Axial Motion Characterization of a Helical Ionic Polymer Metal Composite Actuator and Its Application in 3-DOF Micro-Parallel Platforms

: In this work, a helical ionic polymer metal composite (IPMC) was fabricated by thermal treatment in a mold with helix grooves. The axial actuation behaviors of the helical IPMC actuator were observed, and the electromechanical and electrochemical characteristics were evaluated. The experimental results showed that as the voltage increased and the frequency decreased, the axial displacement, axial force, and electric current of the actuator all increased. Compared with square wave and sinusoidal signals, the actuator exhibited the most satisfactory motion under the direct current (DC) signal. For the electrochemical test, as the scanning rate decreased, the gravimetric speciﬁc capacitance increased. Within a suitable voltage range, the actuator was chemically stable. In addition, we coupled the Electrostatics module, Transport of Diluted Species module, and Solid Mechanics module in COMSOL Multiphysics software to model and analyze the helical IPMC actuator. The simulation data obtained were in good agreement with the experimental data. Finally, by using three helical IPMC actuators as driving components, an innovative three-degree-of-freedom (3-DOF) micro-parallel platform was designed, and it could realize a complex coupling movement of pitch, roll, and yaw under the action of an electric ﬁeld. This platform is expected to be used in micro-assembly, ﬂexible robots, and other ﬁelds.


Introduction
In recent years, the rapid development of precision positioning technology has promoted a large number of applications of multi-degree-of-freedom (multi-DOF) motion platforms in fields such as optical microscopes [1,2], micro-assembly stations [3], and micro-robots [4][5][6]. Multi-DOF platforms are usually classified into two typical system configurations, serial and parallel [7]. The serial configuration adopts a stacked or nested structure, which has the advantage of independent motion decoupling. However, it also has some shortcomings, for example, different axes have different dynamic characteristics, and positioning errors produced by each axis will accumulate [8], leading to a decline in accuracy. For the parallel configuration, the inertia is small, and the closed-loop kinematic chains enable multi-DOF platforms to achieve high rigidity, carrying capacity, and accuracy [9]. Therefore, the parallel configuration is more popular than the serial one. At present, piezoelectric actuators [10][11][12][13], electromagnetic actuators [14][15][16], and magnetostrictive actuators [17][18][19] are used as the driving components of multi-DOF microparallel platforms. However, the platforms driven by these actuators suffer from the defects of complex structure and high power consumption. Hence, it is a current challenge to 1. Cut the commercial membrane Nafion-117 into a strip; 2.
Deposit platinum nanoparticles on both surfaces of the Nafion membrane by electroless plating to obtain an IPMC strip [31]; 3.
Coil the IPMC strip in a prepared mold with helix grooves, and put a Teflon tube outside the mold to prevent the IPMC strip from expanding outward and releasing from the mold; 4.
Immerse the mold in deionized water at 90 • C for 5 h; 5.
Remove the helical IPMC from the mold.
The fabricated specimen is shown in Figure 1b, and its structural parameters are listed in Table 1.

Experimental Setup
In the electromechanical test, the experimental setup (shown in Figure 2a) was composed of a signal generator, a high-speed camera, a load cell, a current sensor, a clamping device, and an industrial computer. A signal generator (JDS6600, JUNTEK, Hangzhou, China) produced various electrical signals. The motion behaviors of the helical IPMC actuator were captured and recorded by a high-speed camera (i-SPEED 3, Olympus, Tokyo, Japan), and then the image information was processed to obtain the axial displacement data. The force of the helical IPMC actuator expanding along the axial direction (hereinafter referred to as axial force) was measured by a load cell (20 g, AVIC ZEMIC, Xi'an, China). Before the measurement, the helical IPMC actuator contracted to the shortest state by an electric field, and then its end point was in contact with the surface of the load cell. Afterward, a reverse voltage was applied to make it elongate, so that the axial force data obtained in this experiment were continuous. A current sensor (self-made current acquisition system embedded with STM32F405RGT6 chip) was employed to detect and display the corresponding electric current. A clamping device was used to fix the specimen and adjust its height. Last but not least, an industrial computer controlled the whole system. This test was conducted in air at room temperature.
In the electrochemical test, a three-electrode system was used to evaluate the electrochemical characteristics of the actuator, as shown in Figure 2b. Platinum electrodes on both sides of the IPMC served as the working electrode and counter electrode, an Ag/AgCl electrode served as the reference electrode, and 1 M of hydrochloric acid solution served as the electrolyte. The CV curves of the helical IPMC actuator were obtained by an electrochemical workstation (CHI604E, Shanghai Chenhua Instrument Co., Ltd., Shanghai, China). The scanning rates were set to 100 mV, 200 mV, 500 mV, 1000 mV, and 2000 mV, and the voltage range was set to −0.5 V to 0.5 V [22].

Experimental Setup
In the electromechanical test, the experimental setup (shown in Figure 2a) was composed of a signal generator, a high-speed camera, a load cell, a current sensor, a clamping device, and an industrial computer. A signal generator (JDS6600, JUNTEK, Hangzhou, China) produced various electrical signals. The motion behaviors of the helical IPMC actuator were captured and recorded by a high-speed camera (i-SPEED 3, Olympus, Tokyo, Japan), and then the image information was processed to obtain the axial displacement data. The force of the helical IPMC actuator expanding along the axial direction (hereinafter referred to as axial force) was measured by a load cell (20 g, AVIC ZEMIC, Xi'an, China). Before the measurement, the helical IPMC actuator contracted to the shortest state by an electric field, and then its end point was in contact with the surface of the load cell. Afterward, a reverse voltage was applied to make it elongate, so that the axial force data obtained in this experiment were continuous. A current sensor (self-made current acquisition system embedded with STM32F405RGT6 chip) was employed to detect and display the corresponding electric current. A clamping device was used to fix the specimen and adjust its height. Last but not least, an industrial computer controlled the whole system. This test was conducted in air at room temperature.
In the electrochemical test, a three-electrode system was used to evaluate the electrochemical characteristics of the actuator, as shown in Figure 2b. Platinum electrodes on both sides of the IPMC served as the working electrode and counter electrode, an Ag/AgCl electrode served as the reference electrode, and 1 M of hydrochloric acid solution served as the electrolyte. The CV curves of the helical IPMC actuator were obtained by an electrochemical workstation (CHI604E, Shanghai Chenhua Instrument Co., Ltd., Shanghai, China). The scanning rates were set to 100 mV, 200 mV, 500 mV, 1000 mV, and 2000 mV, and the voltage range was set to −0.5 V to 0.5 V [22].

Actuation Behaviors
A high-speed camera was used to observe the motion behaviors of the helical IPMC actuator from the frontal direction. The actuated signal was a sinusoidal wave of 3.5 V and 0.1 Hz. The captured images are shown in Figure 3 and Video S1, and the time interval of each image is 1 s. From the figure, it can be seen that the helical IPMC actuator is able to generate complicated three-dimensional motion under the stimulation of the electric field, which can be decomposed into three branches: radial movement, axial movement, and torsional movement. This phenomenon is attributed to the electro-active properties of the IPMC and the particularity of the actuator's shape. The actuation principle of IPMC is shown in

Actuation Behaviors
A high-speed camera was used to observe the motion behaviors of the helical IPMC actuator from the frontal direction. The actuated signal was a sinusoidal wave of 3.5 V and 0.1 Hz. The captured images are shown in Figure 3 and Video S1, and the time interval of each image is 1 s.

Actuation Behaviors
A high-speed camera was used to observe the motion behaviors of the helical IPMC actuator from the frontal direction. The actuated signal was a sinusoidal wave of 3.5 V and 0.1 Hz. The captured images are shown in Figure 3 and Video S1, and the time interval of each image is 1 s. From the figure, it can be seen that the helical IPMC actuator is able to generate complicated three-dimensional motion under the stimulation of the electric field, which can be decomposed into three branches: radial movement, axial movement, and torsional movement. This phenomenon is attributed to the electro-active properties of the IPMC and the particularity of the actuator's shape. The actuation principle of IPMC is shown in From the figure, it can be seen that the helical IPMC actuator is able to generate complicated three-dimensional motion under the stimulation of the electric field, which can be decomposed into three branches: radial movement, axial movement, and torsional movement. This phenomenon is attributed to the electro-active properties of the IPMC and the particularity of the actuator's shape. The actuation principle of IPMC is shown in Figure 4. After an electric field is applied between the two deposited electrodes, the hydrated cations inside the polymer membrane rapidly migrate to the cathode. Due to the uneven distribution of water molecules, the IPMC bends toward the anode side. This internal ion-water movement like electrophoresis produces effective strains for actuation [32]. Considering our actuator, if there is no electric field, it is in a natural state. When a positive voltage is applied to the outer surface of the actuator while a negative voltage is applied to the inner surface, the water molecules carried by cations inside the polymer membrane will migrate to the inner surface side, resulting in increases in stress and strain here. On this account, the helical IPMC expands as the number of turns decreases and the pitch increases, which causes the actuator to elongate along the axial direction. In contrast, when an opposite voltage is applied, the stress and strain of the outer surface side will increase and the actuator will tend to contract tightly, leading to its axial shortening. The behaviors of the helical IPMC actuator are abstracted and presented in Figure 5.  . After an electric field is applied between the two deposited electrodes, the hydrated cations inside the polymer membrane rapidly migrate to the cathode. Due to the uneven distribution of water molecules, the IPMC bends toward the anode side. This internal ion-water movement like electrophoresis produces effective strains for actuation [32]. Considering our actuator, if there is no electric field, it is in a natural state. When a positive voltage is applied to the outer surface of the actuator while a negative voltage is applied to the inner surface, the water molecules carried by cations inside the polymer membrane will migrate to the inner surface side, resulting in increases in stress and strain here. On this account, the helical IPMC expands as the number of turns decreases and the pitch increases, which causes the actuator to elongate along the axial direction. In contrast, when an opposite voltage is applied, the stress and strain of the outer surface side will increase and the actuator will tend to contract tightly, leading to its axial shortening. The behaviors of the helical IPMC actuator are abstracted and presented in Figure 5.

Displacement Characteristics
The axial displacement intuitively demonstrates the linear actuation performance of the helical IPMC actuator. Figure 6 shows the axial displacement responses of the helical IPMC actuator driven by three different electrical signals (see Appendix A for the detailed repeatability test). It is worth noting that the excitation frequencies of the sinusoidal and  . After an electric field is applied between the two deposited electrodes, the hydrated cations inside the polymer membrane rapidly migrate to the cathode. Due to the uneven distribution of water molecules, the IPMC bends toward the anode side. This internal ion-water movement like electrophoresis produces effective strains for actuation [32]. Considering our actuator, if there is no electric field, it is in a natural state. When a positive voltage is applied to the outer surface of the actuator while a negative voltage is applied to the inner surface, the water molecules carried by cations inside the polymer membrane will migrate to the inner surface side, resulting in increases in stress and strain here. On this account, the helical IPMC expands as the number of turns decreases and the pitch increases, which causes the actuator to elongate along the axial direction. In contrast, when an opposite voltage is applied, the stress and strain of the outer surface side will increase and the actuator will tend to contract tightly, leading to its axial shortening. The behaviors of the helical IPMC actuator are abstracted and presented in Figure 5.

Displacement Characteristics
The axial displacement intuitively demonstrates the linear actuation performance of the helical IPMC actuator. Figure 6 shows the axial displacement responses of the helical IPMC actuator driven by three different electrical signals (see Appendix A for the detailed repeatability test). It is worth noting that the excitation frequencies of the sinusoidal and

Displacement Characteristics
The axial displacement intuitively demonstrates the linear actuation performance of the helical IPMC actuator. Figure 6 shows the axial displacement responses of the helical IPMC actuator driven by three different electrical signals (see Appendix A for the detailed repeatability test). It is worth noting that the excitation frequencies of the sinusoidal and square wave signals are both 0.1 Hz. As shown in the figure, as the voltage amplitude increases, the axial displacement of the helical IPMC actuator increases correspondingly. This is because the higher voltage drives more hydrated cations to migrate to the cathode, which greatly increases the stress and strain on the inner or outer surface of the helical IPMC. Macroscopically, the actuator has greater deformation, which means the value of ∆x 1 + ∆x 2 shown in Figure 5 increases.
Actuators 2021, 10, x FOR PEER REVIEW 6 of 19 square wave signals are both 0.1 Hz. As shown in the figure, as the voltage amplitude increases, the axial displacement of the helical IPMC actuator increases correspondingly. This is because the higher voltage drives more hydrated cations to migrate to the cathode, which greatly increases the stress and strain on the inner or outer surface of the helical IPMC. Macroscopically, the actuator has greater deformation, which means the value of x x Δ +Δ 1 2 shown in Figure 5 increases. When a sinusoidal signal is input, as shown in Figure 6a, the axial displacement curve of the helical IPMC actuator exhibits a sinusoidal trend as well. At voltage amplitudes of 1 V, 2 V, and 3 V, the maximum axial displacements are 0.57 mm, 0.84 mm, and 2.86 mm, respectively. When a square wave signal is input, as shown in Figure 6b, once the actuator reaches the peak displacement, it rapidly reverses its motion direction; thus, sharp points appear on the curve. At 1 V, 2 V, and 3 V, the maximum axial displacements are 1.25 mm, 3.13 mm, and 5.52 mm, respectively, which are 119%, 272%, and 93% larger than those driven by the sinusoidal signal. During the 30 s test period, the axial displacement response of the helical IPMC actuator has good repeatability under either sinusoidal signal or square wave signal. In stark contrast, when a DC signal is input, the axial displacement of the actuator rises slowly and has no periodicity, as shown in Figure 6c. At 1 V, 2 V, and 3 V, the actuator reaches the maximum axial displacements of 2.66 mm, 5.82 mm, and 10.47 mm, respectively, which are increased by 113%, 86%, and 90% compared with those driven by square wave signal. As the moisture loss (evaporation and electrolysis) inside the polymer membrane accelerates under the DC signal, it takes a longer time to reach the maximum axial displacement. If the working time is not taken into account, the helical IPMC actuator driven by the DC signal presents the best axial motion.
In addition to the waveform and amplitude of the input signal, the frequency also has a great influence on the axial displacement of the helical IPMC actuator. The related curves are plotted in Figure 7, in which the applied voltage is 3 V. The presented results indicate that the axial displacement of the actuator decreases with the excitation frequency. This phenomenon is due to the fact that the time for the movement of the hydrated cations inside the polymer membrane toward the cathode is not sufficient [33]. At 0.25 Hz, 0.5 Hz, and 1 Hz, the maximum axial displacements of the actuator driven by the sinusoidal signal are measured to be 1.68 mm, 1.26 mm, and 0.77 mm, respectively. Under the square wave signal, the maximum displacements are measured to be 3.84 mm, 2.17 mm, and 1.26 mm, respectively. The results show that at any frequency, the maximum axial displacement of the helical IPMC actuator driven by a square wave signal is always greater than that driven by a sinusoidal signal. More importantly, because of the unique relationship between input and output, the axial displacement of the helical IPMC actuator can be accurately controlled by input signals. When a sinusoidal signal is input, as shown in Figure 6a, the axial displacement curve of the helical IPMC actuator exhibits a sinusoidal trend as well. At voltage amplitudes of 1 V, 2 V, and 3 V, the maximum axial displacements are 0.57 mm, 0.84 mm, and 2.86 mm, respectively. When a square wave signal is input, as shown in Figure 6b, once the actuator reaches the peak displacement, it rapidly reverses its motion direction; thus, sharp points appear on the curve. At 1 V, 2 V, and 3 V, the maximum axial displacements are 1.25 mm, 3.13 mm, and 5.52 mm, respectively, which are 119%, 272%, and 93% larger than those driven by the sinusoidal signal. During the 30 s test period, the axial displacement response of the helical IPMC actuator has good repeatability under either sinusoidal signal or square wave signal. In stark contrast, when a DC signal is input, the axial displacement of the actuator rises slowly and has no periodicity, as shown in Figure 6c. At 1 V, 2 V, and 3 V, the actuator reaches the maximum axial displacements of 2.66 mm, 5.82 mm, and 10.47 mm, respectively, which are increased by 113%, 86%, and 90% compared with those driven by square wave signal. As the moisture loss (evaporation and electrolysis) inside the polymer membrane accelerates under the DC signal, it takes a longer time to reach the maximum axial displacement. If the working time is not taken into account, the helical IPMC actuator driven by the DC signal presents the best axial motion.
In addition to the waveform and amplitude of the input signal, the frequency also has a great influence on the axial displacement of the helical IPMC actuator. The related curves are plotted in Figure 7, in which the applied voltage is 3 V. The presented results indicate that the axial displacement of the actuator decreases with the excitation frequency. This phenomenon is due to the fact that the time for the movement of the hydrated cations inside the polymer membrane toward the cathode is not sufficient [33]. At 0.25 Hz, 0.5 Hz, and 1 Hz, the maximum axial displacements of the actuator driven by the sinusoidal signal are measured to be 1.68 mm, 1.26 mm, and 0.77 mm, respectively. Under the square wave signal, the maximum displacements are measured to be 3.84 mm, 2.17 mm, and 1.26 mm, respectively. The results show that at any frequency, the maximum axial displacement of the helical IPMC actuator driven by a square wave signal is always greater than that driven by a sinusoidal signal. More importantly, because of the unique relationship between input and output, the axial displacement of the helical IPMC actuator can be accurately controlled by input signals.

Force Characteristics
The axial force is another important parameter to evaluate the actuation performance of the helical IPMC actuator. Figure 8 illustrates the effect of voltage amplitude on the axial force of the actuator, and the frequency of the sinusoidal signal and square wave signal shown in the figure is 0.1 Hz. The axial force characteristics of the helical IPMC actuator are similar to the axial displacement characteristics. Likewise, it can be concluded that as the voltage amplitude increases, the axial force increases correspondingly. In addition, the axial forces of the actuator under the sinusoidal signal and square wave signal are both periodic, while the force under the DC signal is in a single direction, which is instructive for different applications. Under a DC signal of 3 V, the actuator reaches its maximum axial force of 6.63 mN at 6.57 s.
Under an AC signal of 3 V, the axial force responses of the actuator at different frequencies are shown in Figure 9. The results indicate that the axial force decreases with the frequency. Furthermore, the helical IPMC actuator driven by a square wave signal produces a greater axial force when experimental conditions are identical.

Force Characteristics
The axial force is another important parameter to evaluate the actuation performance of the helical IPMC actuator. Figure

Force Characteristics
The axial force is another important parameter to evaluate the actuation performance of the helical IPMC actuator. Figure 8 illustrates the effect of voltage amplitude on the axial force of the actuator, and the frequency of the sinusoidal signal and square wave signal shown in the figure is 0.1 Hz. The axial force characteristics of the helical IPMC actuator are similar to the axial displacement characteristics. Likewise, it can be concluded that as the voltage amplitude increases, the axial force increases correspondingly. In addition, the axial forces of the actuator under the sinusoidal signal and square wave signal are both periodic, while the force under the DC signal is in a single direction, which is instructive for different applications. Under a DC signal of 3 V, the actuator reaches its maximum axial force of 6.63 mN at 6.57 s.
Under an AC signal of 3 V, the axial force responses of the actuator at different frequencies are shown in Figure 9. The results indicate that the axial force decreases with the frequency. Furthermore, the helical IPMC actuator driven by a square wave signal produces a greater axial force when experimental conditions are identical. The axial force characteristics of the helical IPMC actuator are similar to the axial displacement characteristics. Likewise, it can be concluded that as the voltage amplitude increases, the axial force increases correspondingly. In addition, the axial forces of the actuator under the sinusoidal signal and square wave signal are both periodic, while the force under the DC signal is in a single direction, which is instructive for different applications. Under a DC signal of 3 V, the actuator reaches its maximum axial force of 6.63 mN at 6.57 s.
Under an AC signal of 3 V, the axial force responses of the actuator at different frequencies are shown in Figure 9. The results indicate that the axial force decreases with the frequency. Furthermore, the helical IPMC actuator driven by a square wave signal produces a greater axial force when experimental conditions are identical. Actuators 2021, 10, x FOR PEER REVIEW 8 of 19

Electric Current Characteristics
The electric current characteristics of the helical IPMC actuator can also reflect its actuation performance to a certain extent. The electric current of the IPMC is believed to originate from the migration of hydrated cations between two electrodes [34]. The more hydrated cations migrate, the greater the electric current. It can be seen from Figures 10  and 11 that the current increases with the increase in voltage and decrease in frequency, which is the same as the above-mentioned conclusions. However, the trend of the electric current curve is completely different from those of axial displacement and force curves. The electric current of the helical IPMC actuator under the sinusoidal signal does not present a perfect sinusoidal curve, which is related to the nonlinear characteristics of the material. When the input signal is a square wave or DC, the current reaches its peak in an instant, and then drops to a stable state within a few seconds. Under a DC signal of 3 V, the maximum electric current is 45.5 mA.

Electric Current Characteristics
The electric current characteristics of the helical IPMC actuator can also reflect its actuation performance to a certain extent. The electric current of the IPMC is believed to originate from the migration of hydrated cations between two electrodes [34]. The more hydrated cations migrate, the greater the electric current. It can be seen from Figures 10 and 11 that the current increases with the increase in voltage and decrease in frequency, which is the same as the above-mentioned conclusions. However, the trend of the electric current curve is completely different from those of axial displacement and force curves. The electric current of the helical IPMC actuator under the sinusoidal signal does not present a perfect sinusoidal curve, which is related to the nonlinear characteristics of the material. When the input signal is a square wave or DC, the current reaches its peak in an instant, and then drops to a stable state within a few seconds. Under a DC signal of 3 V, the maximum electric current is 45.5 mA.

Electric Current Characteristics
The electric current characteristics of the helical IPMC actuator can also reflect its actuation performance to a certain extent. The electric current of the IPMC is believed to originate from the migration of hydrated cations between two electrodes [34]. The more hydrated cations migrate, the greater the electric current. It can be seen from Figures 10  and 11 that the current increases with the increase in voltage and decrease in frequency, which is the same as the above-mentioned conclusions. However, the trend of the electric current curve is completely different from those of axial displacement and force curves. The electric current of the helical IPMC actuator under the sinusoidal signal does not present a perfect sinusoidal curve, which is related to the nonlinear characteristics of the material. When the input signal is a square wave or DC, the current reaches its peak in an instant, and then drops to a stable state within a few seconds. Under a DC signal of 3 V, the maximum electric current is 45.5 mA.

Electrochemical Characteristics
In order to probe into the electrochemical characteristics of the helical IPMC actuator, its voltage/current response was measured by cyclic voltammetry. The experimental results are shown in Figure 12a. In the measured reversible CV curves, there are no obvious redox peaks during a charge-discharge cycle, and the curve shape is approximately rectangular. This means that under given conditions, the fabricated helical IPMC actuator is chemically stable and can be used as an ideal double-layer capacitor. The gravimetric specific capacitance C g of the helical IPMC actuator can be evaluated by the following formula: where I p is the peak-to-peak value of the current when the voltage is 0 V, V s is the scanning rate of the voltage (V·s −1 ) [35], and m is the weight of the helical IPMC actuator. The calculation results are presented in Figure 12b. As the scanning rate increases, the gravimetric specific capacitance decreases. When the scanning rate is 100 mV·s −1 , the calculated gravimetric specific capacitance is 53.56 mF·g −1 , which is approximately 2.8 times that of the value for the IPMC reported by Ma et al. [22]. Large capacitance may be conducive to forming an excellent electric double layer at the electrode interface [22], thereby facilitating ion diffusion and charge accumulation.

Electrochemical Characteristics
In order to probe into the electrochemical characteristics of the helical IPMC actuator, its voltage/current response was measured by cyclic voltammetry. The experimental results are shown in Figure 12a. In the measured reversible CV curves, there are no obvious redox peaks during a charge-discharge cycle, and the curve shape is approximately rectangular. This means that under given conditions, the fabricated helical IPMC actuator is chemically stable and can be used as an ideal double-layer capacitor.

Electrochemical Characteristics
In order to probe into the electrochemical characteristics of the helical IPMC actuator, its voltage/current response was measured by cyclic voltammetry. The experimental results are shown in Figure 12a. In the measured reversible CV curves, there are no obvious redox peaks during a charge-discharge cycle, and the curve shape is approximately rectangular. This means that under given conditions, the fabricated helical IPMC actuator is chemically stable and can be used as an ideal double-layer capacitor. The gravimetric specific capacitance C g of the helical IPMC actuator can be evaluated by the following formula: where I p is the peak-to-peak value of the current when the voltage is 0 V, V s is the scanning rate of the voltage (V·s −1 ) [35], and m is the weight of the helical IPMC actuator. The calculation results are presented in Figure 12b. As the scanning rate increases, the gravimetric specific capacitance decreases. When the scanning rate is 100 mV·s −1 , the calculated gravimetric specific capacitance is 53.56 mF·g −1 , which is approximately 2.8 times that of the value for the IPMC reported by Ma et al. [22]. Large capacitance may be conducive to forming an excellent electric double layer at the electrode interface [22], thereby facilitating ion diffusion and charge accumulation. The gravimetric specific capacitance C g of the helical IPMC actuator can be evaluated by the following formula: where I p is the peak-to-peak value of the current when the voltage is 0 V, V s is the scanning rate of the voltage (V·s −1 ) [35], and m is the weight of the helical IPMC actuator. The calculation results are presented in Figure 12b. As the scanning rate increases, the gravimetric specific capacitance decreases. When the scanning rate is 100 mV·s −1 , the calculated gravimetric specific capacitance is 53.56 mF·g −1 , which is approximately 2.8 times that of the value for the IPMC reported by Ma et al. [22]. Large capacitance may be conducive to forming an excellent electric double layer at the electrode interface [22], thereby facilitating ion diffusion and charge accumulation.

Modeling and Simulation
It is essential to model and simulate the helical IPMC actuator to enhance the predictability of its actuation behaviors before it is used in practical application. Similar to other IPMC models [36][37][38][39], we regard the helical IPMC as a cantilever beam. Three physical phenomena are mainly considered: (i) electrical signals applied externally; (ii) cation migration inside the polymer; (iii) macroscopic deformation caused by the stress difference between the inner and outer surfaces. COMSOL Multiphysics 5.6 (a cross-platform finite element analysis, solver, and multiphysics simulation software) is utilized for geometry and material description, meshing, and calculation, involving multi-field coupling among Electrostatics, Transport of Diluted Species, and Solid Mechanics modules.

Mass Transfer Model
The mass transfer model of the IPMC was used to describe the transport process of cations and water molecules inside the polymer membrane under the action of electric field or force, which includes the friction model [40], irreversible thermodynamic model [41], and Nernst-Planck model [42]. Among them, the Nernst-Planck model is the most widely accepted at present, and its general form is [43][44][45]: where J, D, C, and z are the flux, diffusion coefficient, concentration, and charge number of mobile ions (here, hydrated cations), respectively, t is the time, e is the elementary charge, K B is the Boltzmann constant, T is the absolute temperature, u is the fluid velocity, E is the electric field intensity, Φ is the electric potential, and B is the magnetic field vector. The Nafion membrane is regarded as a static system and IPMC usually works under a static magnetic field; thus, u = 0 and ∂B/∂t = 0. According to the Nernst-Planck equation, the diffusion coefficient of the mobile ions D can be correlated with their mobility µ [46]: where R is the gas constant, given by: in which N A is the Avogadro constant and F is the Faraday constant. Thus, the final form of the Nernst-Planck equation is: Furthermore, for coupling the ion transport field with the electrostatic field, it is also required to consider the Poisson equation [47]: where ε stands for the absolute dielectric permittivity and ρ stands for the space charge density, which is defined as: where C 0 represents the concentration of anions, which is a constant as the anions are immovable inside the Nafion membrane.

Hygroscopic Swelling Model
In previous experiments, it was found that the volume of the Nafion membrane would increase due to the change in internal stress after contacting with water or other liquids. We call this phenomenon the hygroscopic swelling property of the Nafion membrane. Assuming that the volume change ∆V has a linear relationship with the water absorption quality ∆m, where β h is defined as the hygroscopic swelling coefficient. The difference between the volume V after swelling and the volume V 0 before swelling can be calculated as: in which l 0 and l, w 0 and w, and h 0 and h are the length, width, and thickness before and after swelling, respectively. Assuming that the Nafion membrane is an ideal elastomer and its linear strain is α, then: Hence, The water absorption quality ∆m can be obtained by the following equation: where M is the molar mass of the cations. Finally, the relationship between the linear strain of the Nafion membrane α and the concentration of the mobile ions C can be derived as follows:

Boundary and Initial Conditions
In the electrostatic field, we require that the surface potential of the helical IPMC actuator changes periodically with time: In the ion transport field, the solute leakage from electrode surfaces is ignored, that is, the ion flux of each surface is zero. When t = 0, the concentration of the mobile ions inside the Nafion membrane is set to C 0 .
In the solid mechanics field, the helical IPMC is regarded as a cantilever beam. One end is fixed and the displacement u(x, y, z) = 0, while the other end is free to deform without constraint.

Model Parameters and Meshing
The physical parameters contained in the above equations, as well as the geometric and material parameters required for model establishment, are summarized in Table 2. Some of them have been obtained from our previous experiments, and some are from references [39,48]. In COMSOL Multiphysics software, the partial differential equation (PDE) module was adopted to simulate the helical IPMC actuator. A free triangular mesh was created for the geometric model, and one was refined near the electrode surfaces to enhance the calculation accuracy. Solution convergence was found to be highly affected by the size of the mesh. In our model, the entire mesh contained 26,656 domain elements, 9268 boundary elements, and 1028 edge elements, with an average quality of 0.7026, as shown in Figure 13. In COMSOL Multiphysics software, the partial differential equation (PDE) module was adopted to simulate the helical IPMC actuator. A free triangular mesh was created for the geometric model, and one was refined near the electrode surfaces to enhance the calculation accuracy. Solution convergence was found to be highly affected by the size of the mesh.

Data Analysis and Model Verification
In this work, for the sake of simplicity, we only considered the sinusoidal wave as the input signal, and employed a transient solver. For the axial displacement of the end point P (shown in Figure 13), Figures 14 and 15 present the comparison between the experimental data (see Section 3.2) and the simulated data. It can be seen that the simulation

Data Analysis and Model Verification
In this work, for the sake of simplicity, we only considered the sinusoidal wave as the input signal, and employed a transient solver. For the axial displacement of the end point P (shown in Figure 13), Figures 14 and 15 present the comparison between the experimental data (see Section 3.2) and the simulated data. It can be seen that the simulation curve maintains good consistency with the experiment curve under the condition of voltage transformation or frequency conversion. Errors may be caused by the simplified factors in the modeling process, which need to be further optimized in the future. curve maintains good consistency with the experiment curve under the condition of voltage transformation or frequency conversion. Errors may be caused by the simplified factors in the modeling process, which need to be further optimized in the future.   Figures 16 and 17 show the concentration of the mobile ions and the von Mises stress in a period, respectively. At 0-4 s, the hydrated cations inside the Nafion membrane are densely distributed on the outer surface side, and the stress here is obviously greater than that near the inner surface, which makes the actuator tend to contract. At 5-9 s, the dense area of the hydrated cations is transferred to the inner surface side, where the stress is greater than that near the outer surface, giving the actuator a tendency to expand. This simulation result verifies the actuation principle of the helical IPMC actuator. curve maintains good consistency with the experiment curve under the condition of voltage transformation or frequency conversion. Errors may be caused by the simplified factors in the modeling process, which need to be further optimized in the future.   Figures 16 and 17 show the concentration of the mobile ions and the von Mises stress in a period, respectively. At 0-4 s, the hydrated cations inside the Nafion membrane are densely distributed on the outer surface side, and the stress here is obviously greater than that near the inner surface, which makes the actuator tend to contract. At 5-9 s, the dense area of the hydrated cations is transferred to the inner surface side, where the stress is greater than that near the outer surface, giving the actuator a tendency to expand. This simulation result verifies the actuation principle of the helical IPMC actuator.  Figures 16 and 17 show the concentration of the mobile ions and the von Mises stress in a period, respectively. At 0-4 s, the hydrated cations inside the Nafion membrane are densely distributed on the outer surface side, and the stress here is obviously greater than that near the inner surface, which makes the actuator tend to contract. At 5-9 s, the dense area of the hydrated cations is transferred to the inner surface side, where the stress is greater than that near the outer surface, giving the actuator a tendency to expand. This simulation result verifies the actuation principle of the helical IPMC actuator.

Application to a 3-DOF Micro-Parallel Platform
Considering the unique performance of the helical IPMC actuator, a novel type of flexible 3-DOF micro-parallel platform was developed (shown in Figure 18). The device comprised a base part, a driving part, and a movable platform. The base part was made of resin material by 3D printing, which was responsible for clamping the actuators and sending signals to them. The driving part consisted of three helical IPMC actuators with the same structural parameters of diameter, pitch, width, and length. Finally, the movable platform was a light carton with a weight of 40 mg.

Application to a 3-DOF Micro-Parallel Platform
Considering the unique performance of the helical IPMC actuator, a novel type of flexible 3-DOF micro-parallel platform was developed (shown in Figure 18). The device comprised a base part, a driving part, and a movable platform. The base part was made of resin material by 3D printing, which was responsible for clamping the actuators and sending signals to them. The driving part consisted of three helical IPMC actuators with the same structural parameters of diameter, pitch, width, and length. Finally, the movable platform was a light carton with a weight of 40 mg.

Application to a 3-DOF Micro-Parallel Platform
Considering the unique performance of the helical IPMC actuator, a novel type of flexible 3-DOF micro-parallel platform was developed (shown in Figure 18). The device comprised a base part, a driving part, and a movable platform. The base part was made of resin material by 3D printing, which was responsible for clamping the actuators and sending signals to them. The driving part consisted of three helical IPMC actuators with the same structural parameters of diameter, pitch, width, and length. Finally, the movable platform was a light carton with a weight of 40 mg. The deformation of the three helical IPMC actuators generated by electrical signals enables the movable platform to realize a 3-DOF coupling movement of pitch, roll, and yaw ( Figure 19 and Video S2). The device possesses three linear-motion driving units, which are consistent with the DOF of the movable platform; thus, there is no actuation redundancy in this case. When DC signals in range of −3 V to 3 V are input, the pitch angle that the movable platform can reach is about 30°, the roll angle is about 30°, and the yaw angle is about 45°. Compared with conventional 3-DOF platforms, the newly designed micro-parallel platform has the advantages of simple structure, good compliance, low power consumption, and easy miniaturization, which can meet the requirements of small size, millimeter-level stroke, and high stability. The deformation of the three helical IPMC actuators generated by electrical signals enables the movable platform to realize a 3-DOF coupling movement of pitch, roll, and yaw ( Figure 19 and Video S2). The device possesses three linear-motion driving units, which are consistent with the DOF of the movable platform; thus, there is no actuation redundancy in this case. When DC signals in range of −3 V to 3 V are input, the pitch angle that the movable platform can reach is about 30 • , the roll angle is about 30 • , and the yaw angle is about 45 • . Compared with conventional 3-DOF platforms, the newly designed micro-parallel platform has the advantages of simple structure, good compliance, low power consumption, and easy miniaturization, which can meet the requirements of small size, millimeter-level stroke, and high stability. (e,f) yaw.

Conclusions
In this paper, a helical IPMC was fabricated in a water bath by using a mold with helix grooves. Due to the electroactivity of the material and the particularity of the designed shape, the helical IPMC can produce complicated three-dimensional motion. We paid more attention to its axial movement and tried to apply it in practice, which differ- (e,f) yaw.

Conclusions
In this paper, a helical IPMC was fabricated in a water bath by using a mold with helix grooves. Due to the electroactivity of the material and the particularity of the designed shape, the helical IPMC can produce complicated three-dimensional motion. We paid more attention to its axial movement and tried to apply it in practice, which differentiates from others' work. For evaluating its actuation performance, the axial displacement, axial force, and electric current were tested and analyzed. It was found that with the increase in the voltage amplitude and the decrease in the excitation frequency, the actuator tended to work better (larger displacement and higher axial force). In addition, the electrochemical test results showed that the actuator had good chemical stability. To enhance the predictability of the actuation behaviors, we coupled several physical fields and established a model. The simulation results were basically consistent with the experimental results. In the last part of this work, a 3-DOF micro-parallel platform with three helical IPMC actuators as driving components was designed and manufactured, and it could generate a coupling movement of pitch, roll, and yaw under the electric field. By controlling the input signal, precise positioning could be realized. This research promotes the multi-scale development of smart materials and the wide application of multi-DOF precision platforms. Future research will concentrate on the performance improvement of the actuator, accuracy optimization of the model, and cooperative control of the 3-DOF platform.

Data Availability Statement:
The data presented in this study are available on request from the corresponding author.

Conflicts of Interest:
The authors declare no conflict of interest.

Appendix A
To investigate the performance stability of the helical IPMC actuator, a repeatability test was carried out. Under sinusoidal and square wave signals of 3 V, 0.1 Hz, the axial displacements in 100 cycles were measured, respectively. The experimental results are shown in Figure A1. It can be found that when a sinusoidal signal is input, there is no significant reduction in axial displacement during the test period, indicating that the actuator has stable actuation performance. However, when a square wave signal is input, the axial displacement begins to decrease after about 10 cycles and declines by 41% after 50 cycles. The reason for this phenomenon may be that the large deformation driven by the square wave signal leads to an acceleration of the water evaporation and electrolysis inside the polymer membrane.
shown in Figure A1. It can be found that when a sinusoidal signal is input, there is no significant reduction in axial displacement during the test period, indicating that the actuator has stable actuation performance. However, when a square wave signal is input, the axial displacement begins to decrease after about 10 cycles and declines by 41% after 50 cycles. The reason for this phenomenon may be that the large deformation driven by the square wave signal leads to an acceleration of the water evaporation and electrolysis inside the polymer membrane.