Armor-Based Stable Force Pneumatic Artificial Muscles for Steady Actuation Properties

Abstract

In this article, a novel actuator called armor-based stable force pneumatic artificial muscle (AS-PAM) is presented. AS-PAM has a sealed chamber made of polygonal parts and film, which helps the actuator to be lightweight (∼100 g) and achieve a large contraction ratio (>60%). It has an armor and a constraint to guide its motion, which keeps its force output [6.25 N/(cm²·bar)] stable over its operating range (<10% deviation). An analytical model is presented to predict and control the behavior of the actuator, and various experiments were conducted to show the validity of the model. Afterward, a gripper using the actuators is presented to illustrate how it can be used in real applications. With its characteristics, the actuator shows interesting behaviors that cannot be found in other soft pneumatic actuators, and it would allow AS-PAM to expand the range of applications in which soft robots cooperate with humans.

Introduction

Traditional rigid robots can offer high performance in terms of speed, precision, and force. These are ideal characteristics for repetitive tasks, which has made these robots to be widely used in industry. However, these robots cannot handle tasks where unexpected events may occur, and where safety matters.^1,2

Soft robots were introduced to overcome the limitations of rigid robots, and from previous researches, it has been shown that soft robots can handle various tasks including crawling, gripping, swimming, and can outperform rigid robots when subjected to unpredictable events.^3–8 Following this interest in developing more capable robots, many types of soft actuators have been developed.

Although all being classified as soft actuators, they each have unique characteristics, but also have problems that prevent them from being used for a wide range of applications as follows: limitations in either force (∼10 N) or contraction ratio (∼10%) in the case of shape memory alloy-based actuators,^9,10 limited contraction ratio (∼10%) in the case of twisted-coiled polymer fiber actuator,¹¹ high-voltage requirement (∼1 kV) in the case of dielectric elastomers,¹² slow speed ( $100 μ m ∕ s$ ) in the case of shape memory polymers,¹³ and low efficiency (∼1%) in case of phase-change material-based actuators.¹⁴

Due to this, soft actuators based on fluids such as air, or soft pneumatic linear actuators to be specific, are one of the main branches of soft actuation that have a high potential for future robotic applications, and many soft pneumatic linear actuators have been developed so far. One of the most commonly used soft actuator is the pneumatic artificial muscle (PAM), which utilizes positive pressure and a flexible rubber membrane that expands laterally and contracts longitudinally upon inflation.^15–19 Alternative designs capable of extending have also been demonstrated,²⁰ but contractile actuators are generally considered to be more useful.

Other forms of positive pressure linear actuators using lateral expansion for contraction have been developed including film-based actuators such as serial PAMs, which are basically film-based PAMs connected in series,²¹ pouch motors, which are actuators made of two bonded films,^22–24 fiber-reinforced origami robotic actuators, which can achieve a relatively large contraction ratio (>50%) by using origami patterns,²⁵ fabric PAMs, which are tubular structures made from an anisotropic fabric that can actuate with little hysteresis (<1%),²⁶ and lastly, bellow type actuators, which can either expand in the lateral direction to create contractile force, achieve percentage extension of 900%, and can move in a three-dimensional (3D) space, respectively.^27–29 However, these positive pressure actuators generally have a contraction ratio limited to 30% to 50% depending on the design and a force that diminishes throughout the contraction.

Vacuum-based soft actuators have been proposed as a solution to increase the contraction ratio of soft pneumatic actuators since producing a reduction in volume more easily translates into a reduction in length of the actuator. Vacuum-actuated muscle-inspired pneumatic structures that operate through the buckling of an elastomeric structure were proposed although their contraction ratio was quite limited.^30,31 Fluid-driven origami-inspired artificial muscles use a skeleton and origami patterns with the ability to lift, twist, and grasp objects capable of contraction ratios up to 90% with minimal payloads,³² and lastly, origami-based vacuum pneumatic artificial muscles (OV-PAMs) have the unique behavior of being able to lift heavy payloads up to its maximum contraction point (40 kg payload, ∼90% contraction ratio) and achieve an extremely large contraction ratio even with a payload (2 kg payload, >99% contraction ratio).³³

However, these vacuum-based actuators maintain a common point with positive pressure-based soft actuators: their isobaric force diminishes significantly throughout the stroke due to the shape of their displacement/force curve. Even though their maximum forces and contraction ratios are different, the shape of the curve is similar in that their force is large at small contraction ratios while being small at large contraction ratios resulting in zero net force at their maximum displacement in most cases. To the best of our knowledge, all soft pneumatic actuators show such a reduction in the force throughout the displacement, and it means that those actuators may not make use of their full operating range unless large pressure variations are applied, resulting in issues such as slow actuation speed, high-energy requirement, or failure of the actuator.

A constant force would allow even heavy payloads to be operable throughout the entire range of the actuator, reduce energy requirements, and produce a stable actuation speed. Some mechanism-based solutions to make a stable force have been proposed including a gravity-balancing mechanism,³⁴ a constant force mechanism (CFM) based on a spring,³⁵ a CFM based on a link,^36,37 and constant force actuators based on dielectric elastomers.³⁸ However, gravity-balancing mechanisms and spring-based CFMs are rigid and cannot directly produce a linear motion, link-based CFMs cannot change their output force in real-time, and the output force of constant force actuators based on dielectric elastomers is too small (∼1 N). There is a need for a soft pneumatic actuator capable of producing a stable force without using any rigid mechanisms.

In this article, a novel actuator named armor-based stable force pneumatic artificial muscle (AS-PAM) is presented, which can help resolve these issues. This actuator makes a stable force (∼10% deviation) over its entire operating range (>60% contraction ratio) by implementing an armor and a constraint that guide its pattern of deformation. The results of the proposed AS-PAM match well with the theoretical force output even when the actuator is fully extended and the reduction in force output of the AS-PAM is about 15% over its operating range of 60% contraction ratio. This behavior is in contrast with other soft pneumatic actuators whose force reduces significantly throughout the contraction.

First, the design, manufacturing, and modeling are presented followed by its actuation characteristics, including its blocked force and contraction ratio/pressure relationship. Then a simple system consisting of a gripper attached to a retracting arm based on the proposed actuator is presented to show how it could be used in real applications. The proposed actuator has unique actuation characteristics not found in any of the previous soft pneumatic linear actuators and it makes the actuator an ideal candidate for future soft robotic applications.

Methods

Actuator concept

The force produced by a pneumatic actuator for a fixed pressure at a given length is proportional to the change in volume of air corresponding to a change in actuator length at this length, as shown in the modeling section of this article. Previous soft pneumatic actuators relied on membranes that would deform from a straight configuration when the actuator is fully extended into a circular shape with a decreasing radius of curvature. The rate in change of the volume resulting from this pattern of deformation of the membrane exhibits a rapid change in volume early in the deformation and a much smaller rate of change in volume in the later portion of the motion. This behavior can be seen both for the rate of increase in volume for positive pressure actuators and for the rate of decrease in volume for negative pressure actuators, which results in a large force early in the contraction and a greatly diminished force in the later part of the contraction.

Using only the early portion of the motion of the soft actuator is a viable solution, but this significantly decreases the contraction ratio and increases the required total length of the soft actuator for a given displacement. The proposed AS-PAM is an actuator that makes use of an armor so that the side walls of the actuator fold outward resulting in a stable and even slightly increasing rate of volume change over the later portion of its contraction. The initial position of the actuator can be adjusted as to operate within the portion of the motion, which produces a relatively constant force, and to obtain a force profile that any other surveyed soft actuator cannot replicate.

The AS-PAM consists of top and bottom plates, a soft sealed chamber, reinforcements, a rigid armor, and constraints. As shown in the conceptual side view (Fig. 1a), two plates at each end of the sealed chamber and reinforcements are evenly placed parallel to each other along the length as in the OV-PAM presented in the previous work.³³ During assembly, the rigid armor parts are fixed onto the side facets of the soft sealed chamber, which makes the structure function as an origami structure where the armors form a network of rigid panels, and the soft chamber functions as the interconnecting compliant hinges. However, corner facets of the chamber are left as flexible elements without armor as the actuator would otherwise be overconstrained and not be able to deform. This kind of hybrid origami structure combining rigid and soft facets as to not overconstrain the structure has previously been used in deformable origami wheels.³⁹

FIG. 1.

(a) Conceptual cross-sectional view of the proposed actuator, (b) manufacturing steps of the actuator, (c) fabricated AS-PAM with the manufacturing steps, (d) folding of the armor of the actuator, and (e) deformations of the actuator showing its flexibility. AS-PAM, armor-based stable force pneumatic artificial muscle.

The armor placed on the side facets causes the side of the chamber to assume a triangular shape, which moves outward during the motion. From the straight position where the height of the triangle is zero, the volume of these triangular volumes would increase as the height increases and then decrease as the base length goes to zero. This causes the rate of decrease of the volume of the actuator to be initially small and rapidly changing but large and stable later in the later portion of the motion of the actuator. The constraints connect two successive reinforcements to limit the range of motion of the actuator and constrain the motion within the later part of the contraction, producing a high and stable force.

Actuator assembly

For the actuator to work properly, the top and bottom plates, the reinforcements, and the armor should be rigid, while the sealed chamber and the constraints should be flexible. Thus, 1-mm-thick 3D-printed polylactic acid (PLA) parts are used for the reinforcements and the armor, 5-mm-thick 3D-printed PLA parts are used for the top and bottom plates, and 100-μm-thick polyvinyl chloride film is used for the soft sealed chamber and the constraints. Other materials can be used if they meet the requirements outlined previously. The rigid top and bottom plates have a triangular shape in this article but can have any polygonal shape.

To manufacture the actuator, the armor is attached to the chamber using double-sided tape and the reinforcements are placed in between the armors using tape (Fig. 1b). Afterward, the faces of the armor are pushed outward, and the constraints are placed at the center of each side and are connected to the reinforcements with tape. Finally, the edges of the top and bottom plates are coated with a thin layer of glue and sealed to the chamber.

An actuator with three chambers was fabricated using this method and was used in most experiments (Fig. 1c). The general behavior of the actuator and of the armor can be verified by applying vacuum pressure to the actuator (Fig. 1d), and it can be seen by manually deforming the actuator that it retains most of its flexibility and compliance in any direction even though it utilizes a rigid armor, which enables to freely deform the actuator on demand (Fig. 1e and Supplementary Video S1).

Analytical model

The AS-PAM can be modeled using the principle of virtual work. To do so, the volume of one chamber of the actuator is divided into two sections with a triangular prism shape and each section is denoted with a number (Fig. 2a). Although the first section includes voids denoted with the letter “A” and the second section needs additional flaps denoted with the letter “B” at each end of the section, these parts can be ignored as their sizes are similar, while their effects on the volume are opposite. Thus, the volume of the chamber can be obtained as follows:

FIG. 2.

(a) Four volume sections of the proposed actuator, (b) volume profile of the actuator with dimensions of $D = 90 m m$ and $l_{m a x} = 30 m m$ , and (c) the corresponding force profile as a function of the contraction ratio.

where V is the volume, D is the edge length of the plate, l is the current height of the chamber, and $l_{m a x}$ is the maximum height of the chamber.

The profile of the volume as a function of the contraction ratio of the actuator was calculated for an actuator with dimensions of $D = 90 m m$ and $l_{m a x} = 30 m m$ (Fig. 2b). The work input of the fluid and the work output of the actuator can be balanced using Equation (1), which results in the following:

where F is the force produced by the actuator and all other parameters are as previously defined.

However, Equation (2) ignores the force required for the elastic deformation of the structure of the actuator, which returns the actuator to an initial stretched position as shown in Supplementary Figure S1.

As further explained in Supplementary Data, the magnitude of this force can be measured experimentally at different points and interpolated between these points as shown in Supplementary Figure S2. This term was determined to be a function of the displacement and a corresponding term was added to the model, which results in the following:

where F_e is the force required for the elastic deformation of the structure of the actuator.

The profile of the force as a function of the contraction ratio with the same dimensions as previously defined shows that the force increases throughout the motion unlike other surveyed soft pneumatic actuators (Fig. 2c). It can also be noticed that the force produced by the actuator at very low contraction ratios is negative due to the increase in volume in this region. By adding a constraint, it is possible to remove this region from the actuation range and make the actuator to stay within the range with a larger and more stable force. The actuator used in this article has a constraint length set as half of $l_{m a x}$ and this makes the force stable throughout the chosen region as its variation is less than 10% in this region (Fig. 2c).

Assuming that the payload is fixed and that the pressure remains constant throughout the motion, the actuation time can be calculated using Equations (1) and (3), as follows:

where $t_{t o t a l}$ is the total actuation time required, t₁ is the duration of the stationary phase, which is the time required to reach a sufficient pressure to actuate, and t₂ is the duration of the moving phase, which is the time required to reach the target displacement after the stationary phase. P is the pressure, Q is the flow rate, P_i is the initial pressure, P_c is the critical pressure where the actuator starts to move, V_i is the initial volume, V_f is the final volume, $P_{a t m}$ is the atmospheric pressure, m is the mass of the payload, g is the gravitational constant, and $F_{m a x}$ is the maximum force that the actuator can produce under atmospheric pressure.

The t₁ term can be calculated numerically once the flow rate is known, and although this term is negligible for other soft pneumatic actuators, it has a significant effect for the presented actuator and will be used in the prevacuuming test, which is shown later.

Experiment method

Vacuum pressure is supplied to the actuator using a portable vacuum pump (SP V 700 EC-VD; Schwarzer) and the pressure is regulated using an electropneumatic vacuum regulator (ITV2090; SMC). A force/torque sensor (RFT60-HA01; robotous) and a linear encoder (LM10; RLS) were used to measure the blocked force (Fig. 3a) and the displacement of the actuator (Fig. 3b), respectively.

FIG. 3.

(a) Experimental setup for measuring the force, and (b) setup for measuring the displacement.

Results

In this section, the characteristics of the actuator are demonstrated. The blocked force at various contraction ratios shows the main characteristic of the proposed AS-PAM, followed by the contraction ratio under various payloads, prevacuuming control for faster actuation, and finally, the actuator's implementation into a gripper, which shows how the armored OV-PAM can be utilized. All experiments were done using an actuator with dimensions of $D = 90 m m$ and $l_{m a x} = 30 m m$ , and all error bars show minimum, average, and maximum values.

Blocked force at various contraction ratios

The first experiment is about the blocked force of the actuator at different contraction ratios. In this experiment, the actuator was fixed vertically with the lower side of the actuator connected to an adjustable displacement constraint to which the force torque sensor is connected. The blocked force of the actuator at contraction ratios of 0%, 20%, 40%, and 60% were measured with vacuum pressures ranging from 5 to 25 kPa in increments of 5 kPa, three times for each point.

The reason why the maximum contraction ratio is set to 60% is that the actuator's motion is limited by many factors, including the thickness of the armor, and 60% is the maximum contraction ratio possible for the configuration used in these experiments. Also, although applying higher pressure is possible as shown in the following experiments where 60 kPa of pressure is applied to the actuator, the maximum pressure was fixed at 25 kPa since applying higher pressure can cause various problems, including failure of the armor and sensor.

The blocked force as a function of the pressure shows that the actuator can produce ∼40 N of linear force per 10 kPa of vacuum pressure (Fig. 4a). Results show that the trend of the force as a function of the vacuum pressure is approximately a straight line for the tested pressure range regardless of the contraction ratio. This indicates that the concept of the actuator and the proposed numerical model are valid, and that the actuator makes a stable force throughout its entire contraction range as expected. The largest deviation between the experimental results and the model is 7.09 N at a pressure of 25 kPa, corresponding to an error of 6.86%. The error between each measurement for a given point is about 1 to 2% such that the error bars are not visible on the figure.

FIG. 4.

(a) Results for the blocked force at different contraction ratios, and (b) the isobaric curves at different pressures.

The main source of error between the model and the experimental values is the flexible portions of the actuator, such as the vertices of the actuator, which allows for unexpected deformations as these portions of the actuator are not covered by the armor. An improved design to remove such uncovered parts could suppress the error but would be hard to implement with the current manufacturing method.

Next, the blocked force as a function of the contraction ratio is represented using the data of the previous experiment to obtain further insights (Fig. 4b). One key characteristic of the actuator that can be observed in this experiment is that the force increases slightly for all tested pressures with an increase in the contraction ratio up to 40%, and that this increase in force reaches up to 7.78% from the force produced at 0% contraction ratio at a pressure of 15 kPa. This behavior is a distinctive characteristic of the proposed actuator as previous soft pneumatic linear actuators have a force that diminishes significantly throughout the contraction. This could make the actuator uniquely well suited for specific situations such as for compensating force losses from compressible elements during the motion.

It is also worth noting that the actuator makes a larger force than expected under high pressure especially at low contraction ratio. This may be due to the high pressure acting on the surfaces of the actuator, which makes them behave differently than predicted by the model. More rigid parts may be required to remove these errors. Overall, the proposed actuator displays unique characteristics and has good potential as a constant force actuator.

Contraction ratio at various payloads

The second experiment aims to measure the contraction ratio as a function of the pressure under various payloads. In this experiment, the contraction ratio of the actuator was measured for vacuum pressures ranging from 5 to 60 kPa in increments of 5 kPa and payloads of 5, 10, 15, and 20 kg (Fig. 5a).

FIG. 5.

(a) Contraction ratio as a function of pressure with various payloads, and (b) the deformation of the armor due to high pressure on its surface.

The model predicts that the contraction ratio will make a vertical line at the critical pressures of 12.3, 24.5, 36.8, and 49.1 kPa, which are proportional to the payload. Results indicate that the contraction ratio remains small until enough vacuum pressure is applied and shows a sharp increase to about 70% at pressures of 15, 30, 40, and 55 kPa, respectively. After this point, the contraction ratio continues to increase slowly, up to 85.5%. This is the maximum feasible contraction ratio considering the thickness of the armor. For a payload of 5 kg, the actuator contracts by 64.7% from 10 to 15 kPa, a difference of just 5 kPa, out of a total contraction ratio of 85.5%, and similar tendencies are observed for other payloads.

In this case, an increase in the contraction ratio after the critical pressure is an undesirable behavior, and it happens since the parts inside the actuator start to interfere with each other as the available volume decreases and because the compressed parts hinder actuation as a spring would. This phenomenon enables the actuator to achieve higher contraction ratios, but the usable force in this range becomes small. A better design should be able to eliminate this phenomenon, making the contraction ratio reach its maximum value for any pressure larger than the critical pressure. Also, there is a nonzero contraction ratio before the critical pressure that reaches up to 10% contraction for the 20 kg payload.

This behavior becomes significant with larger payloads and is due to the armor bending and deforming under high pressure (Fig. 5b). These deformations are an undesirable behavior, and stronger materials will be needed to eliminate this error. Once such undesirable behaviors get eliminated, the actuator will have high potential to perform all-or-nothing actuation within an extremely narrow pressure range using pressure control.

Prevacuuming control

Based on the results of the previous experiment, this section introduces a prevacuuming strategy for rapid actuation where the pressure is set to just below the critical pressure for a given payload. The proposed model indicates that the actuation of the AS-PAM can be divided into two phases: a stationary and a moving phase. During the stationary phase, the actuator does not move even with an increase in the vacuum pressure. The pressure is increased until it becomes just below critical pressure, and the duration of the stationary phase t₁ is shown in Equation (5). During the moving phase, the actuator moves with little change in its pressure, and its duration is t₂ as shown in Equation (6).

The total actuation time required without any control, $t_{t o t a l}$ , is the sum of the two time segments t₁ and t₂ as shown in Equation (4). Reducing or even eliminating t₁ can be achieved by prevacuuming the actuator to just below the critical pressure and operating only around this critical pressure. By doing this, the actuator will move faster, and it will make the actuator more attractive for applications with large and known payloads as the effect of this prevacuuming strategy is increased with a larger gap between the initial and critical pressures.

To demonstrate the effect of the prevacuuming strategy, the contraction ratio as a function of time with the actuator lifting 5, 10, 15, and 20 kg of weight was measured and compared with the modeling results (Fig. 6a). The model predicts that there will be a noticeable stationary phase especially for large payloads, and that the total actuation time will be 0.618, 0.922, 1.44, and 2.5 s for each weight, respectively. The experimental results show that the actual actuation time is 0.66, 0.94, 1.38, and 2.67 s, respectively. These results confirm that the actuator remains in a low contraction ratio until the critical pressure is reached and then enters a fast-moving phase after the critical pressure is reached, as predicted by the model.

FIG. 6.

(a) Contraction ratio as a function of time without prevacuuming, (b) contraction ratio as a function of time with prevacuuming, and (c) power of the actuator for each payload.

It can be observed that there is a nonzero contraction during the stationary phase, especially for the 20 kg case. This is due to the deformation of the armor as shown in the previous experiment, indicating it is not sufficiently strong to maintain its shape. However, the maximum error measured remains within 7%.

Next, the same experiment was repeated but by prevacuuming the actuator by setting the initial vacuum pressure at 10, 20, 35, and 45 kPa for payloads of 5, 10, 15, and 20 kg, respectively. The actuator is then actuated after the actuator becomes stable (Fig. 6b).

The model predicts that there will be a short stationary phase, and that the actuator will start moving immediately resulting in a total actuation time of 0.528, 0.702, 0.918, and 1.59 s, respectively. The corresponding experimental results show that the actual actuation time is 0.41, 0.55, 0.63, and 1.42 s, respectively. From these results, it is shown that prevacuuming does significantly reduce the duration of the stationary phase and the total time required to reach the target position. It also means that the actuator can make the same amount of work in less time and a comparison of power for the two actuation cases shows that prevacuuming can boost the power (Fig. 6c).

The power without prevacuuming is 0.668, 0.939, 0.960, and 0.661 W for each payload, while the corresponding power with the prevacuuming strategy is 1.04, 1.53, 1.95, and 1.08 W, respectively. The increase in power by prevacuuming at given payloads can be as high as 92% and the increase becomes larger with increasing payloads as expected, except for the 20 kg case possibly because of the unintended deformation of armor. Further improvements to the stiffness of the armor will enable zero contraction during the stationary phase, which will enable the actuator to achieve an even faster response time and to be useful as a high-power system for future robots.

Gripper demonstration

In this section, the actuator is implemented into a soft gripper to show that the actuation properties of the proposed AS-PAM are significantly different from other soft pneumatic actuators and how this can be helpful for real applications. A gripper with two AS-PAMs, which is referred to as “armored gripper,” is manufactured where one AS-PAM is used to close the jaw of the gripper and produce the gripping force, while the second AS-PAM is used to lift the payload. As a first test, 20 kPa of vacuum pressure is applied to the actuators and the armored gripper was able to successfully grasp and lift a load of 5 kg (Fig. 7 and Supplementary Video S2).

FIG. 7.

Armored gripper lifting 5 kg under 20 kPa of vacuum pressure.

Next, we wanted to compare the armored gripper to one making use of an actuator where the force diminishes throughout the contraction. The requirements for the comparison gripper are to have the same length as the armored gripper such that it can be implemented in the same configuration, for its actuators to have a contraction ratio similar or even greater than the AS-PAM and for it to have a greater maximum blocked.

To this end, a gripper using two OV-PAMs without reinforcements was selected for comparison such that it can be implemented in the same configuration as the AS-PAMs in the armored gripper force. The absence of reinforcements will increase its blocked force while accentuating the behavior through which the force will reduce throughout the contraction, which better approximates the surveyed soft pneumatic actuators. This gripper is referred as “normal gripper” thereafter.

A testing jig with widths of 4 and 2 cm at the contact point with the gripper was built to approximate different object widths such that the grippers are at different contraction ratios when gripping each object. A vacuum pressure of 20 kPa was applied to lift a payload of 2 kg attached to the jig. In the case of the jig with a 4 cm gripping width, the two grippers were able to lift the payload without any problem (Fig. 8a, b). However, in the case of the jig with a 2 cm gripping width, the normal gripper failed to lift the weight, while the armored gripper succeeded (Fig. 8c, d, and Supplementary Videos S3 and S4).

FIG. 8.

(a) Normal gripper lifting a payload with a 4 cm gripping width, (b) armored gripper lifting a payload with a 4 cm gripping width, (c) normal gripper failing to lift a payload with a 2 cm gripping width, (d) armored gripper lifting a payload with a 2 cm gripping width, and (e) effective contraction ratios of the two grippers with force requirement.

Since both grippers use friction to lift the payloads, the forces produced by actuator are the key factor that determines the maximum payload that the grippers can lift. Based on the previous test where an armored gripper required 20 kPa of vacuum pressure to lift a payload of 5 kg and the results for the force characteristics of the actuator, it can be derived that the minimum force required to lift 2 kg of payload is about 30 N. Assuming that twice this force is required to lift a payload regardless of change in a contact angle due to the two jaws of the gripper, the actuators should produce at least 60 N of force to lift this payload.

In the case of the OV-PAM, the force produced by the actuator decreases as it shrinks and its effective contraction ratio for the given condition is about 40% (Fig. 8e). In contrast, the force produced by the AS-PAM remains stable resulting in an effective contraction ratio of 60%, which is larger than that of the OV-PAM, and this explains why the armored gripper succeeded, while the normal gripper failed.

Another significant difference between the proposed AS-PAM and other soft linear actuators is its stable movement speed. In the previous prevacuuming experiment, it can be seen that the AS-PAM moves at a stable speed during its moving phase (Fig. 6a). This is due to the actuator moving mainly around a fixed critical pressure and it has a constant rate of volume change produced by a pump with a constant flow rate for a given pressure. To show this more clearly, the vacuum pressures were released without any control for the two grippers holding 2 kg of payload (Fig. 9a, b). Red lines are added on the figure to indicate the instantaneous position of the gripper at different times.

FIG. 9.

(a) Normal gripper releasing a payload with a drastic speed change, (b) armored gripper releasing a payload at a stable speed, (c) relaxation ratio as a function of volume for origami-based vacuum pneumatic artificial muscles, and (d) relaxation ratio as a function of volume for armor-based stable force pneumatic artificial muscles.

It can be seen that the speed of the armored gripper remains stable throughout the motion, while that of the normal gripper changes drastically from fast to slow, which can be further explained by deriving the volume/relaxation ratio relationships for each gripper (Fig. 9c, d). In the case of the normal gripper, a small change in the volume makes a large change in the relaxation ratio in the early stage of deformation. The opposite happens at the final stage of deformation, which results in a drastic speed change. In the case of the armored gripper, the change in the relaxation ratio remains stable at any point and thus the gripper moves at a stable speed.

Having a stable speed can significantly increase safety in the case of unexpected events by decreasing the maximum speed, which also minimizes the maximum impact force. In such events, the armored gripper will handle the object with a stable speed to minimize impact, while the normal gripper can cause much larger impacts as shown at the end of Supplementary Video S5. Furthermore, a steady movement speed is a desirable property for robots interacting with humans as it decreases the likelihood of unexpected motions and facilitates control.

Discussions

The proposed AS-PAM is a soft pneumatic actuator that is light and flexible and can output a large and stable force over its working range. The blocked force results indicate that it can make ∼400 N of force at 100 kPa, or 1bar, when its area is about $64 c m^{2}$ . That means that its force output is about 6.25 N/(cm²·bar) and could be further increased by increasing the dimensions of the actuator so that it becomes comparable with a pneumatic piston, which is its rigid counterpart, but lighter and more efficient.

Readers may also note that the AS-PAM also contains more rigid parts than any of the surveyed soft pneumatic actuators as a means to shape the deformation of the side walls of the actuator and obtain the desired actuation characteristics. This might stretch the definition of what a soft actuator is, but the actuator is able to function as it does because it relies on soft robotic concepts and hybrid origami structures through which soft materials are deforming to permit its motion. This creates a trade-off between being highly deformable in all modes of motion, which to some might be the essence of a soft robot, and having stable actuation properties that have, so far, not been achieved by other soft pneumatic actuators.

Because of its characteristics, AS-PAM allows several operating strategies to be used that other actuators cannot make use of. First, it can make use of a nonzero initial pressure by prevacuuming to enhance its speed and power when a known payload is applied. This actuation strategy is only possible because the actuator exerts a stable force and barely moves below the critical pressure. Second, it has a stable actuation and releasing speed without the need for any control methods, which increases the safety of the actuator. This behavior is due to the volume/contraction ratio profile of the actuator being linear resulting in a stable movement even without the use of other control methods.

The maximum contraction ratio of AS-PAM is higher than the vast majority of soft pneumatic linear actuators, but it is lower than our previously proposed OV-PAM mainly due to the thickness of armor. This is a reasonable trade-off for many applications considering the higher force at high contraction ratios and larger effective operating range as shown in the gripper demonstration.

When the maximum contraction ratio is the main target such as when payloads are very lightweight, a number of approaches may be used to increase the maximum contraction ratio. In this article, the constraint length was set to be half of the maximum length of the actuator. However, Equation (2) and the force profile in Figure 2c suggest that it is possible to use a longer constraint while keeping the actuator's stable force by adjusting its dimensions. With a longer constraint, the actuator would have a longer initial length and the same contracted length, which would help the actuator achieve a higher contraction ratio.

The actuator tested in this article should have been able to reach a contraction ratio of 80% while maintaining a stable force, but the maximum contraction ratio achieved was 60% as the current manufacturing method and materials do not allow the parts to be placed in exactly the right position, resulting in the parts interfering with each other and some parts having undesired deformations. With a better design and manufacturing method, the actuator should be able to have a seamless deformation that will lead to a better performance.

Conclusion

In this article, a novel vacuum-based soft actuator called AS-PAM is presented, which has unique characteristics that cannot be found in any other soft pneumatic linear actuator. With the help of its armor and constraints, its volume changes linearly along with a change in length, which results in a large [6.25 N/(cm²·bar)] and stable (<10 deviation) force over its operating range (>60% contraction ratio). Although its operating range is relatively narrow compared with some other vacuum-based soft pneumatic linear actuators, it can offer a wider effective operating range due to its stable force. Its behavior can be compared with a heavier rigid pneumatic piston considering its stable force, but without the friction force that these pistons generally exhibit.

As shown in the demonstration, the proposed actuator can be used to make a gripper that can handle heavy objects of various diameters due to its stable force output. Also, the proposed actuator has many other potential applications as a lightweight piston alternative due to its stable force and safe manipulation for human/robot cooperative applications utilizing its stable speed during motion. The AS-PAM is a nice fit for such applications and there could also be applications where its increasing force profile could become a key point of interest.

With these unique characteristics, the proposed actuator could lead to a new direction in the field of soft robotics and may open the door to new applications. Other actuator configurations and mechanisms could also lead to similarly steady or even steadier linear contractile forces produced by such pneumatic actuators and we hope that this study will spur more effort in this direction of research. To bring forth its implementation in a wide range of fields, future research will be focused on the analysis of the armor to improve the actuation behavior, the development of improved manufacturing processes with better materials to enhance its performance, and new control methods for high-precision operation.

Footnotes

Author Disclosure Statement

No competing financial interests exist.

Funding Information

This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (Ministry of Science, ICT & Future Planning) (No. 2018R1C1B6003990 and No. 2020R1A4A1018227).

Supplementary Material

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Supplementary Material

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