Benchmarking of a Commercially Available Stacked Dielectric Elastomer as an Alternative Actuator for Rehabilitation Robotic Exoskeletons

Abstract

Recent commercial availability of a stacked dielectric elastomer actuator (SDEA) has opened up possibilities of their use as “artificial muscles” for rehabilitation robots and powered exoskeleton devices. Made by CTsystems, this actuator (CT_SDEA) is made from soft materials, and offers a lightweight and acoustically noiseless alternative to DC motor actuators used in conventional rehabilitation robotic systems. The purpose of the present work was to benchmark the electromechanical properties of CT-SDEAs to assess its capabilities and limitations for mechanizing rehabilitation robots. The CT-SDEAs tested in this study showed 21 ms electrometrical delay, and their calculated strain-rate was 660 %/s. They could generate 21.74 N of force and have a 426 W/kg power-to-mass ratio. Their longitudinal strain was measured at 3.3%. Additionally, their steady state current consumption was measured 39 μA. CT-SDEAs’ fast response, short electromechanical delay and high strain-rate, make them highly suitable for closed-loop control. Additionally, their force generation capability, fast response, high power-to-mass ratio, and low steady state power consumption make them a strong candidates for exoskeleton applications. It’s longitudinal strain (3.3%) however, was less than that of skeletal muscle (20%). Depending on the application, their use may require the addition of mechanical linkages, for force to displacement conversion.

I. Introduction

To improve the acceptability and performance of rehabilitation robots, development of actuator technology with natural feel is highly desirable. Softness, i.e., having Young’s modulus in the range of biological tissues, may improve degrees of freedom, safety and natural feel of the device [1]. If softness combines with noiseless and linear operation, the resultant muscle-like actuator will be a versatile alternative for rehabilitation purposes, especially exoskeletons, where the actuator is functioning in close proximity to human-limbs. Linear actuation of alternative actuators allows them to be placed along the skeletal system, like skeletal muscle, and reduce the overall bulk of the exoskeletal system. A reduction in bulk is achieved because rotational actuators require gears to convert rotation to linear motion, lower actuation speeds and increase torque. Furthermore, linear actuation, when combined with softness, can follow complex geometries and result in multiple degrees of freedom using a single actuator [2]. For exoskeleton applications, it is desirable for the actuator to have force and displacement generation comparable to that of mammalian skeletal muscle. We call an actuator that is soft, noiseless, has linear actuation, and produces comparable force and displacement to skeletal muscle, an artificial skeletal muscle.

The prospective artificial skeletal muscle candidates mostly fall into two categories, thermally driven or electroactive polymers. Thermally driven polymer actuators are usually more powerful than electroactive actuators, especially in their strain capacity. For example, a 2 g ethanol-based phase-change actuator, proposed by Miriyev’s group, could produce up to 120 N force and 140% strain [3]. Unlike electroactive polymers, however, these actuators have low actuation velocities (about 2.5 %/s strain-rate) and more importantly, low efficiencies (0.2%) [3]. These are major limitations in exoskeleton applications where fast and repetitive longitudinal displacement (contractions) are needed.

Soft electroactive polymer actuators, such as dielectric elastomer actuators (DEAs), are fast, efficient and offer a lightweight and acoustically noiseless alternative to DC motor actuators used in conventional rehabilitation robotic systems. DEAs have outstanding muscle-like behavior, which make them one of the most anticipated and studied soft actuators. Comparatively, mammalian skeletal muscle is essentially an electroactive polymer. Dielectric elastomer actuators consist of a compliant capacitor, an elastic dielectric sandwiched between two mechanically compliant electrodes (Fig. 1). When a DC voltage is applied to the electrodes, the resultant Maxwell pressure, the pressure between to oppositely charged plates due to electrostatic force, squeeze the dielectric in thickness direction. Equation (1), shows the parabolic relation of the Maxwell pressure and voltage, were Ɛ and Ɛ₀ are polymer and void permittivity respectively, V is the applied voltage between electrodes, and d is the thickness.

$$P=\epsilon {\epsilon }_0{\left(\frac{V}{d}\right)}^2$$ (1)

Figure 1.

Maxwell pressure and the resultant compression or contraction of the elastic dielectric in a DEA compliant capacitor.

High power to mass ratios that can surpass human skeletal muscles, fast response, length self-sensing, and energy recuperation capability are among DEAs unique features [4], [5]. These actuators are also highly efficient. When a capacitor is fully charged, i.e., DEA is fully contracted, very small dielectric leakage currents (in the range of μA) are the only causes of energy consumption [6]. The high driving voltage (>1 kV), however, can be disadvantageous in some applications, because, it limits the available electrical components that can be used within the system, and more importantly, create safety concerns. Their low power (usually in the range of few watts), which is due to their low current needed for operation, however, keeps them in the non-hazardous range, and if appropriate insulating precautions are used. Additionally, under constant DC voltage, the applied electrical current dictates how fast a capacitance charges, and consequently, the speed of DEA’s contraction. Depending on the desirable actuation velocity, the current can be limited non-hazardous values. Equation (2) shows the relationship between charge Q and instantaneous current i. The discharge rate of the DEA also needs to be taken into account in safety analysis. Zhang et al. simulated the electrical circuitry of their system and showed the safety of their DEA as a glove-like force feedback device [7], in accordance to IEC TS 60479–2 specifications [8].

$$Q={\int }_{-\infty }^{\infty }idt$$ (2)

DEAs have already shown some promise as artificial skeletal muscles for orthotics and prosthetics. In a novel approach, Carpi et al. showed the feasibility of using the multilayer DEA to mechanize a hand orthosis [9]. Furthermore, DEAs have been formed into cylindrical rolls that have strain, shape, and performance similar to natural skeletal muscles [10]. One such actuator was configured to be a similar shape to a biceps muscle and to act on a life-size skeletal arm [11].

There are two main DEA configurations: 1) freestanding DEAs; and 2) DEAs with rigid frames. The rigid frames may not be ideal where soft actuators are preferable. Additionally, they are often heavier and bulkier than the freestanding designs due to their rigid frame. One of the most promising DEA with a rigid frame configurations is the DE membrane actuator by Hodgin et al. [12] (Fig. 2). Hau et al. stacked multiple such actuators and showed 72 N of force production, which is substantially higher than that of most proposed free-standing DEAs [13]. The cross-section of this actuator (85×85×35 mm), however, was bulkier than most other proposed linear DEAs. Pei et al. proposed the more compact spring-rolled DEA which could generate 15 N force and 23% strain with a 60 mm cylindrical actuator [14] (Fig. 2). Despite the versatility, the cycle life of the rigid-frames DEAs may be limited due to unpredictable mechanical failure [15].

Figure 2.

Various configurations of DEA. Stacked [18], Folded [17], Helical [17], Membrane [13], and Spring roll [28]. The black area in each configuration is the compliant electrode and the lighter area shoes the elastomer.

In artificial skeletal muscle applications, the freestanding configurations offer more natural feel to the design. Various free-standing configurations are proposed such as, tubular [16], helical [17], folded [18], and stacked DEAs [19] (TABLE I). Fig. 2 shows the aforementioned DEA configurations. Stacked DEAs proposed by Kovacs et al. [19] are powerful versatile DEA configurations that shows the most similarity to human skeletal muscle compared with other linear DEA configurations. Kovacs et al. stacked multiple layers of thin enhanced DEAs to create this novel actuator. In this configuration, each layer can be considered as sarcomere within a myofibril of skeletal muscle. This group of tensile actuators were capable of producing 32N of isometric force and 15% strain while lifting a 1.1Kg tensile load [19]. These capabilities led these actuators to become the first and only commercially available Stacked DEA, which is manufactured by a company called CTsystems [20].

TABLE I.

The properties of the freestanding DEA configurations. The strain column are the values reported under no load conditions. The reported weight in the stroke column is the load that was used for the measurement. The forces column reports the isometric (blocked) force. In the dimension column, the value in parenthesis represents the active length, i.e., the portion of the total length that was sandwiched between electrodes.

Configuration	Stroke mm	Strain	Force	Dimension (mm)	Voltage	Weight
Tubular [16]	1.25 mm No load	3%		100 (60 active)	2700 V	105 g
Helical [17]		8%	~0.65 N	80×13	~1200V
Folded [18]		5%	~3 N	85×25	~1000 V
Stacked [19]	2.5 2.0 kg	18%	32 N	25×20	4200 V	4 g

To evaluate the reported properties and measure additional electromechanical properties that may be needed for exoskeleton applications, stacked DEAs by CTsystems (CT25.0-15-15-71, Compliant Transducer Systems, Dubendorf, Switzerland), which we call CT-SDEAs, were benchmarked in this study. The CTsystems’ reported properties for this actuator is presented in TABLE II.

TABLE II.

The reported mechanical property of CTsystems’ CT25.0-15-15-71, which we call CT-SDAE in this study [19].

	Max Force	10 N
	Max strain	5%
	Shortening	1.17 mm
	Elastic Modulus	1.4 MPa
	Cycle life	50 Mio cycles
	Long term stability	>5 years
	Actuation frequency	<100 Hz
	Dimension	39×17×17 mm
	Weight	11.3 g
	Layer thickness	25 μm
	Number of layers	1600
	Max driving voltage	1200 kV
	Charge time	<5ms at 100 mA

II. Methods

A. Testing Procedure

Thirteen CT-SDEAs were tested under isometric and isotonic contraction conditions. Under each condition, the CT-SDEAs were activated by three main waveforms; 1) triangular: an isosceles triangle shape waveform with period of 10 s and amplitude of 1230 V; 2) linear: a right triangle waveform with amplitude of 1230 V and period of 5 s; 3) square: a square waveform with amplitude of 1230 V and period of 5 s. The square waveform was proceeded and followed by a period of 5 s at 0 V. Note that the maximum recommended driving voltage of the CT-SDEA is 1200 V and its maximum tolerable driving voltage is 1400 V. While CT-SDEAs were receiving the activation waveforms, the generated force and/or longitudinal displacement (contraction) was recorded.

1). Isometric Condition

The length of the CT-SDEAs was held constant at its rest length, i.e., 39 mm, under no compression or extension, throughout the trials. The generated force under each activation waveform was recorded. To this end, the CT-SDEAs was screwed to a rigid frame from one end and to the load-cell from the other end in a vertical position.

Using the data collected during the isometric condition, the following measures were calculated;

Force generation response

Force generation response was analyzed by superimposing the generated force of thirteen CT-SDEAs to the square waveform. Then, the similarity in response profile and maximum force generation, were compared between samples.

Maximum stress

Maximum stress was calculated, using the aforementioned force generation dataset, by dividing the averaged maximum force, reported as mean and one standard deviation (SD), of the thirteen CT-SDEAs, divided by the area of the CT-SDEA’s end-plate, 289 mm².

Electromechanical delay

Electromechanical delay was calculated using the square activation waveform. This measure was defined as the time difference between the onset of the square waveform, and the onset of force generated by the CT-SDEAs. The onset of both force and voltage was calculated as follow: 1) the mean and standard deviation (SD) of the baseline, i.e., the first 4 s of each signal without activation, was calculated; 2) the onset threshold was set at mean of the baseline + 4SD; 3) the first value equal or higher than the threshold value was considered the onset of the signal.

Current consumption

Current consumption was reported as the peak transient current, its time constant and its steady state value using the square activation waveform.

Length-tension curve:

Length-tension curve: to determine this curve the maximum force of a representative CT-SDEA generated by the square activation waveform was measured while it was at its rest length, nine compressed lengths (nine different lengths from 99.5% to 95.5% of its rest length), and ten extended lengths (ten different lengths from 100.5% to 105% of its rest length). The passive force at each length is defined as the pulling, (negative) or pushing (positive) elastic force exerted by the CT-SDEA at the baseline, i.e., under 0 V activation voltage. Active force at each length was defined as the total force generated by the CT-SDEA minus the baseline. This graph provides crucial information in applications where agonist/antagonist pairs of artificial skeletal muscles are needed at a joint.

Force generation hysteresis

Force generation hysteresis was determined by activating a representative CT-SDEA, using the triangular waveform, and plotting the force generated by the CT-SDEA against the HV amplifier’s output voltage, i.e., 0 to 1230 V. To report the hysteresis quantitatively, the force generated in the ramp-up phase was subtracted from the force generated in the ramp-down phase at a certain activation voltage; then, the maximum of these differences was reported as the hysteresis, both as the absolute value, and the percentage of the maximum generated force. Additionally, another triangular waveform was used with shorter period, 1 s, to show the effect of speed of contraction on the hysteresis.

Axial Young’s modulus

Axial Young’s modulus was calculated using (3), where F is force, L₀ is the initial length, ΔL is the length change and A is the CT-SDEA’s end-plate area. The data collected for length-tension curve was used to calculate this measure.

$$Y=\frac{\text{F}\times {\text{L}}_0}{\text{A}\times \Delta \text{L}}\left(\text{i}.\text{e}.\frac{\mathit{\text{Stress}}}{\mathit{\text{Strain}}}\right)$$ (3)

2). Isotonic Condition

For the isotonic condition, the CT-SDAEs were hung from the load-cell and a set of tensile loads were attached to them using 3D printed couplers. Then, the contraction for each loaded conditions were measured under the activation waveforms.

The following measures were calculated using the isotonic contraction data.

Displacement generation Hysteresis

Displacement generation Hysteresis was measured similar to force generation hysteresis. The displacement of the actuator was measured, instead of force, during the ramp-up and ramp-down of the triangular waveforms with 10s and 1s periods.

Maximum longitudinal strain

Maximum longitudinal strain was calculated by dividing the averaged maximum longitudinal contraction, reported as mean (SD), of thirteen CT-SDEAs to their normal length, 39 mm, using the linear activation waveform and 80 g of tensile load.

Strain-rate

Strain-rate, as measure of contraction speed, was calculated using the reported charge time and measured maximum longitudinal strain. Because the CT-SDEA is essentially a capacitance, its charge time is the same as its actuation time. This is also observable in the reported actuation frequency (100 Hz). To assess the possibility of evaluating the calculated strain-rate, the maximum rate of voltage increase in the square activation waveform was measured to calculate the maximum generated current, as a measure of charge time, using (4). Where C is the CT-SDEA’s capacitance.

$$i=C\frac{dV}{dt}$$ (4)

Power to mass ratio

Power to mass ratio was calculated using a 40 g tensile load under the square activation waveform, during sharpest rise of the contraction, onset to %88.5 of maximum contraction, i.e two time constants (τ). The onset detection methodology was the same as the aforementioned electromechnical delay measure. The maximum power was calculated using (5). where m is the mass of the tensile load v(t) is the speed of the contraction and a(t) is its acceleration. Then the calculated max power was normalized to the weight of the actuator, 11.3 g.

$$P(t)=\frac{d\left(\frac{1}{2}mv{(t)}^2\right)}{dt}+\frac{d(mgy(t))}{dt}=mv(t)[a(t)+g]$$ (5)

B. Testing setup

To benchmark the CT-SDEAs under isometric and isotonic contractions, a test-rig was designed and implemented (Fig. 3). The main components of this test-rig were: 1) a laser displacement sensor (ILD 1420–25, Micro-Epsilon, Ortenburg, Germany) to measure longitudinal contraction displacement, with 1 μm precision; 2) a load-cell (LSB302, 25 lb, FUTEK Advanced Sensor Technology, Inc., Imine, CA, USA) to measure active and passive force; 3) a precision translational stage, with 10 μm graduation and 102 N axial load capacity, to fine tune the load-cell position; 4) a high voltage (HV) amplifier (RC250–1.5P, Matsusada Precision Inc., Shiga, Japan) with 1500 V and 165 mA max output voltage and current respectively, to provide the necessary driving voltage, 0–1230 V, for the CT-SDEAs, 5) a Compact DAQ data acquisition system (CDAQ) (CDAQ-9174, National Instrument, Austin, TX, USA) containing an analog input module (NI 9215), an analog output module (NI 9263), a digital input and output module (NI 9375), and a H-bridge input module (NI 9237) for recording the load cell data; 6) two laser levels (GLL2,Robert Bosch GmbH, Stuttgart, Germany) to align the CT-SDEAs vertically for isometric contraction conditions; 7) a software developed in LabVIEW (National Instrument, Austin, TX, USA), to record the data from the sensors, and monitor and control the HV amplifier.

Figure 3.

The test-rig used in isometric (left panel) and isotonic contraction (right panel)

Fig. 4 shows the electrical circuitry of the HV amplifier, V_DC, discharge resistance, R_dis, and CT-DEA. The CT-SDEA is modeled as a parallel variable capacitor, C, and resistor, R_L, in series with two electrode resistors, R_E. R_L model the non-ideal leakage current through the dielectric. The variability in C, R_L, and R_E is due to the length modulation of the CT-SDEA, and consequently, changes in the electrical characteristics of the compliant capacitor. Electrode resistance of each CT-SDEA’s layers was reported at 50 kΩ. Considering 1600 parallel layers of the CT-SDEA, the total electrode resistance, R_E, was as small as, 31.25 Ω. A 1 MΩ discharge resistor was connected in parallel to increase the discharge rate the CT-SDEA, and thereby, increase the pace of returning back to initial length.

Figure 4.

Electrical circuitry of the HV amplifier, V_DC, a discharge resistance, R_dis, and the CT-SDEA, in parallel with each other. The CT-SDEA is modeled as a variable capacitance, C, and leakage resistor, R_L.

Preliminary results of our triangular waveform showed lack of symmetry between the ramp-up and ramp-down portion of the waveform using the Matsusada HV amplifier, due to its low slew-rate- that is the maximum rate at which an amplifier can respond to an abrupt change of input level. Therefore, for both force and displacement hysteresis, a faster HV amplifier was used (HA51U-1.6P10–3, hivolt.de, Hamburg, Germany), with 80 V/μs slew-rate. A 10 MΩ (recommended by CTsystems) discharge resistor was used for the hysteresis tests.

To generate and monitor the activation waveforms and record the data from the sensors, a LabVIEW code was developed. The LabVIEW code generated a set of command signals, similar to activation waveforms in period and profile, to be amplified by the HV amplifier. The sampling rate of the command signal was 1 kS/s via analog output of the CDAQ. While applying the command waveform, the LabVIEW code simultaneously recorded the input signals via the analog input modules of the CDAQ. The LabVIEW code collected data from load-cell and displacement sensors while monitoring the output current and voltage of the HV amplifier (Fig. 5). Force (load-cell signal) and the monitoring signals (i.e., output current and voltage of the HV amplifier) were collected via CDAQ, synchronously, having negligible time differences between them. The laser displacement signal, however, was collected via a USB port and was synchronized as close as possible with other input signals via our designed software.

Figure 5.

The block diagram of the testing setup.

III. Results

On average, the 13 CT-SDEAs generated 10.01 (0.2) N, i.e., 35 kPa stress, and 1.30 (0.8) mm of shortening. The amount of shortening was slightly higher than that of reported by CT-SDEAs (TABLE II).

The force generation profile of the thirteen actuators were identical, however, the maximum force variation between CT-SDEAs ranged 9.741 N to 10.337 N (Fig. 6). Additionally, the CT-SDEAs had fast response times, with electromechanical delay shorter than that of mammalian skeletal muscle, 21 ms (TABLE III). Young’s modulus, 0.87 MPa had lower value in comparison with mammalian skeletal muscle (TABLE III). Power-to-mass ratio and electromechanical delay of the CT-SDEA were higher than that of skeletal muscle (TABLE III). Using %3.3 measured longitudinal strain (TABLE III) and charge time, 5 ms (TABLE II), the strain-rate was measured at 660 %/s. Using (4), the measured maximum transient current, and CT-SDEA’s capacitance the $\frac{dV}{dt}$, i.e., slew-rate, was measured 9 × 10⁷ V/s, which was substantially lower than the needed slew-rate, 4.2 × 10⁸V/s, to produce 100 mA needed for 5 ms of charge time.

Figure 6.

The force generation response of thirteen CT-SDEAs in generating force under the square activation waveform superimposed on top of each other. A01 to A13 are each of the thirteen actuators tested for this measurement.

TABLE III.

CT-SDEA comparison to properties of mammalian skeletal muscle [29]

Property	Typical	Max	CT-SDEA
Max Strain (%)	20*	>40	3.3
Max Stress (MPa)	0.1	0.35	0.037
Strain-rate (%/s)		500	660
Power to mass (W/kg)	50	200	429.1
Cycle life (Mio Cycle)		1000	>50**
Axial Young Modulus (MPa)	10–60		0.87
Electromechanical delay (ms)	54 [30]		21

^**This is reported by the CTsystems [19].

^*The reported value for biceps [23].

The CT-SDEA showed 22.77 mA max transient current with 35.8 ms time constant, and a steady state current of 39 μA. Consequently, at full contraction, R_L was calculated at 35.1 MΩ. The CT-SDEA capacitance, C, was measured 237 nF.

The Length-Tension curve (Fig. 7) shows active and passive force generation capability of the CT-SDEA under different levels of extension/compression. Although small, the more extended the CT-SDEA, the less force it could generate. The active force ranged from 11.01 N to 8.98 N for 4.5% compression and 5.0% extension, respectively. The CT-SDEA showed a substantial passive force under compression and extension due to the elasticity of the dielectric layers, i.e., silicone elastomer (Fig. 7, grey trace). The passive force ranged from −12.54 N to 12.76 N for 4.5% compression and 5.0% extension, respectively. Thus, the maximum total force was 21.74 N.

Figure 7.

The active and passive force generation of a representative CT-SDEA under different levels of compression and extension. The 0.0% is the normal length of the actuator. Positive and negative percentages are extension and compression, respectively.

Fig. 8 shows the low force generation hysteresis of the CT-SDEAs for both 10 s and 1 s triangular waveforms (upper panels), at 0.41 N (4.14%) and 0.33 N (3.44%), respectively. The shape of this graph shows the parabolic relationship between Maxwell pressure and applied voltage (1). In comparison with force, the displacement hysteresis was much higher, 0.15 mm (11.77%) and 0.19 mm (14.16%) for the 10s and 1s triangular waveforms respectively. The hysteresis graph is important for assessing the complexity of the needed control mechanism.

Figure 8.

The force and displacement hysteresis of a representative CT-SDEA.

The maximum longitudinal contractions of the thirteen CT-SDEAs under eleven different tensile loads, from 80 g to 1080 g, were averaged and depicted in Fig. 9. As tensile load increased, the maximum reachable contraction decreased.

Figure 9.

Averaged maximum (Max) longitudinal contraction of 13 CT-SDAEs, under 11 tensile load.

IV. Discussion

The mechanical properties of the CT_SDEA, a commercially available stacked DEA, was measured. Aside from substantial force generation, noiseless operation, and high power to mass ratio, in comparison to other alternative actuators, the CT-SDEAs’ high cycle life, reported by CTsystems, and low energy consumption are outstanding. The results were compared with CTsystems reported values, and that of the mammalian skeletal muscle. When compared with the CTsystems reported values, CT-SDEAs showed similar force generation capability, however, the measured shortening was slightly higher. The calculated Young’s modulus were smaller than the reported value. Almost all measured properties were comparable to those of skeletal muscle, except strain and cycle life.

CT-DEAs showed substantially higher power-to-mass ratio and lower electromechanical delay, 429 w/kg and 21 ms respectively, in comparison with skeletal muscle, 200 w/kg and 54 ms, respectively. The former is mostly the result of their light weight, 11.3 g, high strain-rate and force generation capability. The low electromechanical delay, i.e., fast response-time, in combination with short actuation time, i.e., strain-rate, will help in the design of a fast and effective closed-loop control mechanism. This is highly desirable in rehabilitation robotics.

One of the outstanding feature of CT-SDEAs in comparison to other alternative soft actuators, such as hydraulically amplified self-healing electrostatic (HASEL) [21], polymer fiber and plasticized poly vinyl chloride (PVC) gel [22], are their high cycle life, >50 million (Mio) cycles. Recently, >70 Mio cycle is reported for the new models. In comparison, PVC gel performance decreased by 60% after only 170 k cycles [22] and the reported cycle life for HASEL is 158 k cycles [21]. Although shorter than skeletal muscle, this feature makes CT-SDEAs a desirable alternative for active exoskeletons, where many contractions are needed per day to assist an individual with an impaired musculoskeletal system.

As expected from a capacitor, steady state current consumption, at full contraction, i.e., the dielectric leakage current of the CT-SDEA, was very low, less than 39 μA. Ideally, once a capacitor is charged the current consumption must be zero, however, in reality there is always a small leakage through the dielectric material. This low power consumption, 0.047 W (39 μA × 1230 V), for holding the contraction is remarkable, whereas, the versatile soft ethanol-based phase-change actuators consume 45 W to flex the forearm of a skeleton [3]. To charge the CT-SDEA for full contraction, the transient current consumption of one actuator, however, reaches as high as 22.77 mA for a couple of milliseconds. For safety concerns, one can trade off the contraction velocity by limiting the current, (2).

In active exoskeletons, where assisting motion is usually the main goal, the shortening, of the artificial skeletal muscle must be large enough to allow for its contraction alongside the impaired muscle. The maximum strain of the CT-SDEAs (3.3%), however, was substantially lower than skeletal muscle (20%). Pappas et al. [23] showed about 4 cm of shortening in maximum voluntary contraction of biceps muscle in adults. The averaged upper-arm length of these participants were about 32 cm. Thus, if an artificial skeletal muscle contains eight CT-SDEAs in series, total length of about 32 cm, its maximum shortening would be about 1.4 cm (each CT_SDEA producing 1.3 mm of shortening), which is about one third of the biceps muscle [23]. Therefore, assisting the biceps in its full range of motion is quiet challenging. However, one can either leverage the substantial force of the SDEAs, 21.74 N total force (Fig. 7), to magnify the displacement using mechanical linkages; or assist the skeletal muscle’s contraction in its partial range of motion. Alternatively, this artificial muscle can be deployed for ankle dorsiflexion assistance during gait. Full range of ankle dorsiflexion is about 15° [24], vs 149° [25] elbow flexion. and the length of the lower leg is substantially longer than the upper arm, 0.246 vs 0.186 of total height, respectively [26], thus, there is more space to increase the artificial muscle’s displacement by adding CT-SDEAs in series.

The difference in Young’s modulus between our measurement and the reported value by CTsystems, may be due the limitations of our testing setup compared to that of the manufacturer. Similarly, the incapability in recreating the reported charge time, to reach the reported actuation frequency, and thereby, measuring the maximum strain-rate, was due to the slow slew-rate of the Matsusada HV amplifier and the maximum reachable transient current of the hivolt amplifier, 20 mA. The necessary transient current to replicate the reported charge time, i.e., actuation time, was 100 mA (TABLE II), which was not reachable in activation of one CT-SDEA using the square waveform. The small range of extension/compression, 4.5%/5%, that we used for calculating Young’s modulus, may also be a contributing factor in the resultant smaller value.

V. Conclusion

To assess the capability of stacked DE actuators for rehabilitation robotic applications, CT-SDEAs were benchmarked; and their mechanical properties were compared to the reported values for skeletal muscle. The CT-SDEAs showed comparable properties to skeletal muscle in some features of interest, including response time, and power to mass ratio. Their cycle life, although shorter than skeletal muscle, appear sufficient for rehabilitation purposes and was substantially higher than other alternative soft actuators. Their strain, however, were substantially lower than those of human skeletal muscles, which may impose challenges in design.