Electrostatic chuck having compliant multi-beam structures with rotatable bipolar pad-shaped electrodes

The demand for the manipulation of flexible film-like objects and those with non-planar surfaces, which cannot be handled using current technologies, has increased considerably. A bipolar electrostatic chuck (ESC) is a device that clamps target objects using a uniform electrostatic force. Traditional ESCs cannot satisfy these demands because of their planar surfaces. Bipolar ESCs with a compliant multi-beam assembly have been proposed to manipulate such objects while leveraging the uniform force distribution of ESCs. Although the proposed compliant ESCs have the potential for such manipulations, increasing the attractive force remains a critical technical issue. This study aims to develop a compliant ESC with pad-shaped bipolar electrodes connected to beam tips with rotational degrees of freedom (RDOFs). Four ESC models with pad-shaped electrodes with different RDOFs between zero and three and one without a pad-shaped electrode are fabricated via 3D printing. The experimental comparison of the five models indicates that an increase in the RDOFs significantly improves the attractive force of each electrode. The high potential of compliant ESCs with three RDOFs at the beam tips is illustrated using three different demonstrations: picking and placing dielectric films, a rigid object with a plane surface, and a rigid object with a curved surface. The results provide insights into the development of industrial electrostatic grippers.


Introduction
Object handling is an essential technology in the automation of manufacturing processes.Significant numbers of studies on manipulation techniques have been conducted, such as mechanical grippers [1], passive dry adhesion-based grippers [2], and adoptive probe grippers [3].The recent growing demands for wearable devices and flexible and large displays [4][5][6][7] increased the number of devices having curved surfaces.The manufacturing processes of such devices require picking large thin films from planar surfaces and placing them on curved surfaces.Handling thin films requires distributing a uniform force in the contact area between the grippers and target objects and adapting the grippers' shapes to the curvature of the target objects during pasting.This unique requirement makes traditional mechanical grippers unsuitable for thin-film handling because a local force is applied to the target objects during gripping.Moreover, the active adaptation of the shapes of grippers to curved surfaces requires sensitive control.Therefore, a gripper that can generate a uniform attractive force and passively adapt its form during manipulation is needed.One of the passively deformable mechanisms is the geckoinspired fine hair structure.Gecko adhesive is generated by van der Waals forces, which require close contact with target objects.The foot structure of a gecko has setae, spatulae, and numerous arrays of microbeam structures, which individually conform to a variable surface profile [8,9].This unique and functional structure has inspired studies on manipulation techniques [9][10][11].Although its original foot structure employs van der Waals forces, the research expands to grippers exhibiting electrostatic forces, which are more controllable and robust than van der Waals forces [12].
Grippers using electrostatic forces, namely electrostatic chucks (ESCs), have been widely used in the semiconductor industry for transporting silicon wafers [13][14][15][16][17][18].Generally, bipolar ESCs possess two electrodes (positive and negative) to pick target objects via electrostatic force by applying voltages and to place the objects by eliminating the voltage.ESCs generate more uniform attractive forces than mechanical grippers, rendering them promising candidates for handling flexible and thin objects.However, conventional ESCs for handling flat shapes cannot place thin films on curved surfaces by adopting their shape to the target objects.Therefore, the need for thin-film handling methods for flexible displays may be fulfilled with an ESC that can passively deform during placement on curved surfaces.Bipolar ESCs with compliant beams were developed to satisfy the requirements above [19][20][21][22].Previous studies have fabricated ESCs with a beam-array assembly using several methods, such as lithography and additive manufacturing [21,22].Compliant ESCs stack several ESC layers with a compliant beam array assembly to generate a large contact area, as shown in figure 1(A) [23].Although the beam structure provides flexibility, it increases the non-contact area with the target object, as shown in figure 1(A).A large non-contact area results in a low attractive force and non-uniform force distribution because non-contact area can generate a small attractive force.On the other hand, increasing the attractive area by increasing the number of beams can also increase the elastic force from the beams to the target objects.This means that an increase in the beam can mitigate the advantage of a compliant ESC structure, which is, for example, flexibility in the contact area.Therefore, increasing the density of beam-tip electrodes while maintaining flexibility is an essential technical issue to increase the attractive performance.
One of the technical challenges of conventional ESCs is residual charge and attractive force in detachment.Due to the residual charge after cutting off the applied voltage, ESCs retain their attractive electrostatic force when detaching target objects.ESCs with compliant beams also face the disadvantage.The residual force made placing a film by the ESCs challenging.It is also essential to investigate the placement of the target object and concurrently increase the attractive performance.
This study proposes an ESC with pad-shaped bipolar electrodes at the beam tips to increase the attractive force.Figure 1(B) shows that this structure might provide both softness owing to the multi-beam structure and a large attractive area owing to the pad-shaped electrodes.The beams connecting the pad-shaped electrode and the bases will receive a force as a cantilever beam without a rotaional degree of freedom in gripping and releasing an object.Introducing a rotational degree of freedom at the end of a beam generally decreases elastic force due to deformation.Thus, the attractive force might increase by introducing a rotational degree of freedom at the connection between the pad-shaped electrodes and beam.Therefore, this study aimed to develop bipolar ESCs with multiple pad-shaped bipolar electrodes supported by thin beams.Four ESC models with pad-shaped electrodes with rotational degrees of freedom (RDOFs) varying from zero to three and one ESC model without pad-shaped electrodes were 3D printed, and their attractive performances were compared.The usefulness of the proposed ESCs was demonstrated by gripping and releasing a dielectric film, picking a heavy object, and gripping a curved surface object.

Materials and methods
This study compared five ESC models in order to investigate the effect of pad-shaped electrodes on attractive force performance and to observe the effect of RDOF on beam tips.Four ESC models with pad-shaped electrodes having different RDOFs ranging from zero to three and one ESC model without pad-shaped electrodes were fabricated.Figure 2 shows the images of the fabricated ESCs and their dimensions.Four models, namely a zero-RDOF (0-RDOF), a 1-axis rotation (1-RDOF), 2-axis rotation (2-RDOF), and ball joint models (3-RDOF), were created.The proposed 1-beam ESC with a pad-shaped electrode (figures 2(C), (D), (F)-(J)) consisted of a pad-shaped bipolar probe and a base with a beam.The pad-shaped part was rectangular with dimensions of 11 mm × 13 mm.An insulating section surrounded the two conductive sections.The conductive area was 4 mm × 10 mm, and the insulative width between the conductive areas was 0.8 mm.The base of the ESC had a 45-degree-slanted beam, which was 50 mm and had a rectangular cross-section of 1.2 mm × 1.6 mm.The pad-shaped electrodes and beams were fixed in the 0-RDOF model and connected with mechanical couples in the 1-RDOF, 2-RDOF, and 3-RDOF models.A model without a pad-shaped electrode was also fabricated (figures 2 (A), (B), (E), and (J)) to compare the proposed model with the models developed in related studies [22,23].The beam and insulating layer dimensions were the same as those for the ESC with a pad-shaped model.An effective area for the attractive force was defined to compare the attractive force performance of the ESC with and without the pad-shaped electrodes.The effective area is calculated to reflect the attractive force performance of each beam in the stacked modules.Therefore, this area also includes those that do not come into contact with the target object.The area of the 1-beam module is 153.4 mm 2 and that of the 2-beam module is 306.8 mm 2 .
All ESC models were fabricated using a 3D printer (Ultimaker 3, Ultimaker, Netherlands).The material of the conductive layers was Proto-pasta PLA Conductive Black, and the material of the insulative layer was Ultimaker PLA transparent.The 1-and 2-RDOF models had SUS bearings (NSK SMF63ZZ, an inner diameter of 3 mm, an outer diameter of 6 mm, and a width of 2.5 mm, 313 mg) and plastic rods (Hikari-mole white ABS round rod; rod diameter of 3 mm) to ensure the rotation mechanism.The bearings were manually inserted into 3D-printed parts after printing.The pad-shaped electrode of the 3-RDOF was created by placing a metal bead (UNICRAFTALE Rondel Beads made of 304SUS pink gold 4 mm, hole diameter: 1.8 mm, 130 mg in average) during the 3D printing.The metal bead was placed in the 3D printed part when the printing was stopped halfway through.After the bead was placed, printing was resumed, and 3D printed around the bead.The tips of the beam and metal bead were manually fixed with glue.An ultrathin copper wire connected each conductive electrode part of the pad-shaped electrodes to a conductive part attached to the base.
Figure 2(K) shows the schematic of the experiment instruments.It consists of two DC power supplies (Matsusada HJPM-3R5), an analytical balance (Sartorius QUINTIX224-ISJP, resolution: 0.1 mg, stabilization time: 2 s), a motorized stage, and a Faraday cage.The Faraday cage was used to minimize the surrounding effects.The target object placed on the balance was created by gluing five glass slides (Matsunami Glass Ind. Co., Ltd.S1111, dimensions 76 ×26 x 0.91, mass 4.59 g).The ESCs with and without pad-shaped modules were installed on the motorized stage.Steel spheres were placed under the object to reduce the horizontal force to the target object.The balance recorded the attractive force generated between the ESCs and the target object.The experiment procedure has five steps: The ESCs were moved at a speed of 0.01 mm s −1 throughout the process.
(1) Calibration: the stage was manually moved down until probe tips touched with the target object without applied voltage.The surface was defined as Z = 0 mm (the downward direction is positive), (2) Initializing: the stage was moved up until Z = −1 mm, (3) Loading: the ESC was moved down until Z = 1 mm with a DC applied voltage of ±600 V, (4) Stabilizing: the ESC was kept at Z = 1 mm for 10 s, (5) Unloading: the ESC was moved up to Z = −5 mm; and (6) Ending: after the ESC was detached from the object, the applied voltage is cut off.
Increasing the number of beams and electrodes decreases the attractive force per unit area because of the beam tips' misalignment [23].The attractive force of the 2-beams module was measured to investigate the effect of arraying beams and electrodes.The attractive force of both beams (F 2beams ) and their individual attractive forces (F left beam and F right beam ) were measured.The performance retention rate is defined in equation (1).The performance retention rate is 100% when the attractive force of the assembly of both beams is equal to the sum of their individual attractive forces.

Performance retention rate
Result Figure 3(A) shows the plots of the force of the 1-beam modules having a single ESC beam, with and without the pad-shaped bipolar electrodes against the motorized stage' displacement.The horizontal axis is the displacement of the beam tips from the target objects (Z-axis), and the vertical axis shows the attractive force.The pressure was obtained by dividing the force's recorded value by the effective area (1-beam module: 153.4 mm 2 ).Each color represents the measured value of each ESC model.For example, green dots represent ESC without pad-shaped electrodes, and red dots represent ESC with 3-RDOFs.For the same Z, the higher force was measured in the loading phase and the lower force was recorded in the unloading phase.The difference between the two values was the effects of electrostatic force.The slope of the loading phase, when Z was from −1 to 1 mm, indicated that the ESC was being pushed toward the object, thereby applying pressure to it.The differences in the slopes of each ESC at loading were observed even though the beam dimensions were the same in all models.An attractive force was observed as the ESCs moved upward; when the ESC pads moved away from the object, Z was from −1 to 5 mm.During the unloading phase, owing to the sufficient attractive force and the compliance of the beams, the beams were slightly bent and maintained contact with the object.As the ESC was moved up, its beam tips were detached from the object.The maximum attractive force was recorded immediately before detachment.The points of detachments and the maximum attractive forces are shown with the black dotted lines in figure 3(A).
The comparison of the ESC without pad-shaped electrodes and 0-RDOF shows that the attractive force of the proposed ESC with pad-shaped bipolar electrodes is larger than that without pad-shaped electrodes.The attractive performance of the 1-beam model was significantly improved owing to the increased electrode area of the tip.As the RDOF increases, the point of detachment from the target object increases.In particular, the presence of one RDOF (0-RDOF or 1-RDOF) resulted in a significant difference in the attractive force.The maximum attractive force and the vertical displacement on detachment increased as the RDOF increased.The exact values of attractive forces and the points of detachments are shown in the row 1-beam module in table 1. Figure 3(A) also shows that the loading force on the target object is larger than that of the ESC without pad-shaped electrodes during the loading phase.The increased contact area may have increased the shearing force by rendering it harder for the pad-shaped electrode to slip.
Figure 3(B) shows the state of the pad-shaped electrode during the experiment.Figure 3(B-2) shows that the left side of the pad-shaped electrode without R-DOF has a distance from the target object during the loading phase, indicating that concentrated stress is applied to the fulcrum of the pad-shaped electrode.Figure 3(B-3) shows that the right side of the pad-shaped electrodes without R-DOF is not in contact during the unloading phase, indicating that the contact area with the target decreases.Figure 3(B-4) shows that when the elastic force of the beam exceeds the attractive electrostatic force, the electrode loses contact with the object.The gap between the pad-shaped electrodes without R-DOF and the object suggests that the potential attractive performance of the pad-shaped electrode was not sufficiently demonstrated.Figure 3(b) also explain the significant difference in the attractive force between the 0-and 1-RDOF, which could facilitate contact with the object.In the 0-RDOF, one side of the pad-shaped electrode was detached, whereas in the 1-RDOF, the pad-shaped electrodes slipped on the target object.This slipping maintained the attractive area constant with the target object, resulting in a  significant attractive force.An increase in the RDOF enabled tilting in any direction; thus, a stable point could easily be attained to hold the object when unloading the device.Table 1 summarizes the points where the ESCs detach from the target object, the maximum attractive force, and the performance retention rate to assess the effects of arraying electrodes.The pressure of 2-beam modules was calcurated by dividing the measured force values with the effective area (2-beam module: 306.8 mm2).The results show that the performance retention rate increases with an increase in the RDOF.The difference between the 0-and 1-RDOF is particularly significant.The result of the 3-RDOFs model demonstrated that 99.9% of the attractive performance is maintained when the number of beams doubles.Misalignment of the pad-shaped electrodes might cause a significantly lower performance retention rate of the proposed 2-beams module with 0-RDOF.Because the electrodes and beams of the pads were assembled manually, the inclination to the horizontal surface between the two pads was different.This indicated that when one pad-shaped electrode attracted the object, the other could have pushed the target object.Consequently, the total attractive force may have been significantly reduced.The increasing performance retention rate was also explained by the fact that the RDOF can easily eliminate the height difference between the left and right beam tips and the difference in inclination with respect to the horizontal plane.This result suggests that the attractive performance of the ball joint model (3-RDOF) can improve as the number of beams increases.

. Materials and methods
This section aims to demonstrate the capabilities of the proposed ESC for thin-film handling.The ESCs with ball joints (3-RDOF) were used because the 3-RDOF model exhibited the highest attractive performance.Because the residual charge remains after cutting off the applied voltage, the residual attractive force can prevent the ESCs from detaching from the target objects.Therefore, investigating detachment methods is equally important as measuring the attractive force.
This study compared seven experiment conditions, as detailed in table 2. The experiment conditions differed in three variables: applied voltage, trajectory, and RDOF.As for applied voltage, simply cutting the voltage and attenuation were compared.Attenuation is used in industry to decrease residual charge by gradually decreasing the applied voltage to zero while repeatedly inverting the positive and negative [24].This study compared two trajectories: simple vertical displacement and tilting trajectory.Implementing a tilting trajectory in ESCs with beam electrodes has been demonstrated to facilitate the placement of a thin film.This approach, characterized by concurrent vertical displacement and rotational movement, induces a peeling effect at the interface between the electrode and the target object [23].The RDOF of the beam tips was controlled because a decrease in the RDOF decreases the attractive performance.The RDOF was removed by gluing the rotational joints.In table  (1) The device was lowered until it contacted the target object with an applied DC voltage of ±500 V (Z = 0).
Then, the device was moved upward to pick up the thin film with an applied DC voltage of ±500 V (Z = −10 mm).
(2) The device was lowered according to different trajectories.In conditions A, B, C, and E, the device was lowered to Z = 0 with applied DC voltages of ±500 V.In conditions D, F, and G, the ESC was lowered towards the point where the beam was deformed significantly with applied DC voltages of ±500 V (Z = 10 mm).
(3) The voltages were cut off in different ways.In conditions A, B, D, and F, the applied voltage was cut off to 0 V.The voltages were cut off with attenuations in conditions C, E, and G.The attenuations were performed at ±500 V and decreased by 100 V while alternating between positive and negative every 5 s.
(4) In conditions D, F, and G, the ball joints at the end of the beam were fixed using an adhesive.(5) The device moved away from the object along different trajectories as detailed in table 1.In conditions A, C, D, and G, the device was moved upwards.In conditions B, E, and F, it moved by tilting trajectory, simultaneous vertical displacements and rotations.

Result
Figure 4 shows the time-lapse images of the releasing experiments.In condition A: the vertical displacement; condition B: the tilting trajectory; and condition C: the attenuation of the applied voltage, the film remained gripped after release trials.In condition B, the significant shear force dragged the thin film.In condition D, the RDOF was removed, and in condition G, the film was peeled off with the left pad-shaped while the film remained gripped with the right-side pad-shaped electrode.In condition D, the pad-shaped electrode's angle was not parallel to the target surface when the device was pulled up.The inclination and removal of the RDOF facilitated the detachment of the target object.Moreover, in condition D, the pad-shaped electrode on one side was successfully detached.In condition E, with the combination of the tilting trajectory and attenuation voltage, the film was completely detached from the ESC at the intended detachment point.In condition F, the film was detached by the combination of the tilting trajectory and removal of the RDOF, although the left leg of the ESCs dragged the film.The combination of factors demonstrated the possibility of successful placement.The results show that a tilting trajectory successfully detached the target object while the attenuation voltage reduced the attractive force.

Rigid object handling using ESCs with different beam compliances 3.2.1. Material and method
To verify the gripping performance of the 3-RDOF model, two types of objects were gripped: a rigid object with a flat surface and an object with a curved surface.We fabricated ESCs having two different compliances.The compliance ( ) l denoting the softness of the beam is expressed by equation (2), where E(3570 MPa) is Young's modulus of polylactic acid [21], and I is the moment of inertia of the area.I is expressed using the length (l , ) width (b , ) and height (h , ) as shown in equation (3).
shows the dimensions and images of each device.The stacked devices comprised four layers of ESC modules with five beams and pad-shaped electrodes attached with 3-RDOF.The compliance of the lowcompliance model was 0.142 m N −1 , and that of the high-compliance model was 4.83 m/N.Figures 3(A), (B) illustrates the experimental setup.The fabricated ESCs were attached to a motorized stage, and the demonstrations were recorded with a video camera.Throughout this process, ESC devices were moved at a speed of 0.5 mm s −1 .A glass slide, which was attached to a weight with a double-sided tape, was used as the object.The total weight was 81 g.The curved object consisted of a 3-D printed body (Polylactic Acid, Ultimaker 3, Ultimaker, Netherlands) and a 100 μm thin polyimide (3 M PIA220 50 Polyimide Electrical Insulation Tape, 3 M, US).The radius of curvature of the fabricated surface was 200 mm, and the total weight of the curved object was16 g.The demonstration was conducted in three steps: (1) Calibration: the device without the applied DC voltages was lowered towards the target object until the device contacted with the target object or the top of the curved surface to set Z = 0. (2) Picking: with an applied DC voltage of ±900 V, the device was moved down to

Result
Figures 6(A) and (B) show the results of grasping both objects and time-lapse pictures of gripping the rigid-plane target using both ESCs with low and high compliance.The results showed that the low-compliance device successfully griped the target, whereas the high-compliance device did not.As the stage was moved up, some of the pads on the high-compliance device began to detach.On detachment of a pad-shaped electrode, the device shook considerably.The vibration caused the other pad-shaped electrodes to fall off, and eventually, all the pads were detached.
Figures 6(C) and (D) show time-lapse pictures of gripping the target object with a curved surface using ESCs with low and high compliances, respectively.The results showed that the high-compliance device successfully griped the target, whereas the low-compliance device did not.The five beams were significantly deformed because the beams followed the curved surface.However, the low-compliance module could not follow the curved surface.Consequently, the left beams of low-compliance module were detached from the target objects in a gripping.

Discussion
The force measurement of the ESCs, table 1, shows that the ESCs having R-DOF performed more than 350 N m −2 attractive force.Considering Liquid Crystal Polymer (LCP) as a target object in LCD display manufacturing industry, for example, a density of an LCP material, E3008 by Sumitomo Chemical Co., Ltd., Japan, is 1.69 g/ cm 3 .[25].A 1 mm thickness of the E3008 film requires 16/66 N m −2 force that balances the gravity of the materials.The result shows that the proposed ESCs having R-DOF may provide enough attractive force for handling such film in such applications.Indeed, figures 4 and 6 show the proposed ESCs having compliant multi-beam structures with rotatable pads that could successfully manipulate a thin film, a rigid object having a flat surface, and a rigid object having a curved surface.
The results of force measurement and demonstrations show that the RDOFs at the tip and beam compliance influence the performance of the ESCs with a beam-array assembly.The compliance of a beam influences the success of picking in the following ways: (1) ensuring the stability of the grip, and (2) flexibly changing the shape according to the target surface.Low compliance renders the beam less flexible and leads to a more stable grip on the target.Therefore, a low-compliance model is suitable for gripping objects with planar surfaces.Contrarily, the higher the compliance of a beam, the more flexible it is according to the shape of the object.The gripping becomes less stable once the ESCs grip the target object.Therefore, a high-compliance model is suitable for gripping objects with curved surfaces.In the industrial use of ESCs, compliance settings should consider the weight, shape, and material of the object to be designed.
A simple mechanical model is adopted to discuss the effect of RDOFs on the attractive force of the ESCs. Figure 7 shows the application of the forces in the unloading step for the RDOF and fixed models of the ESCs with pad-shaped electrodes.In the model with RDOFs at the ends of the beams, the force exerted on the padshaped electrode by the elastic beams acts only vertically when the device is raised.The pad-shaped electrode is pulled vertically in the same direction as the displacement of the device because the RDOF renders the boundary condition at the end of the beam free.On the other hand, for the model with the beam tip and pad-shaped electrode fixed, the force exerted on the pad-shaped electrode splits into vertical and horizontal directions when the device is pulled up.The force is generated in the direction of the beam because the boundary condition at the end of the beam is fixed.The difference in boundary conditions may increase the beams' elastic force in ESCs without the RDOF when the ESCs moved for the same displacement.Owing to the difference in the force, the detachment of the pad-shaped electrode from the object when both models are pulled up is different.The RDOF model is pulled up while the pad-shaped electrode and the object surface are parallel, whereas the fixed model is pulled up while the pad-shaped electrode is tilted from one side.We verified and found that, between these two methods, the fixed model is more likely to detach from the target faster than the RDOF model.In other words, the RDOF model has a better attractive performance.
Two forces are applied to the beam tips: (1) the electrostatic force between the electrode and target object and A more rigorous theoretical analysis determining the total energy of the entire system would be a future research topic.

Conclusion
This study fabricated bipolar ESCs with a compliant beam with pad-shaped bipolar electrodes having rotational degrees of freedom at the beam tips and evaluated them by assessing the attractive force and observing the ESCs' deformation.The results show that an increase in RDOF significantly improves the attractive force performance of ESCs.Demonstrations were also conducted using the ESC with 3-RDOFs.It was shown that combinations of the tilting trajectory and the voltage attenuation were effective for releasing the dielectric film.The model with low compliance was also found to be suitable for gripping heavy objects, and the model with high compliance was suitable for gripping curved surfaces.The demonstrations illustrate the need for a theory synthesizing the effect of the RDOF, the electrostatic force, and the elastic force due to the beam deformation to describe the behaviors of the compliant ESCs.This study contributes to the advancement of manipulation methods for handling objects having curved surfaces and pasting thin films onto curved surfaces.

Figure 1 .
Figure 1.Concept of ESCs having compliant beam structure: (A) non-contact area of bipolar electrostatic chucks without pad-shaped electrodes and (B) concept of ESCs with pad-shaped bipolar electrodes at the beam tips.

2 .
Experiment: effects of ESCs with pad-shaped electrodes and RDOF on the beam tips 2.

Figure 2 .
Figure 2. The pictures and dimensions of fabricated ESCs with or without pad-shaped electrodes and experiment setup for attractive force measurement: (A) 1 beam model without pad electrodes, (B) 2 beams model without pad electrodes, (C) 1 beam model with padshaped electrodes of 0-RDOF, (D) 2 beams model of pad-shaped electrodes of 0-RDOF, (E) Beam tip without pad-shaped electrode, (F) Beam tip of 0-RDF , (G) Beam tip 1-RDF, (H) Beam tip of 2-RDF , (I) Beam tip of 3-RDF (J) The dimensions of tip with and without pad-shaped electrode, (K) The experiment setup for attrative force measurement.The edges of the pad and wires were emphasized by black lines.

Figure 3 .
Figure 3.The result of the force measurement: (A) Displacement and force curve of 1-beam ESC without pad-shaped electrodes module and with different RDOFs pad-shaped electrodes (B) Time-lapse of beam tips of 0-RDOF module.

3. 1 .
Placing a dielectric film using ESC with ball joints 3.1.1 1, four conditions changed single factor: (A) control condition: vertically moving ESCs up; (B) tilting trajectory: rotating the ESC while moving it vertically up; (C) attenuation of the applied DC voltage; (D) removing the RDOF of the beam tips.Three conditions included two factors for detachment: € combination of B and C; (F) combination of B and D; (G) combination of C and D. The experimental setup is shown in figure 5(a).A rectangular polyimide film (DuPont Electronics, Kapton film: 20 mm × 55 mm × 12.5 μm, 22.4 mg) was used as the target object.The object was placed on a piece of acrylic covered with tissue paper.A video camera recorded the experiments.Each demonstration was conducted in the following five steps.

Figure 4 .
Figure 4. Time-lapse images of placing and releasing thin film.Applied voltage was 0 V at all conditions.

Figure 5 .
Figure 5. (A) Experiment method: (a) placement of a film, (b) gripping rigid object, (c) object with a curved surface.(B) Dimensions and pictures of stacked device: (d) Front view of low compliance model, (e) side view of low compliance model, (f) picture of low compliance model, (g) front view of high compliance model, (h) side view of high compliance model, and (i) picture of high compliance model.

Figure 6 .
Figure 6.Time-lapse image of gripping: (A) Low compliance module gripping target with heavy weight, (B) high compliance module gripping target with heavy weight, (C) low compliance module gripping the target object with a curved surface, and (D) high compliance module gripping the target object with a curved surface.

( 2 )
the elastic force due to the beam deformation.The total energy during the movement of the ESCs can be expressed as the sum of the energies due to electrostatic force and elastic deformation of the beam and the work done by the applied voltage, as shown in equation (4).

Figure 7 .
Figure 7. Methods of applying force and types of unloading phase in RDOF and fixed model.

Table 1 .
The maximum attractive force and performance retention rate of 1 beam and 2-beams modules.

Table 2 .
The experiment conditions of releasing a dielectric film.