Multi-Axis Soft Sensors Based on Dielectric Elastomer

SOFT ROBOTICS Volume 3, Number 1, 2016 ª Mary Ann Liebert, Inc. DOI: 10.1089/soro.2015.0017

ORIGINAL ARTICLE

Multi-Axis Soft Sensors Based on Dielectric Elastomer Hongying Zhang1 and Michael Yu Wang1,2

Abstract

This article proposes a methodology to design, analyze, and fabricate a multi-axis soft sensor, made of a dielectric elastomer (DE) that is capable of detecting compressive and shear loads. The multi-axis soft sensors are applicable to soft robots because of low stiffness and large strain properties. The sensor consists of four modules aligned in a 2 · 2 array, each module can be modeled as a capacitor—a DE membrane with an embedded air chamber sandwiched by compliant electrodes. To investigate the effect of structure on sensitivity, detection range, linearity, and hysteresis, rectangular and circular prototypes are analyzed, fabricated, and tested. When the multi-axis soft sensor is subject to compressive or shear load, the induced deformation of thickness or overlapping area results in capacitance change. We build an analytical model to describe the mechanical–electrical property of the soft sensor induced to shear load. Because of the complexity of compressive load, the mechanical–electrical property in this case is obtained numerically through the finite element method. Specially, a strategy to decouple shear and compressive loads is proposed in this article. By detecting a capacitance signal of four modules, both direction and magnitude of external stimuli are obtained. From experimental and analytical results, the rectangular prototype is superior to the circular one in sensitivity, linearity, and stability. based soft sensors that show better performance in terms of accuracy and repeatability are adopted in this paper. Previous works have been conducted on capacitance-based soft sensors, which are capable of detecting shear and compression loads individually, but fail to decouple multi-axis loads. These soft sensor designs differ mainly on electrode material and pattern. For the rectangular pattern copper electrodes designed by the Lee group,15–17 the sensor was applicable to detect normal and shear loads; the full-scale detectable force obtained in the experiment was about 10 mN, which limited the application on macroscopical stress detection occasions. Likewise, the Mazzolai group replaced copper electrodes with copper/tin textile electrodes18,19; the detection range was improved to 1 N at the expense of resolution of 0.1 mN. However, these metal-based electrodes were not sustainable to large strain. Moreover, the rectangular electrode pattern was not direction orientated. The triangular electrode pattern improved the directionality of the rectangular prototype; when this electrode pattern is subjected to the shear load, only capacitances of modules that aligned in parallel with load direction will change oppositely. The Majidi group designed a sensor based on this concept,20 and the fabrication process was relatively complex, which must be fabricated by laser machining, masked deposition,21

Introduction

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oft robots are built intrinsically with soft materials, which are sustainable to high strain and of comparative stiffness with human tissue.1–3 Nowadays, dielectric elastomers such as PDMS and Ecoflex series are widely used in fabricating devices applicable to soft robots.4,5 In contrast with traditional rigid robots, soft robots are characterized by distributed deformation and infinite number of degree of freedom, and these inherent properties enable soft robots in interacting with human beings and navigating through constrained or uncertain environments.6,7 However, due to the requirements of deformation and stiffness, commonly applicable devices on rigid robots are not suitable on soft robots. A multi-axis soft sensor made of PDMS applicable to soft robots is proposed in this article. When a sheet of soft rubber is subject to compressive or shear load, deformation induces in-thickness or cross-sectional direction. There are mainly two ways to convert induced deformation to electrical signals: converting to resistance changes by syringing conductive liquid into microchannels8–11 or converting to capacitance changes by coating the body with electrodes.12 However, unpredictable behavior and large hysteresis exist in resistance-based sensors.13,14 The capacitance1

Department of Mechanical Engineering, National University of Singapore, Singapore, Singapore. Department of Mechanical and Aerospace Engineering & Department of Electronic and Computer Engineering Director, HKUST Robotics Institute, Hong Kong University of Science and Technology, Kowloon, Hong Kong. 2

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or stencil lithography.22 Moreover, the sensor might get failed due to the contact of channel surfaces in high compression. Therefore, the detection range was limited to 25 kPa with the resolution of 5 kPa. To overcome the limitations of existing soft sensor designs— rigid electrodes, low sensitivity, limited detection range, and inability in decoupling multi-axis loads, a methodology to design, analyze, and fabricate multi-axis soft sensor is proposed in this article. The multi-axis sensor is composed of four capacitor modules aligned in a 2 · 2 array; each module is fabricated by coating soft electrodes on a sheet of PDMS membrane with an embedded air chamber. To study the effect of electrode pattern on sensitivity and detection range, rectangular and circular prototypes are also analyzed and fabricated. Analytical models of the rectangular and circular multi-axis soft sensors are proposed, which describe the mechanical–electrical property induced by the shear loads. It is relatively complex to describe the relationship between compression and relative capacitance change explicitly; therefore, the mechanical–electrical property is obtained numerically through the finite element method (FEM). It is crucial to detect both magnitude and direction of external loads; herein, we proposed a methodology to decouple shear and compressive loads, which is applicable to similar soft sensor designs. Fabrication processes of two prototype soft sensors are described, especially the fabricate processes of the soft electrodes based on carbon grease are highlighted. Then, step shear loading experiments are conducted to test the samples, the experimental results are consistent with the analytical predictions, and the errors are within 0.0023 pF-1. Comparing the two prototypes, the rectangular prototype is superior to the circular prototype: for shear loads, sensitivity of the former prototype is 0.0106 pF-1/N, which is higher than the latter prototype, whose sensitivity is 0.0093 pF-1/N; for compression loads, the detection range of the former prototype is larger, while sensitivity is identical. From both analytical and experimental results, we verified that the multi-axis soft sensors proposed can detect and decouple multi-axis loads. Prototype and Analysis Prototype of multi-axis soft sensor

Side view of the multi-axis soft sensor is shown in Figure 1a; when the sensor is subject to concentrated or distributed compression load, the thickness decreases and capacitance of each module increases; when a shear load is applied, induced deformation in cross section results in overlapping area changes, and the capacitance of modules aligned in parallel with the shear load changes oppositely. Two prototypes of multi-axis soft sensor—rectangular and circular—are shown in Figure 1b and c. The multi-axis sensor consists of four individual modules that share a common square- or circular-shaped electrode. Each module of the soft sensor is composed of three layers: the top and bottom PDMS membrane layer and the inner air chamber layer. Because the electrodes are coated on the top and bottom layers, each module can be viewed as three capacitors in a series. When the multi-axis soft sensor is subject to shear load, deformation on the top and bottom rubber layers is negligible. While the deformation of the inner air chamber layer is relatively large, it accounts for the capacitance change in shear loading condition. The thickness of the PDMS layers

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is the same, and described by t0 = 1 mm, the height of the inner layer is d0 = 4 mm, the initial overlapping area is A0, and er, e0 are relative and vacuum dielectric permittivity, and then, the initial capacitance of one module can be described as follows: 1 1 1 1 2t0 d0 ¼ þ þ ¼ þ C0 Ctop Cinner Cbottom er e0 A0 e0 A0

(1)

Under shear loading condition, the induced deformation along cross-sectional direction results in overlapping area change, and the deformed capacitance is as follows: 1 1 1 1 2t0 d0 þ þ ¼ þ ¼ C Ctop Cinner Cbottom er e0 A0 e0 A

(2)

where A is the deformed overlapping area, calculate the subtraction of equations (1) and (2) as follows:   1 1 d0 A  A0 (3)  ¼ e0 AA0 C0 C In this study, we define the relative capacitance change as follows: DCi ¼ C1i0  c1i , i ¼ 1, 2, 3, 4. The mechanical– electrical properties of two prototype soft sensors under shear loading condition are analyzed in the following chapters. Mechanical–electrical analysis of rectangular prototype

The dimension of the rectangular multi-axis soft sensor is shown in Figure 2a, l0 is the width of the electrodes, the Heaviside discrete step functions H(–x), H(–y), and H(+z) are adapted to describe deformation in x, y, and z directions, for example: H(+x)—deformation along +x direction and H(-x)—deformation along -x direction. As shown in Figure 2b, when the multi-axis sensor is subject to shear force in +x direction, overlapping area of Cr1 increases by the purplelabeled rectangle and Cr3 decreases by the red-labeled trapezoid, while overlapping areas of Cr2 and Cr4 keep constant. That is to say, for shear loads along +x direction, capacitances of Cr1 and Cr3 change inversely, while Cr2 and Cr4 keep unaltered. The occasion of shear load along +y direction is shown in Figure 2c, this is similar to shear loading in +x direction, and Cr2 and Cr4 change oppositely, while the Cr1 and Cr3 keep constant. The term f(z) is used to describe the relationship between applied compression and relative capacitance change, and the Heaviside step function H(+z) shows direction of the applied load; it is obtained through FEM analysis due to the complicated elaboration. Then, the capacitance change of each module under multiaxial loading condition can be described as follows:   d0 l0 x DCr1 ¼ H( þ x) e0 (A0 þ l0 x)A0   (4) d0 (l0 þ x)x þ H(  x) þ f (z)H( þ z) e0 [A0 þ (lo þ x)x]A0   d0 (l0  y)y H( þ y) e0 [A0  (l0  y)y]A0   d0 l0 y  H(  y) þ f (z)H( þ z) e0 (A0  lo y)A0

DCr2 ¼ 

(5)

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FIG. 1. Multi-axis soft sensor prototype. (a) Multiple loading conditions. (b) Rectangular prototype. (c) Circular prototype. Color images available online at www.liebertpub .com/soro

  d0 (l0  x)x H( þ x) DCr3 ¼  e0 [A0  (l0  x)x]A0   d0 l0 x  H(  x) þ f (z)H( þ z) e0 (A0  lo x)A0

(6)

  d0 l0 y DCr4 ¼ H( þ y) e0 (A0 þ l0 y)A0   d0 (l0 þ y)y þ H(  y) þ f (z)H( þ z) e0 [A0 þ (l0 þ y)y]A0 (7) Analytical results of the rectangular prototype multi-axis soft sensor under shear load are shown in Figure 2b and c, and the sensitivity is 0.0123 pF-1/mm. Direction of the applied shear load is distinguished by observing the relative capacitance change, for example, if capacitance of Cr1 increases, then direction of the shear load is along the +x direction.

In the case of multi-axis sensor subject to compressive load, FEM analysis is adopted to obtain the resultant deformation. Because structure of the multi-axis soft sensor is symmetric, one module of the sensor is analyzed in detail. The workflow of analyzing mechanical property is shown in Figure 3: first, the stereolithography format CAD model is created in Solidworks2014 (Fig. 3a); second, import the CAD model to MATLAB2015b (Fig. 3b); third, the model is meshed by quadratic tetrahedral elements (Fig. 3c); finally, varying compressive loads are applied on the top face, and the model is solved by adopting the partial differential equations toolbox (Fig. 3d). The material properties of PDMS are Young’s modulus: 870 kPa, Poisson’s ratio: 0.4999, and dielectric permittivity: 3.65. For analyzing electrical property, we still use the relative capacitance definition DCi ¼ C1i0  C1i . Capacitance of the three layers—top PDMS layer, inner air chamber layer, and the bottom PDMS layer is calculated individually. For each layer, the total capacitance is the summation of all the meshed capacitor elements in parallel, and each meshed capacitor is computed by Ce ¼ er e0 Adee , where Ae is area of each element and de is thickness of each element.

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FIG. 2. Rectangular prototype multi-axis soft sensor. (a) Dimension of the rectangular soft sensor. (b) Shear deformation in +x direction and simulation result. (c) Shear deformation in +y direction and simulation result. Color images available online at www.liebertpub.com/soro

The same FEM analyzing method is adopted to obtain the mechanical–electrical property of the circular prototype soft sensor. The sensors fail when the largest deformation equals thickness of the chamber; the simulation results of two prototypes are shown in Figure 4; both rectangular and circular prototype soft sensors show almost identical sensitivity and linear response to compressive load, except that the detection range of the rectangular prototype is larger. The detection range difference may be due to the structure difference of these two prototypes. Mechanical–electrical analysis of circular prototype

Figure 3a shows dimension of the circular prototype, and the initial overlapping area of each module is A0 ¼ p4 r 2 , r ¼ 20mm. As shown in Figure 3b, when shear deformation is along +x direction, analyzing the triangle formed by radius of

deformed overlapping area and radius of the fan-shaped overlapping area can be described individually as follows:   pffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2r2  x2 þ x 2 2r2  x2  x r1 ¼ , r3 ¼ (8) 2 2 Therefore, the deformed overlapping area of Cc1, Cc3 changes oppositely, while area of Cc2, Cc4 keeps constant. In this study, we introduce a parameter cx ¼ xr as deformation ratio along x direction, and the deformed overlapping area can be rewritten as follows:   qffiffiffiffiffiffiffiffiffiffiffiffi qffiffiffiffiffiffiffiffiffiffiffiffi 2 A1 ¼ 1 þ cx 2  cx A0 , A3 ¼ 1  cx 2  c2x A0 (9) Then, substitute the deformed area (9) into equation (3), relative capacitance changes of Cc1 and Cc3 are as follows:

MULTI-AXIS LOADS DETECTION SOFT SENSOR

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FIG. 3. Workflow of finite element method analysis. (a) CAD model. (b) Import .stl file to MATLAB2015b. (c) Mesh with tetrahedral elements. (d) z-displacement with applied compressive load (0.5 N). Color images available online at www.liebertpub.com/soro

pffiffiffiffiffiffiffiffiffiffiffiffi cx 2  c2x d0 pffiffiffiffiffiffiffiffiffiffiffiffi , DCc1 ¼   e0 1 þ cx 2  c2x A0 pffiffiffiffiffiffiffiffiffiffiffiffi  cx 2  c2x d0 pffiffiffiffiffiffiffiffiffiffiffiffi DCc3 ¼   e0 1  cx 2  c2x A0

(10)

Similarly, the case of shear load along y direction is shown in Figure 3c, and the nondirectional deformation ratio along y

direction is defined as cy ¼ yr, therefore, the relative capacitance change of Cc2 and Cc4 is as follows: qffiffiffiffiffiffiffiffiffiffiffiffi 2  c2y  c y d0   , q ffiffiffiffiffiffiffiffiffiffiffiffi DCc2 ¼  e0 1  c 2  c2 A 0 y y (11) qffiffiffiffiffiffiffiffiffiffiffiffi 2 c 2  c y y d0 qffiffiffiffiffiffiffiffiffiffiffiffi DCc4 ¼   e0 1 þ c 2  c2 A y

y

0

Combining with the compressive loads effect f(z)H(+z) obtained through FEM analysis, which is shown in Figure 4, the relative capacitances change of the circular prototype multi-axis soft sensor can be described as follows: pffiffiffiffiffiffiffiffiffiffiffiffi cx 2  c2x d0 pffiffiffiffiffiffiffiffiffiffiffiffi þ f (z)H(þ z) DCc1 ¼   (12) e0 1 þ cx 2  c2x A0 qffiffiffiffiffiffiffiffiffiffiffiffi  cy 2  c2y d0 qffiffiffiffiffiffiffiffiffiffiffiffi þ f (z)H(þ z) DCc2 ¼   e0 1  c 2  c2 A y

FIG. 4. Simulation results of two prototypes subject to compression. Color images available online at www.liebertpub .com/soro

y

(13)

0

pffiffiffiffiffiffiffiffiffiffiffiffi  cx 2  c2x d0 p ffiffiffiffiffiffiffiffiffiffiffiffi þ f (z)H(þ z) DCc3 ¼   e0 1  cx 2  c2x A0

(14)

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qffiffiffiffiffiffiffiffiffiffiffiffi 2  c2y d0 qffiffiffiffiffiffiffiffiffiffiffiffi þ f (z)H(þ z) DCc4 ¼   e0 1 þ c 2  c2 A 0 y y cy

(15)

Analytical results of circular prototype multi-axis soft sensor under the shear loads are shown in Figure 5b and c; comparing with the rectangular prototype Figure 2b and c, the circular type improves linearity with a sacrifice of sensitivity, sensitivity of this prototype is 0.009 pF-1/mm. Because area change of the circular prototype (triangle section marked in Fig. 2) is smaller compared with the rectangular prototype (rectangle section marked in Fig. 5), the sensitivity decreases.

shear and compressive loads, relationships between relative capacitance change and external loads are obtained. Initial capacitances of four modules are detected by a highresolution circuit; when the multi-axis soft sensor is subject to external stimuli, we can only obtain current capacitance of four modules. To obtain both magnitude and direction of the external stimuli, the following strategy is adopted. Compute the relative capacitance of capacitors aligned in parallel, which means C1 - C3 and C2 - C4, for the rectangular prototype: DCr1  DCr3 ¼

d0 (2l0  jxj)x  e0 (A0 þ l0 jxj)[A0  (l0  jxj)jxj]

(16)

DCr4  DCr2 ¼

d0 (2l0  jyj)y  e0 (A0 þ l0 jyj)[A0  (l0  jyj)jyj]

(17)

Decouple of the multi-axis load

Learning from the earlier mechanical–electrical analysis of rectangular and circular multi-axis soft sensors under

FIG. 5. Circular prototype multi-axis soft sensor. (a) Dimension of the circular soft sensor. (b) Shear deformation in +x direction and simulation result. (c) Shear deformation in +y direction and simulation result. Color images available online at www.liebertpub.com/soro

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First, substitute computed relative capacitance changes into the equations (16) and (17), the deformations along x and y directions are computed. Second, substitute the deformations x, y into equations (4) to (7), capacitance change induced by compressive load is obtained. Specially, to reduce errors induced by detecting circuit, mean value of f(z)H(+z) is computed. Finally, refer to the compression-relative capacitance change curve obtained by experiments, the magnitude of compressive load is obtained. In the case of circular soft sensor, procedures to decouple shear and compressive loads are similar. Compute relative capacitance change of capacitors in parallel as follows: pffiffiffiffiffiffiffiffiffiffiffiffi 2cx 2  c2x d0 DCc1  DCc3 ¼  e0 [1  c2x (2  c2x )]A0

DCc4  DCc2 ¼

2cy

qffiffiffiffiffiffiffiffiffiffiffiffi 2  c2y

d0  e0 [1  c2y (2  c2y )]A0

(18)

(19)

The following computation steps are the same, except for substituting the computed deformation into equations (12) to (15). Mechanical property of the soft sensors to external shear load can be modeled as a bending spring with stiffness as k,16 which means the relationship between shear load and deformation obeys Hook’s law. The stiffness coefficient k is obtained experimentally, then substituting into the mechanical–electrical analytical models of two prototype sensors (equations (4) to (7) for the rectangular prototype and equations (12) to (15) for the circular prototype), relationships between shear load and relative capacitance change are established.

Fabrication Process

The rectangular and circular prototype multi-axis soft sensors are fabricated by casting mixed and vacuumized PDMS liquids into three-dimensional (3D) printed molds and then cured in an oven at 85C for 20 min. Difference in fabricating two prototypes lies in the shape of 3D printed molds and the pattern of electrodes, the general fabrication procedures are described in this chapter, and fabrication process of soft electrodes based on carbon grease is highlighted. The multi-axis soft sensor with embedded air chamber can be divided into two layers as shown in Figure 6a, the two layers are fabricated individually, and the air chamber is sequentially formed by attaching the two layers together. As shown in Figure 6b, this attaching process is fabricated by smearing a thin layer of mixed PDMS liquids on the contact surface and then curing in the oven at 85C for 10 min. It is required that stiffness of the soft sensor should be compatible with human tissue, rigid metal electrodes are not applicable, and carbon grease-based soft electrodes are a good choice. However, carbon grease is a kind of highly viscous liquid made by dissolving carbon into an organic solvent, which is not stable. In this article, a method to fabricate solid electrodes based on carbon grease is proposed. First, smear a thin layer of carbon grease with specific rectangular or circular patterns on the soft sensor body (Fig. 6c), then coat a microlayer of uncured PDMS over the carbon grease layer (Fig. 6d), and finally cure

FIG. 6. Fabrication process of compressive sensor. (a) Casting mixed PDMS fluids into molds. (b) Bounding two layers. (c) Smearing carbon grease electrodes. (d) Heating at 85C. (e) Finished. Color images available online at www .liebertpub.com/soro the sensor in the oven at 85C for 10 min. Repeating the earlier procedure, solid and soft electrodes on both sides are fabricated (Fig. 6d). The multi-axis soft sensors with the embedded chamber fabricated by the earlier processes are shown in Figure 1b and c. Experimental Setup and Result Experimental setup

After fabrication of the rectangular and circular multi-axis soft sensor samples, three types of step loading conditions— concentrated, distributed compression, and shear load, are applied on the soft sensors through the Mark-10 testing system. Equipment adopted in this loading test are as follows: a LCR meter with resolution of 0.01 pF at 1 kHz to detect capacitance, a force gauge with a resolution of 0.005 N to detect applied compression and shear load, and a meter with a resolution of 0.01 mm to detect deformation. As shown in Figure 7a, concentrated and distributed compressive loads are applied on the soft sensor through conical and cylindrical punches. While shear load is applied by a configuration

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FIG. 7. Experimental setup. (a) Conical and cylindrical punches. (b) Shear loading setup for rectangular prototype. (c) Shear loading setup for circular prototype. Color images available online at www .liebertpub.com/soro

shown in Figure 7b and c, which is composed of two relatively sliding parallel plates, the multi-axis soft sensor is placed between the two plates with surfaces attached by the corresponding plates; when relative sliding movement is applied on the upper plate using the Mark-10 testing system, shear load is applied on the soft sensor. Due to the weight of the upper plate, constant precompressive load apples on the soft sensor during shear loading test; therefore, the shear loading test is indeed a multiaxis loading condition. Initial capacitances without external load are recorded (4.78 pF for rectangular prototype and 4.47 pF for circular prototype). Under the shear loading setup, the capacitance increased to 5.50 pF for the rectangular prototype and 5.20 pF for the circular prototype. The capacitance change due to the precompressive load is subtracted according to the decouple strategy proposed in this article, the rectangular 1 1 prototype DCc ¼ f (z)H(þ z) ¼ 4:78  5:50 ¼ 0:0274 and the 1 1 circular prototype DCr ¼ f (z)H(þ z) ¼ 4:47  5:20 ¼ 0:0314. Then, refer to Figure 4 where the precompressive load obtained by rectangular prototype is 0.44 N, and 0.47 N by the circular prototype; these results are reasonably corresponding to weights of the plate 45 g. This precompressive loading setup verifies that the decouple strategy is workable. Then, varying shear loads are applied on the soft sensor from zero to maximum; due to the limitation of circuit, capacitance of one module is detected during the loading process, therefore, the

FIG. 8. Experimental and analytical results of multi-axis soft sensor. (a) Deformation— relative capacitance change. (b) Shear load—relative capacitance change. (c) Compressive loading of circular prototype. (d) Compressive loading of rectangular prototype. Color images available online at www.liebertpub.com/ soro

analytical results are obtained from equations (4) and (12) for two prototypes. However, it will be much more accurate to detect capacitance of modules aligned in parallel and using the subtraction of two modules in equations (16) to (19). Experimental results

When the rectangular and circular multi-axis soft sensors are subjected to shear loads, the experimental and analytical results of mechanical–electrical curves are shown in Figure 8a. The experimental result is in reasonable agreement with the analytical one, with errors