Optimization and experimental verification of coplanar interdigital electroadhesives

A simplified and novel theoretical model for coplanar interdigital electroadhesives has been presented in this paper. The model has been verified based on a mechatronic and reconfigurable testing platform, and a repeatable testing procedure. The theoretical results have shown that, for interdigital electroadhesive pads to achieve the maximum electroadhesive forces on non-conductive substrates, there is an optimum electrode width/space between electrodes (width/space) ratio, approximately 1.8. On conductive substrates, however, the width/space ratio should be as large as possible. The 2D electrostatic simulation results have shown that, the optimum ratio is significantly affected by the existence of the air gap and substrate thickness variation. A novel analysis of the force between the electroadhesive pad and the substrate has highlighted the inappropriateness to derive the normal forces by the division of the measured shear forces and the friction coefficients. In addition, the electroadhesive forces obtained in a 5 d period in an ambient environment have highlighted the importance of controlling the environment when testing the pads to validate the models. Based on the confident experimental platform and procedure, the results obtained have validated the theoretical results. The results are useful insights for the investigation into environmentally stable and optimized electroadhesives.


Introduction
Electroadhesion is an electrostatic attractive effect between the electroadhesive pad and the substrate [1]. Electroadhesion has been extensively used for many applications. This includes: electrostatic fixtures to hold workpieces [2], an adhesive method for space missions such as material handling [3] and controllable earth orbit grappling [4], electrostatic chucks for material handling and grasping in semiconductor industries [5], end effectors for gripping advanced composites and fibrous materials such as cloth [6] and carbon fibres [7,8], an adhesion mechanism for robots [9][10][11], and material handling units for manufacturing automation and warehouse automation [12]. This is because, compared with other adhe sion mechanisms [13], • Electroadhesion has an enhanced adaptability as it adheres to both conductive and insulating materials such as smooth aluminium and rough concrete surfaces [14]. In addition, it can be applied in a vacuum, and therefore, space environ ments [3,4]. Vacuum environments are also increasingly desirable for highvalue chip manufacturers [15]. • Electroadhesive grasping is a gentle material handling method as it can be applied without contact with the sub strates [16], so it is nondamaging or lessdamaging to the substrate surface, which is desirable for some high value A simplified and novel theoretical model for coplanar interdigital electroadhesives has been presented in this paper. The model has been verified based on a mechatronic and reconfigurable testing platform, and a repeatable testing procedure. The theoretical results have shown that, for interdigital electroadhesive pads to achieve the maximum electroadhesive forces on nonconductive substrates, there is an optimum electrode width/space between electrodes (width/space) ratio, approximately 1.8. On conductive substrates, however, the width/space ratio should be as large as possible. The 2D electrostatic simulation results have shown that, the optimum ratio is significantly affected by the existence of the air gap and substrate thickness variation. A novel analysis of the force between the electroadhesive pad and the substrate has highlighted the inappropriateness to derive the normal forces by the division of the measured shear forces and the friction coefficients. In addition, the electroadhesive forces obtained in a 5 d period in an ambient environment have highlighted the importance of controlling the environment when testing the pads to validate the models. Based on the confident experimental platform and procedure, the results obtained have validated the theoretical results. The results are useful insights for the investigation into environmentally stable and optimized electroadhesives.
Keywords: electroadhesion, experimental validation, interdigital electroadhesive, optimization modelling (Some figures may appear in colour only in the online journal) Original content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. material handling tasks such as pickandplace of silicon wafers in the semiconductor industries [15].
• Furthermore, electroadhesion can bring lightweight and reduced complexity systems as it can help reduce the weight and complexity of a system in terms of control and the mechanical structure as it enables electrically controllable clamping and unclamping, which means pumps or motors are not required. • Last but not the least, electroadhesion is an ultralow energy consumption adhesion method (usually in the µW to mW range) as a very small current in the µA to mA range runs through the electroadhesive pad [17]. This feature helps to reduce the energy consumed in pickandplace applica tions by up to three orders of magnitude [12,18].
An electroadhesion system contains four essential comp onents: the electroadhesive pad, the substrate the pad to be adhered onto, the high voltage power supply to energize the pad, and the control system. The electroadhesive pad contains conductive electrodes connected with high voltage power sources and embedded in dielectric materials, as seen in figure 1(a). The dielectric material serves as dielectric buffers, preventing the charge neutralization and dielectric break down. The dielectric material can be air, so bare electrodes can be used for electroadhesive grasping some nonconductive materials. Electroadhesion is a multidisciplinary, compli cated, and dynamic electrostatic attraction phenomenon with over 33 variables influencing the electroadhesive forces obtainable between the electroadhesive pad and the substrate based on the literature survey [19]. These influencing factors include: (1) environmental factors such as ambient temper ature, humidity, ambient pressure, contaminates, and the air pres sure between the pad and substrate after applying the voltage, (2) electrode parameters such as electrode pattern, electrode width, space between electrodes, electrode thick ness, electrode length, electrode thickness, conductivity, and effective electrode area, (3) pad dielectric parameters such as dielectric resistivity, dielectric permittivity, dielectric strength, di electric surface texture, dissipation factor, dielectric molec ular structure, weight, and polarizability, crystallinity, elec tronegativity, and electropositivity, (4) substrate parameters such as substrate resistivity, permittivity, dielectric strength, thickness, surface texture, molecular structure, weight, and polarizability, crystallinity, electronegativity, and electropo sitivity, and (5) voltage parameters such as voltage polarity (positive/negative/zero), voltage magnitude, and voltage type (direct/alternating current) [19].
A recognized and costeffective procedure to investigate a research phenomenon like electroadhesion commonly con tains two steps: (1) theoretical modelling or computational simulation and (2) physical experiments to support the model ling results [1]. It is difficult or impossible to derive accurate analytical models to predict the theoretical electroadhesive forces due to inhomogenous materials and electric fields existing in nature. However, approximate or simplified mod elling of electroadhesion based on assumptions is helpful for both understanding of the electroadhesion phenomenon and providing an idea of the scale of the electroadhesive forces obtainable. This can help guide the design, manufacture, testing, and application of electroadhesives.
Interdigital shape based sensors and transducers have been widely used both in research and industrial applica tions [20]. Interdigitated geometry has been one of the most popular designs for electroadhesive applications due to the fact that interdigitated electroadhesives can offer larger elec troadhesive forces and quicker response times on insulating substrates [21]. Theoretical electroadhesive forces can gener ally be derived by the virtual work method [22] and Maxwell stress tensor method [23][24][25]. Simple theoretical models based on classic theories on parallel capacitors have been used by most researchers [26][27][28][29] to derive the electroadhesive forces. These models, however, usually do not include enough geo metric information of the interdigital electroadhesives such as Principle of electroadhesion on conductive and semiconductive substrates: (a) is the cross sectional view of the electroadhesive system, (b) is the equivalent circuit of two adjacent electrodes in series, (c) is charges accumulated between the noncontact areas [35], (d) is the equivalent circuit of the J-R type electroadhesive [35], and (e) is the equivalent circuit of the Coulomb type electroadhesive [36]. electrode widths and spaces between electrodes. Also, there is a significant difference in the results of different publications. Although various theoretical models and electrostatic simula tion models have been used, only the most recent theoretical model by Cao et al [30], the simulation model achieved by Ruffatto et al based on a gradient descent optimization algo rithm coupled with COMSOL [31], the optimization model achieved by Koh et al based on an empirical comb capacitance equation [32], and the simulation model by Sabermand et al based on COMSOL [33], concluded that there is an optimum electrode width for electroadhesive pads to achieve the max imum forces on insulating substrates when the space between the electrodes was fixed (i.e. an optimal width/space ratio). All the other theoretical and simulation models concluded that the smaller the electrode width, the larger the electroadhesive forces obtainable on nonconductive substrates. In addition, few researchers have experimentally validated their theoretical and simulation results due to the reason that it takes efforts, time and fund, to implement a repeatable pad design, manufac ture, and testing platform, and conduct numerous experiments based on a confident and repeatable experiment procedure. Only the work by Ruffatto et al have validated some of their simulation results. However, the tests were not conducted in a controlled environment. In summary, there is little work on the experimental validation of the theor etical optimization model ling of interdigital electroadhesive actuators on both conduc tive substrates and nonconductive substrates.
A simplified and novel theoretical model for optimizing the design of coplanar interdigitated electroadhesives has been developed and validated in this paper. The basic prin ciple of electroadhesion has been presented in section 2. The proposed optimization model for coplanar interdigitated elec troadhesives, with a worked example, has been demonstrated in section 3. In order to further support the theoretical results, a 2D finite element analysis based electrostatic simulation has also been presented, as shown in section 4. Finally, in section 5, an experimental validation of the theoretical and simulation results has been conducted based on an advanced electroadhesive force measurement platform and procedure in a controlled environment, before the conclusions and future work summarized in section 6.

Principle and basic theoretical models of electroadhesion
The principle of the electroadhesive force generation on con ductive and insulating substrate materials is different [26]. For conductive substrates, the electroadhesive forces are gen erated mainly by electrostatic induction. For insulating sub strates, the electroadhesive forces are generated mainly by electric polarizations [31].

Electroadhesive forces on conductive substrates
The electrostatic induction phenomenon is a process where the formation of negative charges on one side and positive charges on the opposite side of a conductor are induced by the external electrostatic field produced by a charged insulator [34]. Conducting materials generally refer to materials con sisting of a large amount mobile free charge carriers. In a metal, the concentration of free electrons (mobile charge car riers) is of the same order as that of the number of atoms, i.e. about 10 22 -10 23 cm −3 [34]. These electrons are able to rearrange themselves quickly and easily. Equal and opposite charges are induced on the surface of conductive substrates after the application of the high voltage on the electroadhe sive pad. The electroadhesive forces between the pad and the conductive substrate are thus formed. When facing conductive substrate materials, dielectric materials with different proper ties such as the volume resistivity will cause different mech anisms of generating the electroadhesive forces. A volume resistivity over 10 14 Ω cm results in Coulomb type electroad hesive pads, whilst the volume resistivity between 10 10 and 10 12 Ω cm results in Johnsen-Rahbek (J-R) type pads. Both the Coulomb and J-R force will exist, to some degree, in all electroadhesive pads [35,36].
The electroadhesive pad can be singlepolar, bipolar, and tripolar [37]. The dual pole design has been the most fre quently used design in electroadhesive applications. For the coulomb type dualpolar electroadhesive, the electroadhesive forces between the pad and substrate can be derived from a series of parallel connections of several ideal capacitors having dielectrics in series. The equivalent circuit of two adja cent electrodes in series from a multielectrode and bipolar electroadhesive during the electroadhesion operation can be seen in figure 1(b), where g is the effective air gap between the pad and the substrate, t 1 is the dielectric thickness, C i 1 denotes the ith capacitance of the dielectric material, and C i 0 denotes the ith capacitance of the air between the dielectric and the substrate surface. The total capacitance between the pad and substrate, therefore, can be given as where n is the total number of capacitors in series or number of electrode pairs, S is the effective electroadhesive pad area, 0 ε is the permittivity of the air, and r1 ε is the relative permit tivity of the dielectrics.
Based on the virtual work method, the electroadhesive forces between the pad and the substrate can be given as where U is the voltage potential, Q is the accumulated surface charge, and the negative sign corresponds to attractive forces. The J-R effect [38], firstly investigated by Johnsen and Rahbek, occurs when attaching the electroadhesive pads made by attaching imperfect dielectrics with finite volume resis tivity such as semiconductive materials onto metal substrates. Current leakage or charge transfer will occur through the con tacting points between the pads and the substrates. A strong electrostatic attractive force can be generated by the interfaces accumulated by charges between the noncontact areas, see figure 1(c). The comparably small gap is due to surface irregu larities in nature, contributing to strong adhesion forces. Hence, for the J-R type electroadhesive, it is the potential difference applied across the interfaces mentioned above, rather than that applied through the dielectric layer and the air gap, leading to the attractive forces. In this case, the J-R electrostatic attractive forces are independent from the dielectric material between the pad and the substrate [35], giving is the capacitance of the noncontact areas, V J-R is the potential difference across the interfaces, and S J-R is the effective J-R noncontacting areas (usually assume to be the same as S), subjected to the surface texture and attractive forces.
Based on the equivalent circuit of the J-R type electroad hesive shown in figure 1(d), the potential difference across the interfaces can be given as [35] where R d is the volume resistivity of the dielectric material and R c , usually much larger than R d , is the contact resistance subjected to surface texture, dielectric material property, and contacting areas. Apart from the J-R electroadhesive forces, the conven tional Coulomb forces will also be generated between the electrodes and the substrates, giving F Coulomb is much smaller than F J-R as the gap between the inter faces is usually much smaller than the thickness of the di electric material, making F Coulomb almost negligible. However, much shorter detachment times can be seen in the Coulomb type electroadhesives [36]. Also, less current leakage occurs in cou lomb type electroadhesives, resulting in significantly lower power consumption. With regard to the Coulomb type elec troadhesive, the equivalent circuit can be seen in figure 1(e).
When the switch S1 is on and S2 is off, the capacitance of the electroadhesive pad, C e , is charged, Q, resulting in the attach ment between the pad and the substrate. When the switch S1 is off and S2 is on (t 0 = ), an exponentially decaying current will be demonstrated, described by [34] where C R e 0 τ = and R 0 is the equivalent external resistance of the electroadhesive system.
The depolarization process, which involves a time period of bringing the excited system back to its original equilib rium state, can be referred to as dielectric relaxation. After switching off the voltage connected with the electrodes, i.e. removing the external electric field, the charge density decays with time and can be expressed as [29] t 0 e , is the dielectric relaxation time and the time needed for the originally induced charge to decay to 36.7% of its original value. d τ can be very large for some insulating materials [34]. However, (6) no longer applies in the J-R type electroadhe sives. A nonexponentially decaying current will be shown, with much longer decrease time which is several orders of magnitude longer depending on the dielectric material prop erty [36]. It is, therefore, necessary to balance the attraction forces and detachment time, tailoring to the specific require ments of tasks such as the pick and place of objects.  [34]. Reproduced with permission from [34]. Copyright 2004 Elsevier.

Electroadhesive forces on insulating substrates
The total polarization of an arbitrary dielectric system can be written as [15] P P P P P P P , polarization e i o d s others where P e is the electronic polarization, P i is the ionic polar ization, P o is the orientational polarization, P P P d hop face = + is the space charge polarization which includes the hopping polarization, P hop and the interfacial polarization, P face , P s is the spontaneous polarization, and P others is other types of polariza tions such as the nomadic polarization.
The approximate time required for each type of the mentioned polarization under a step function electric field figure 2. The electroadhe sive forces generated on insulating substrates can then be expressed by [31] F P E.
It was concluded by Monkman that electric polariza tions, especially the orientational polarization and interfacial polarization, account for the generation of the electroadhesive forces [17]. This is, however, an assumption from Monkman and have not been experimentally validated with confidence. The electroadhesion phenomenon can also be contactless both on conductive substrates such as aluminium disks [39] and insulating substrates such as glass [16]. It was concluded by Jeon et al that the atomic and electric polarization account for the generation of the electroadhesive forces for contact less electroadhesive suspensions. The dynamic nature of the electroadhesion phenomenon manifests that the electrostatic adhesion force on a dielectric material will gradually increase to a steady value with some time. The steady value of the adhesion force is usually much larger than the initial value and the time period to reach the steady value is different. The experimental design and testing should therefore take this into consideration carefully.

Understanding the coplanar interdigital capacitance
The interdigitated electrode geometry (see figure 3(a)) is a comb like periodic symmetric pattern and is the most pre ferred electroadhesive geometry. Detailed electric field lines of an interdigitated electroadhesive system can be seen in figures 3(b) and (c).
Since the length of the electrodes is much larger than their widths and thicknesses, and the electroadhesive pad area is much larger than the gap between the electrodes and the sub strate surfaces, all the related fringing fields, E 1 , resulted from edge/boundary effects, can be ignored. Although E 2 , fields between electrodes due to electrode thickness, can induce relatively large attractive forces between the comb fingers, these forces on both sides of comb electrodes will cancel each other out. Also, due to E 2 and because the electrodes are deposited within the dielectrics, the electrodes will not touch each other. In addition, the effects between adjacent or over lapping fields are assumed to be neglected. As a consequence of these considerations, only the fields between the electrodes and the substrate, E 3 and the fields between the coplanar elec trode surfaces, E 4 (which travel from the positive electrodes, penetrating the dielectric material and the substrate, to the negative electrodes), lead to the attractive forces within the interdigitated electroadhesive system. E 3 is negligible com pared with E 4 . Therefore, only the half side closest to the wall substrate of E 4 contributes primarily to the attractive forces between the pad and the substrate. Based on figures 3(a)-(c), we can create the equivalent circuit for the coplanar interdigi tated capacitance presented in figure 3(d), where C 1 and C 3 are coplanar capacitances based on E 4 , and C 2 can be regarded as the normal parallel capacitance between electrodes because of E 2 . Based on the assumptions and simplification made above, the electroadhesive forces between the pad and the substrate only depend on C 1 , a parallel connection of pairs of coplanar capacitance units.
Various methods have been investigated to compute the coplanar capacitance within the interdigitated electroadhesive system, including the continuum model, finite element calcul ations, nondimensionalized plot of capacitances, approxi mating expressions, and conformal mapping methods [20]. The conformal mapping method can transform a complex and coplanar geometry into a simple parallel circumstance and has been one of the most frequently used methods [40]. The existing approximate expressions were only applied on insulating substrates [41]. A theoretical model that is compu tationally easier and can be used for both conductive and non conductive substrates is thus necessitated.

Optimization modelling of coplanar interdigital electroadhesives
The dimensions of the electrode width and space between electrodes has been assumed to be larger than 1 mm in this paper as the dielectric strength may change when the space between electrodes is smaller than 1 mm and no longer hold the rule, denoted by where γ is the dielectric strength and U max is the maximum voltage can be applied based on the minimum space between electrodes, s. In order to derive the theoretical model, other assumptions have also been made in this paper. These assumptions are: • the substrate thickness is infinite, • no free charge exists in the electroadhesive system except on the electrodes, • the charge distribution along the electrode is uniform thus the electric field distribution is uniform, • the electric fields are continuous, • the dielectric materials involved in the electroadhesive system are homogenous, linear, and isotropic, • the pad is rigid and the contacting surfaces are completely flat, so no air gap exists between the pad and the substrate, • the electrode thickness is negligible, • the environment is stable, • the edge effects are ignored as the length of electrodes or the pad area is assumed to be much larger than electrode widths and spaces between electrodes, • and DC high voltage with dual polarity is used.
Please note that, as aforementioned, it is impossible to have an accurate analytical model that can predict the theor etical electroadhesive forces. Assumptions have to be made to derive a simplified theoretical electroadhesion model. Based on the assumptions above that the materials used in the elec troadhesive system are homogenous, linear, and isotropic, the Gauss theorem can be applied. Theoretically the electric field lines should be distributed elliptically. Here, the electric field ellipse lines are simplified into concentric lines to avoid con ducting the curve integral of an ellipse mathematically. Since it has been assumed that the electric fields are uniformly dis tributed along the electrode length direction, the 3D problem can be transformed into a 2D one by taking the crosssection of the electrode panel into consideration, which can be seen in figure 4.
Since it has been assumed that there is no free charge in the space except the charges on the electrodes, the Laplace equation can then be applied. Therefore, under the polar coor dinate condition, the equation is as follows Any radial plane that goes through the center can be regarded as equipotential planes and the electric field direction of every point on these planes is perpendicular to these equipotential planes. The electric potential of any point in this system, U r, ( ) θ , is a function of only θ, giving Hence, by substituting equation (12) into equation (11), the equation becomes Considering the initial condition The electric potential in the system can be expressed as Based on the Maxwell equation, the electric field is the gradient of the potential field Based on Gauss' theorem, the charge density along the electrode surface is given as where eff ε is the effective permittivity between the coplanar electrodes.
Since the thickness of the electrodes is negligible, all the charges are distributed along the surface of the electrodes, i.e. Simplified electric field distributions within the selected coplanar electrodes, where s is the space between electrodes, w is the electrode width, t 1 is the dielectric thickness, r is the radius of the concentric electric field, θ is the angle between the radius plane and electrode plane radius r, and U 0 is the applied voltage on the electrodes. the horizontal axis. It is then possible to obtain all the charges on the electrodes by integrating the charge density along the horizontal axis, giving The total capacitance of an interdigitated electroadhesive pad with N pair of fingers, based on (19), is Since the selected coplanar unit area of the interdigitated elec troadhesive is S L w s 1 2 ( ) = + , by substituting (19) into (2), the electrostatic attraction force per unit area can be the following equation The problem of obtaining the maximum attraction force per unit area can be converted to a variableconstrained nonlinear optimization problem based on (21). For the purpose of this research, the MATLAB function 'fminsearchbnd()' has been used. The objective function of the proposed optimization model and its constraints can be given as where x 1 is the applied voltage, x 2 is the width of electrodes and smaller than a designated value l 1 , x 3 is the space between electrodes and smaller than a designated value l 2 , x 4 is the thickness of the dielectric film and is smaller than a desig nated value l 3 , x 5 is the permittivity of the dielectric film, x 6 is permittivity of the substrate, 1 γ is the dielectric strength of the dielectrics between the electrodes, 2 γ the dielectric strength of the dielectrics covering the electrodes, and U i max is the max imum voltage that can be applied (i = 1, 2).
When attaching the pad on conductive substrates, the effec tive permittivity can approximately be given by When attaching the pad on insulating substrates, the effective permittivity can approximately be given by where r1 ε is the relative permittivity of the dielectric layer, r2 ε is the relative permittivity of the substrate, and t 1 is the thick ness of the dielectric layer.
The effective permittivity in the equations (23) and (24) was derived using classical equations on parallel capacitors, such as equation (1). The circular coplanar fields were simpli fied into straight fields from the positive electrodes, via the dielectric and substrate layers, to the negative electrodes. The average distance between the positive and negative electrodes was simplified as s w 0.5 0.5 ( ) π + (see figure 5). This has been inspired by the work published by Mamishev et al [20].
From the results, it can be concluded that there is an optimum electrode width of 1.79 mm to achieve the max imum attraction force per unit area when attaching the pad on nonconductive substrates where the space between the electrodes has been fixed at 1 mm (optimum width/space ratio of 1.79). Also, the smaller the space between electrodes and   the di electric thickness, and the larger the permittivity of the dielectric film and the substrate, the larger the attractive forces obtainable. This is similar to the results shown in the work by Liu et al [24], Mao et al [25], and Cao et al [30].
For conductive substrates, the same parameter range as per the nonconductive case has been assumed. The space between electrodes should be as small as possible, as can be seen from figure 7(a). However, a slightly different trend can be seen compared to the results from figure 6(c), manifesting that the change of space between electrodes is less sensitive to conductive substrates. It is obvious from figure 7(b) that the electrode width should be as large as possible to generate larger effective pad area thus larger force per unit area. , t e denotes the thickness of the copper electrodes (preset as 0.035 mm), t a denotes the thickness of the air gap layer (preset as 0.05 mm), and t w denotes the thickness of the glass substrate (preset as 10 mm). The dielectric constant of the dielectric material and glass substrate have been preset as 11.7 and 4.2 respectively. The applied voltage has been preset as 6000 V. The bottom of the wall substrate has been grounded and the potential has been set to 0 V. Since interdigital electroadhesive pads usually have periodical electrode arrays, periodic conditions have been applied.

2D electrostatic simulation
A 2D electrostatic simulation based on COMSOL Multiphysics has been conducted to further support the results obtained from figure 5. The diagram of the 2D model can be seen in figure 8, where a nonconductive substrate such as a glass has been considered.
It can be seen from figure 9(a) that the electrode thickness has little effect on the electroadhesive forces obtainable. This supports the aforementioned assumption that it is reasonable to neglect the thickness of electrodes. It can be concluded from figure 9(b) that the smaller the air gap the larger the forces obtainable. Also, from figures 9(c)-(g), the result of the 2D model with an air gap and without has similar trends but the forces without an air gap are larger than with an air gap.
However, although the forces without an air gap are larger than with an air gap, a slightly different trend as be seen in figure 9(h). For the simulation model without an air gap, the results have shown that • for thinner wall substrates, where the thickness is ⩽1.7 mm, the larger the electrode width, the larger the forces obtainable; • for thicker wall substrates, where the thickness is ⩾2.2 mm, the smaller the electrode width, the larger the forces obtainable; • for wall substrates with thicknesses of x 1. 8 2.2 6 ⩽ ⩽ mm, the optimum electrode widths of approximately 2.7 mm, 2.3 mm, 1.6 mm, and 1.9 mm can be found.    figure 10.
It has to be noted that all the above simulation results have been based on considering the polarization of the whole sub strate, i.e. the surface average of the whole substrate. If only the interfacial effect is considered, i.e. the line average of the contacting surface between the pad and the substrate, the smaller the electrode width, the larger the forces obtainable regardless of the thickness of the wall substrate. This agrees with most published results. The results shown in figure 11 have been based on a wall thickness of 2 mm. Also, the dif ference in the electroadhesive forces obtainable has been relatively small when changing the electrode width from 1 to 3 mm in all cases. Although there is an optimum width/space ratio of around 2 mm, the difference has been within 5% in the forces obtainable from electrode widths of 1 mm-3 mm.
From the simulation results, on nonconductive substrate materials, in order to have more boundaries, it is advisable to have smaller electrode widths. Please note that all the above results have been based on the fact that the space between the electrodes has been fixed at 1 mm.

Electroadhesive pad design and manufacture
The pads have been designed using Solidworks (see figure 12) and based on the following two equations and where L 1 is the total length of the pad, L 2 is the total width of the pad, L is the electrode overlap length,G 1 is the width of electrode connection, G 2 is the space between connection line and comb fingers, w is the electrode width, s is the space between electrodes, N (integral) is the number of electrode pairs, and T is the tail that can be used for the connection to the high voltage supply. It is clear that the dielectric thickness of the dielectric layer should be as small as possible, only the electrode width and space between electrodes have been varied. In order to make all the pad designs the same effective pad area, the param eters have been therefore set as T = 40 mm, L 1 = 270 mm, L 2 = 170 mm, L =150 mm, and G 1 = G 2 = 5 mm.
For the investigation into the relationship between electrode widths and the obtainable electroadhesive force, all the other geometrical parameters have been maintained (s = 1 mm). Five pads that have different electrode widths have been gen erated. For the investigation into the relationship between the space between electrodes and the electroadhesive forces obtainable, all the other geometrical parameters have been maintained (w = 4 mm). Five pads that have different spaces between electrodes have been generated. The geometric infor mation of the ten pads can be seen in table 1. The designed pads have been then professionally manufactured using the procedures presented in figure 13.

Electroadhesive force measurement platform and procedure
A bespoke mechatronic and reconfigurable electroadhesive force measurement platform has been used to obtain the normal electroadhesive forces between the electroadhesive pad and substrates. Please note that all the experimental results in the literature have shown that the shear electroadhesive forces are larger than that of in normal when measuring the shear and normal forces on the same substrate. Most previous recorded results have not presented the inclusion of suction forces (if not tested in vacuum) and van der Waals forces between the pad and the substrate in detail after the application of high voltages. The inclusion of suction forces due to the air gap and van der Waals forces due to the intimate contact can be seen in figure 14(a). The actual normal forces the sensor will obtain can therefore be expressed as where F ea is the normal electroadhesive forces, F suction is the suction forces between the pad and the substrate, and F van is the van der Waals forces. When a shear force is applied on the pad, restriction forces occur, as shown in figure 14(b) [15], which may be the main reason that the recorded shear forces are stronger than the normal forces. Assuming that there is an angle, θ, as illustrated in figure 14(b), between the forces in normal and the restric tion forces, the recorded shear electroadhesive forces can then be expressed as: It is therefore inappropriate to derive the normal electroad hesive forces by the division of the measured shear forces and friction coefficients although this has been used by some researchers [9,10,26]. As it is difficult to quantify the restric tion force, suction force, and van der Waals forces, it is there fore also inappropriate to use the measured shear forces to validate the models considering normal electroadhesive forces. The system diagram of the advanced electroadhesive force measurement setup can be seen in figure 15(a), where a 6axis ATI Gamma Force/Torque (F/T) sensor was used to record the normal electroadhesive forces. The communication between the F/T sensor and the computer has been through a Netbox via an Ethernet cable and the data has been selected to be sampled at 152 Hz. The linear rail can achieve hori zontal movement using a servo motor with an encoder driven by a Kollmorgen motor driver connected with a CompactRio. This has allowed almost real time control of the linear rail via a Xilinx FPGA which has been designed to communicate with the computer via Ethernet. The smallest movement of the linear rail that the encoder can detect has been approxi mately 0.8 µm. The electroadhesive pad has been connected with two EMCO high voltage converters (HVCs) with (±) 0-10 kV output and 0-5 V reference input. The reference input Figure 13. Electroadhesive pad manufacture procedure. The copper electrode thickness has been set to 18 µm, the polyimide base (PI dielectric constant: 3.2) thickness has been set to 12.5 µm including an unknown thickness of adhesive and the PI coverlay has been a combination of a 12.5 µm PI (dielectric constant: 3.8) with a 15 µm adhesive. The copper area outside of the interdigitated pattern has been for supporting the pad flat enough during the coverlaying process. Only the interdigitated pattern part of the design has been used for the electroadhesive force testing. The effective pad area has been designed as 170 mm × 230 mm. has been from a direct current power supply unit (DC PSU), Instek GPD3303, which has been designed to communicate with the computer through via a USB. The physical normal electroadhesive force measurement platform can be seen in figure 15(b). A Labview interface has been developed for interactive control of the movement of the linear rail, changing the supply voltage, recording, and saving the electroadhe sive force data. Please note that an electrical safety interlock system and safety screens have been applied in this advanced measurement platform. The electroadhesive force measurement procedures can be seen in figure 16. The pad has been initially attached on the PEEK pad holder and the substrates have been clamped in the substrate holder. A 30 ± 1 N preload has been then applied on the substrates. The recording of the electroadhesive force has been then started by turning on the power supply, thus providing power to the pad. The pad has been charged for 60 s. After this, the pad has been pulled away by activating the servo motor. When the motor stopped, the data recording has been completed and the data has been exported as text files. These files have been further filtered and analyzed in MATLAB. The next experiment has been conducted after 540 s. The start of this lag time has been at the commence ment of the pulling away of the pad. The dwell time has been useful for residual charge dissipation. During the residual charge dissipation process, the pad has been grounded for 300 s after each test. Also, the aluminium (Al) substrate has been grounded for 300 s each time before the pad has been changed. A SimcoIon electrostatic fieldmeter, mounted on Kanya frames, has been used to compare the surface charge value of the plate before applying the voltage and after the grounding. 300 s have shown to be enough to obtain similar results within less than 5% difference. Also, each time after applying the preload, little difference has been observed after 30 s' stabilizing. A fixed experiment time of 10 min (540 s plus 60 s) for each test has been therefore set for this investigation. The motor pulloff velocity (0.1 mm s −1 ) and pulloff acceler ation (50 revs −2 ), charge time (60 s) and discharge time (540 s) have been maintained at constant values when conducting the experiments for the 10 pads demonstrated in table 1. For each pad, six experiments have been repeated. The first data point for each pad has not been used for data analysis.
To date, little evidence has been found to systematically investigate the influence of environmental factors on the elec troadhesive forces. Environmental factors affect and modify the dielectric properties of electroadhesive pads such as di electric strength, permittivity, and resistivity. Also, they arouse electric discharges and dielectric degradation that causes the failure of the adhesion. Within the research laboratory where our fun damental research has been undertaken, the lab temper ature has changed from 17 to 28 °C, relative humidity changed from 28 to 73% and air pressure changed from 996.3 to 1015.2 hPa between January and August 2015. Preliminary results have been obtained over a 5 d period when all variables have been maintained, as shown in table 2, except the temper ature (20.8-21.5 °C), relative humidity (43-64%) and air pres sure (993.8-1013 hPa). The electroadhesive pad used this test has been based a customized chemical etching and conformal coating. The PUC side (dielectric constant: 3.6) of the pad has been facing the substrate. The results can be seen in figure 17, where a nearly 200% relative difference in forces has been observed. The result shown in figure 17 is maybe the reason that hinders the current application of flexible electroadhesive solutions in ambient industrial environments where unstable and unpredictable forces may be achieved. In order to con trol the environ ment factors to valid ate the proposed model, a wellsealed chamber enclosing the force test rig has been used so that the testing can be free of contaminates/dusts. An air con ditioning unit and a dehumidifier (see figure 13(a)) have been employed to maintain the temperature, humidity, and air pres sure. The temperature has been maintained at 25 °C ± 0.2 °C, humidity at 32% ± 2%, and pressure at 1013 hPa ± 1 hPa, when testing the 10 pads mentioned in table 1.

Results
The electroadhesive forces have been recorded when the PI base side has been facing the substrates: a toughened glass or an Al plate. 2 kV has been applied on the pads. Before each test, the force with no voltage applied has been recorded to check the potential suction forces, van der Waals forces, and surface tension forces. For all the 10 pads, less than 0.05 N has been observed when no voltage has been applied. This means the forces recorded under a voltage are predominately the normal electroadhesive forces. The experimental results manifesting the relationship between the electroadhesive forces obtainable and the spaces between electrodes can be seen in figure 18. For both conductive substrates, such as the Al plate, and nonconductive substrates, such as the toughened glass, the smaller the space between electrodes, the larger the electroadhesive forces obtain able. This agrees with all the theor etical and simulation results.
The experimental results manifesting the relationship between the electroadhesive forces obtainable and the elec trode widths can be seen in figure 19. For nonconductive substrates such as the toughened glass, there indeed is an optimum width/space ration of approximately 1.9 mm.
There is, however, only an approximately 21% relative difference in the electroadheisve forces obtainable when changing the electrode width from 0.9 mm to 3.8 mm. For con ductive substrates such as the Al plate, the width/space ratio should be as large as possible to have a larger effective pad area thus larger force per unit area obtainable. The difference Figure 16. Electroadhesive force measurement procedure [19]. Reproduced with permission from [19]. Copyright 2016 IOP Publishing. between the theoretical and experimental results is relatively small, as compared in figures 18 and 19. Please note that, due to the simplified assumptions mentioned above, a factor has be used to multiply the measured forces in order to compare the theoretical and experimental results. The slight difference in the general trends may due to the fact that there is a layer of air between the pad and the substrate during the force testing.

Conclusion and future work
The work presented in this paper has focused upon the optim ization modelling of interdigital electrodadhesives and its experimental validation of the existence of an optimum width/ space ratio based on a confident testing platform and proce dure. The key findings from this work are that: • The proposed 2D electrostatic simulation results have shown that the wall thickness and air gap have a large bearing on the optimum widths achievable for non conductive substrates. The consideration of only the interfacial electric fields and the electric fields within the whole substrate have generated a different result. If only the interfacial electric fields are considered, the smaller the electrode width, the larger the forces obtainable regardless of the effect of the wall thickness. If the elec tric fields within the whole substrate are considered, an optimum electrode width can always be found when the space between electrodes is fixed. This may be the reason why the existing simulation results have demonstrated different conclusions. • The proposed simplified and computationally easier theoretical optimization modelling of coplanar inter digitated electroadhesives is promising for predicting the performance of an interdigitated electroadhesive actuator. The theoretical model have shown that there is an optimum electrode width/space between electrodes  ratio of approximately 1.8 for interdigital pads to achieve the maximum forces on nonconductive substrates. For conductive substrates, the width/space ratio should be as large as possible. This has been validated by the exper imental results both on conductive substrates such as the Al plate and nonconductive substrates such as the glass. On the Al plate, the larger the electrode width, the larger the effective pad area, thus the larger the forces obtain able. On the glass plate, there is an optimum electrode width of approximately 1.9 mm when the space between the electrodes has been fixed at 1 mm (optimum width/ space ratio of approximately 1.9). • The electroadhesive force analysis proposed in figure 13 highlights the inappropriateness to derive the normal forces by the division of the measured normal forces and friction coefficients. The measured normal forces are therefore only useful for validating the normal force based models. • The result demonstrated in figure 16 not only highlights the importance of controlling the environment when testing the pads to validate the models but also identifies the need for the investigation of environmentally stable electroadhesives.
The understanding and modelling of electroadhesion pre sented in this paper is useful for optimized electroadhesive end effector designs for electroadhesive based robotic mat erial handling applications currently under investigation by the authors. Future work will contain a more comprehen sive experimental validation work using more pads tested in vacuum to both validate the relationship between forces obtainable and other parameters and the obtained simulation results. A theoretical model including the thickness of the wall substrate and air layer will also be considered. A nearly quadratic relationship between the applied voltages and the electroadhesive forces obtainable can only be seen when the applied voltage is less than 6000 V. The proposed model is therefore limited to applied voltages smaller than 6000 V. Future work will also therefore contain the investigation of a more comprehensive model considering voltages beyond 6000 V. In addition, a systematic investigation into the rela tionship between the environmental factors and electroadhe sive forces obtainable is needed, aiming not only to produce environmental stable electroadhesives but also a more accu rate model considering environmental factors and minimising the number of aforesaid assumptions. These will further aid the design and implementation of optimized electroadhesive end effectors for future material handling applications.