are robust to fabrication tolerances. Two types of microgrippers with freeform geometries and one 426 microgripper with orthogonal geometries were optimized by this method. FEA simulations were used to analyze the 427 static and dynamic performance as well as the stress distribution of the designed microgrippers. The experiment showed 428 that the microgripper with freeform geometries had a large XT (91.5 μm) for a low actuation voltage (47.5 V), which 429 agreed well with the theory. This made it possible to manipulate a wide range of objects (size ranging from 10 μm to 430 100 μm). The concept was successfully demonstrated by grasping a human hair with a diameter of 77 μm. A detailed 431 analysis of the pull-in effect due to the Rm of the actuator electrodes was conducted. Possible methods to mitigate this 432 effect were also discussed.

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For the same actuation voltage, microgrippers with freeform geometries improved XT by 150-200% compared with 434 orthogonal geometries in the same die area. Thus, freeform geometries have two advantages i) a lower actuation power 435 to reach the same XT, ii) less harm to fragile objects during gripping and releasing.

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From Table 6, we briefly compare our freeform geometries design with the two best electrostatic microgrippers 437 described in the literature [8,9] in terms of actuation range and XT per voltage2 (actuation ability). Both freeform 438 geometries developed in this work have a larger gripping range compared to Crescenzi et al. [9]. If the same number 439 of actuation comb fingers is considered our designs have a better actuation ability compared to Hao et al. [8].

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The improved performance of the microgripper is mainly due to the use of GA for freeform geometric design. It is 441 worth pointing out that the proposed design methodology enabling freeform geometries can be extended to a wide 442 range of other MEMS devices. Future work will include equipping the microgripper with both force sensing and a 443 feedback system. This will allow the gripping process to be performed with a higher precision more controllable force, 444 creating the ability for fast, automated operation.

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The authors declare no conflicts of interest.