1. Introduction
Pneumatic actuators are extensively used in soft robotics owing to their simple design, structure, and driving principles. Due to their pliant bodies and flexible transformation, soft pneumatic actuators move effectively in complex environments and are predicted to be able to accomplish tasks in difficult terrain and safely interact with humans [
1]. Additionally, pneumatic rubber actuators are able to function in both wet and dry environments.
Compliant mechanisms are often inspired by the morphology and functionality of biological agents and are widely used in the design of robots and devices. A traveling wave operation, inspired by natural creatures such as earthworms, snails, and snakes, is an effective movement method. The applications of pneumatic actuators include conveyance devices [
2], microrobots [
3], peristaltic pumps [
4], annelid robots [
5], and piezoceramics [
6]. The actuators have multiple active regions in a single controllable device; thus, peristaltic motion is manifested by cycling these active regions. This configuration has been extensively used in piezoceramic devices such as conventional ultrasonic motors. Poole et al. [
7] presented a crawling actuator using multi-stack dielectric elastomers to generate locomotion based on the sequential actuation of the segments; however, the maximum attainable velocity was 2.1 mm/min, which was commercially insufficient.
It is very challenging for soft actuators to realize fast locomotion. However, soft actuators driven by pneumatic pressure are promising because of their advantages such as a large deformation and a high output-to-weight ratio. To generate a traveling wave using air pressure, multiple chambers are pressurized with a certain phase difference, which results in the desired output motion [
8,
9]. Suzumori [
10] presented a pneumatic rubber actuator comprising a rubber slab with deformable hollow chambers to produce linear motion on its surface. A walking speed of 4.7 mm/s was obtained from the prototype tests. However, the structure had multiple fins on its surface to generate a traveling wave motion; thus, limitations exist for the shape of objects that can be transported. Furthermore, a soft pneumatic mobile robot [
11] was developed with flexible flat tubes. The prototype produced self-excited vibration for a traveling wave motion to propel through a narrow space with the designed gap. The actuator had a locomotion speed of 3.2 mm/s and could be adjusted with the supply pressure. However, it was necessary to adopt a 3D structure for the airflow path to connect pressure supply hoses with each chamber, which hindered movement and added to production complexity.
A traveling wave motion can simultaneously provide large strokes and high forces with appropriate materials and perfectly configured actuation systems. The desired motion is achieved by predefining the layout and actuation patterns. The output comes from two processes: the production of traveling waves on the surface and the transfer process at the contact interface. A multi-stack dielectric elastomer actuator can travel between two planar surfaces by cycling active stacks [
7]. The parallel stacks are expanded in the planar direction and compressed in the perpendicular direction, thereby repeating locomotion and gripping the friction surface. Qi et al. [
8] proposed a soft pneumatic snake robot to move in complex, constrained environments using a traveling wave motion. Connolly et al. [
12] developed a soft fluidic actuator with a segmented structure for crawling. In addition, in [
13], a fluidic pump consisting of helical electrodes embedded within the walls of a polyurethane tube was designed to generate continuous fluid flow. Ran et al. [
14] developed a miniature piezoelectric actuator without a tooth structure on the stator surface to drive actuation. These actuators were controlled by a single device by designing ports to supply independently applied signals. However, the devices tended to be composed of three or more segments, which made it difficult to build input signal paths on planar structures.
Moreover, the use of structural calculation software is now a common practice when modeling and analyzing compliant mechanisms that are highly nonlinear. To adequately predict behavior, many methods have been developed to incorporate the elastic property into kinematic analysis. A popular approach to model continuum mechanisms is finite element analysis (FEA), in which the finite element meshed model is analyzed; thus, the detailed displacement and stress can be calculated for each element. With this significant advantage, any complex structure that can be employed as a meshed model can be generated from a meshing algorithm. Bieze et al. [
15] have modeled soft continuum manipulators to obtain forward and inverse kinematic models under quasi-static conditions. Sun et al. [
16] integrated the FEA-based mechanics modeling of large displacements, tendon-drive mechanisms, and contact problems. Other methods include the precise constant curvature model (PCCM) and the pseudo rigid body model (PRBM). The PCCM method is suitable for soft mechanisms with snake-like geometries [
17] as each bent section can be modeled as an arc with constant curvature. Using the PRBM method, flexible parts with a large deflection can be modeled based on the classic rigid-joint mechanism [
18]. To apply PRBM, flexure hinges must be determined manually for model simplification; thus, the detailed stress cannot be obtained.
In the present study, a spiral pneumatic rubber actuator is proposed, which utilizes an Archimedean spiral configuration [
19] to develop three airflow paths on a planar surface. The sequential deformations of the successive chambers interact with each other and produce radial traveling waves on the membrane surface, which sort objects by size or align them with the center. The goal is to establish a structural model, estimate the displacement, and optimize the design parameters to generate radial transportation with large strokes. The model is designed using three equidistant active segments with several parameters: membrane thickness, chamber width, chamber depth, and wall thickness. In addition, the effects of the structural parameters on actuation are investigated using 2D and 3D finite element models and then verified experimentally based on observations.
The remainder of this paper is organized as follows:
Section 2 presents an overview of the proposed actuator’s design, operating principles, and fabrication.
Section 3 explains the theoretical models and methods used for FEA.
Section 4 presents the prototype testing to assess its performance characteristics and confirm the theoretical model’s validity. Finally,
Section 5 concludes this study.
2. Design and Fabrication
2.1. Structural Design
The spiral actuator, shown in
Figure 1, comprises a silicone membrane mounted on an elastic substrate. Internal walls divide the actuator interior into three inflatable air chambers. The Archimedean spiral configuration is introduced to generate an inflatable shape at an equal distance from the surface during actuation. The rectangular cross-section allows the input air pressure to act on the membrane surface and internal free walls of the chambers. In
Figure 1b,
a and
b represent the width and depth of the chamber, respectively, and
c and
t describe the wall and membrane thicknesses, respectively.
2.2. Actuator Principle
The relatively thin internal walls deform freely owing to the internal pressure difference in the air chambers. In addition, there is a shift in the center position of the pressurized membrane because of the elastic force caused by the bending motion of the walls and the initial pressure; thus,
x- and
y-axis displacements are generated. A schematic of the actuator used to induce a traveling wave motion is shown in
Figure 2. The green arrows indicate the deformation caused by the applied air pressure, and the red arrows indicate the deformations contributing to the transportation of the object.
In Step 1, chamber A is pressurized, causing the membrane to inflate and the walls of the substrate to bend outward. When air pressure is applied to adjacent chamber B in Step 2, the wall between A and B returns to its original position and the elastic force pushes the membrane of chamber A to the left. In Step 3, chamber A, which inhibited the deformation of chamber B, becomes inactive, and the chamber B membrane is pushed to its center. Next, Step 4 proceeds through Steps 5, 6, and 1 using the same process. By repeating these steps, the actuator continues to deform and realize transportation. To achieve this process, periodic pressure signals are applied with a certain operating frequency to pressurize each chamber. Here, the operating frequency is calculated from the time per cycle for chamber A to reactivate; that is, it is the reciprocal of the time from Step 1 to Step 6.
2.3. Fabrication
Figure 3 shows the three main steps in the fabrication process. A high-precision silicone membrane (ELASTOSIL
® Film 2030, Wacker Chemie AG, Dalton, GA, USA) was cut into sufficiently large pieces to cover the substrate while keeping the surface clean.
The rubber substrate was made by pouring liquid silicone (KE/CAT–1600, Shin-Etsu Silicone, Akron, OH, USA) into a mold. The mold was produced with specific dimensions using a polyjet 3D printer (Stratasys Objet260 Connex3, Stratasys, Austin, TX, USA). The material used was VeroWhite photosensitive resin. The two-component liquid silicone was mixed in a mass ratio of 1:1 and thoroughly agitated using a mixer (ARV–310P, Thinky, Tokyo, Japan). There were two stages of mixing: 30 s at 2000 rpm and 45 s at 2200 rpm. After de-aeration in a vacuum chamber, the rubber was cured at 18 °C for 24 h to maintain constant flexibility properties.
Plasma treatment equipment (CIONE 4, Femto Science Inc., Somerset, NJ, USA) was used for direct bonding via atmospheric plasma treatment. While maintaining the air flow rate at 10 sccm (standard cubic centimeters per minute), plasma was obtained at a predetermined pressure of 7.6 × 102 Torr (101 kPa) with a radio frequency power of 100 W. The base pressure was maintained at less than 5.0 × 10−2 Torr (6.67 kPa), and the plasma exposure time was set to 30 s.
The above process resulted in an actuator made entirely of soft material. The three interior chambers were connected by three air hoses and had independent movement.
5. Conclusions
A spiral pneumatic actuator consisting of a thin film and an elastic substrate with an Archimedean spiral configuration was developed to generate a traveling wave motion for radial transportation. FEA simulations and experimental studies determined the deformation performance with different structural parameters for various predictable structures. The model was designed using three equidistant active segments with several parameters: membrane thickness, chamber width, chamber depth, and wall thickness. A reasonable correlation was obtained between the simulation and experimental results. The maximum deformation of the actuator was obtained considering three structural ratios: t/a, b/a, and c/a. The simulation results predicted the x- and y-axis displacements for each structure and suggested the optimal structure condition to obtain a larger stroke. A spiral configuration was introduced for ease of production, and we proposed a structure that can be applied to a variety of traveling wave actuators to evaluate their displacements. This concept can serve as a platform for other applications, such as conveying devices and crawling robots.
This actuator still has room for improvement in terms of operating frequency, which is currently fixed at 10 Hz. Due to the responsiveness of pneumatics, it is necessary to evaluate the effect of operating frequency on strokes and the resulting transportation speed.
Figure 15 shows a comparison of
y-axis displacements with respect to the operating frequency. Based on the experimental data, the displacement decreased almost linearly with the operating frequency. Larger transport velocities are expected at lower operating frequencies, but it is important to evaluate the effect of frequency on operation. In addition, when considering the contact with and transportation of objects, the limits on their size should be examined. Future work will focus on the robotic applications of the traveling wave actuator and discuss its usefulness.