Soft Pneumatic Actuator with Bimodal Bending Response Using a Single Pressure Source

Abstract

Deformation behavior of soft pneumatic actuators (SPAs) can mechanically be preprogrammed into their architecture during design. To date, the majority of SPAs rely on a unimodal bending design. This paper develops a method of including a bimodal design into the deformed state by means of a bilinear material that replaces the conventional strain limiter. With a simple increase in pneumatic pressure, it is possible to have distinctly different deformation directions in one actuator. While inflating at low pressures, the actuator has a preferential deformation direction. As the pressure continues to increase, this preferential deformation direction changes due to a change in the stiffness of the strain limiter. An example of this behavior is demonstrated by an actuator that initially bends in one direction, but then gradually changes direction in plane as the pressure continues to increase. Three different physical actuators were manufactured, tested, and correlated with preliminary numerical models. The physical and numerical models exhibited the desired bimodal behavior, although at different pressures. Furthermore, it was possible to alter the pressure at which this transition occurs by changing the crimp ratio of the embedded bilinear material.

Introduction

Where traditional robots excel at working in well-defined structured workspaces where each precision move is orchestrated from a central control system, the control of soft robots can be simplified¹ to yield actuators better suited to unstructured environments.² The soft materials support decentralized and simplified control.³ To facilitate this reduced central control requirement, deformation behavior must be preprogrammed into the morphological architecture of the actuator during design. The desired behaviors are therefore achieved by utilizing the passive mechanical dynamics of the actuators.⁴

A soft pneumatic actuator (SPA) using a simple actuation method, such as an increasing pneumatic pressure, will therefore lead to a known deformed state under known loading conditions and external forces.⁵ Common SPAs rely on a unimodal response to proportional pneumatic pressure changes. In the case of a linear actuator, more pressure brings more elongation and, in the case of a bending actuator, more bending. When blocked, they apply more force. Bending-type SPAs make use of an asymmetric stiffness to bias the direction of deformation.⁶ This asymmetric stiffness can be achieved by embedding a flat strip of stiffer material on one side—appropriately termed a strain limiter or strain-limiting layer.⁷ Bond paper has been used successfully in this regard.^8,9 It is, however, conceivable that a more complex response becomes desirable without the need for multiple actuators or actuation sources.

One such response is bidirectional bending or motion. Jeong et al.¹⁰ designed and fabricated some of the earliest bidirectional silicone actuators and were focused on creating microfingers. Their design was constructed using only silicone and the behavior was achieved by using pneumatic balloons with two flexible actuator diaphragms of different thicknesses. They subsequently created an end-effector using multiple of these microfingers on a conventional parallel-link robot.¹¹ Wakimoto et al.¹² investigated the numerical modeling and manufacturing of a miniature curling actuator. For their actuator, a single air supply tube was used, but required both positive pressure and vacuum sources to get the two different bending directions. Paez et al.¹³ successfully manufactured a bidirectional bending SPA using an origami shell reinforcement using only positive pressure, but requiring two separate air supply tubes. Marchese et al.¹⁴ required bidirectional bending in attempting to replicate the swimming motion of an escaping fish. In their work, this was achieved by essentially combining two independent bending actuators back-to-back and inflating each actuator as required.

A method that embeds a bimodal response, as opposed to only a bidirectional response, in an actuator is desired. This bimodal actuator must exhibit different distinct deformed states depending on the internal pressure, that is, an initial bending direction that changes to a second mode once the internal pressure exceeds the specification design parameter. The actuator should use a single air supply tube and a positive linear pressure ramp as its source. The ability of the paper strain-limiting layer in allowing changes to be made to the asymmetric stiffness of the actuator is investigated further as a method of embedding the desired behavior.

Benefits of bimodal behavior include having a power stroke in multiple directions, advantageous in, for example, wearable assistive devices. Hand rehabilitation can be performed using a single actuator and pressure source, but still assist with forced closing and opening of a hand.

This paper proposes that by changing the configuration of the strain-limiting layer in the design of an SPA, a bimodal response can essentially be preprogrammed into the actuator. It is proposed to make use of a silicone–paper composite material that exhibits a bilinear response to tensile loading depending on the strain range to which it is subjected. Physical experimentation was used to manufacture actuators that exhibit the desired behavior. A preliminary study was conducted in parallel to investigate whether a numerical model could capture the behavior and justify further time developing it as a future design tool. No IRB approval was required.

Bilinear Material

The desired bimodal behavior will be facilitated by using a composite material that exhibits a bilinear response to tensile loading; essentially a strain limiter preconditioned to a crimped initial geometry (Fig. 1). In this way, a longer strain limiter can be used in an actuator. Under low strain, the stiffness of the material is mostly that of the silicone matrix material. As the strain increases, the paper strain limiter decrimps, increasing the effective stiffness. Once the strain limiter is fully decrimped, the stiffness becomes that of the paper layer. This crimped layer helps create a bilinear composite material with two, distinctly different, linear elastic regimes over two successive strain ranges. The actuator should therefore have different preferential bending directions dependent on the strain the bilinear material is subjected to.

FIG. 1.

Schematic of the bilinear composite material showing the triangular wave pattern of the crimped strain limiter as well as the boundary of the Ecoflex 0030 silicone. The amplitude, A, and wavelength, λ, are used to parameterize the wave pattern.

Development

A separate study was conducted where development of the required bilinear composite material preceded development of the bimodal actuator.¹⁵ A composite of silicone (Ecoflex 0030) and bond paper yielded the desired response. The cited research showed that the behavior of the bilinear material is dependent on the relationship between the crimped length of the paper and the fully decrimped length. A triangular wave pattern was used as the method of crimping the paper layer. This wave pattern is characterized by its crimp ratio; the ratio of the amplitude (A) to the wavelength (λ), CR = A/λ. An illustration of this terminology is shown in Figure 1. The crimp ratio represents a quantity that is independent of the actuator length. Merely specifying the free length of the paper layer would result in a quantity that is dependent on the overall actuator length.

Under uniaxial tensile loading, the point at which the stiffness provided by the paper dominates that offered by silicone is termed the strain transition point. This transition point is not only tunable but also predictable. This tunable transition point can be used to design bimodal actuators in which the second bending mode is activated at different strains.

White bond paper (80 gsm) was chosen for two reasons; it has been used in prior soft robotics research as a strain-limiting layer and has shown sufficient performance in that application; manufacturing of the bilinear material requires that the folded paper layer hold its shape while assembling the molds. Higher tensile strength materials could be used, but would require a different manufacturing technique.

Modeling

This research aims to construct a preliminary, three-dimensional (3D) numerical model for analysis where the response of the actuator remains the focus. To reduce the possibility of convergence issues stemming from intricacies of the bilinear material, it was decided to directly model the stress–strain response of the bilinear material and use that response in the finite element (FE) model. The stress–strain response was modeled using an Ogden model, which allows for the material to be defined in a similar way as other nonlinear hyperelastic materials within the FE environment. Ogden models were calibrated for the three different crimp ratios used (0.2, 0.25, and 0.3). The performance of the model calibrated for a crimp ratio of 0.3 is shown in Figure 2 along with the experimental results. It is important to note that the strain transition point of the material model (39.9%) is in close agreement with that of the experimental tests (38.8%), even though the curve fit seems less than ideal. This strain transition point was calculated as the intersection of the primary modulus and secondary modulus, which are two linear lines that represent each stiffness value of the bilinear response. The primary modulus was fit to the initial 10% strain that represents the decrimping part of the behavior. This range was chosen as all three of the different crimp ratio materials exhibit clear linear behavior. The secondary modulus was calculated using the last ten data points. This represents the sharp change in stiffness caused by the fully decrimped paper layer. Both these moduli were fit using linear regression, and the transition point was calculated by extrapolating each line and finding the intersection point. This procedure of calibrating the Ogden parameters was repeated for all three crimp ratios to yield three independent models specifically for each crimp ratio used. The parameters for the three-term Ogden model are given in Table 1 with all μ terms in N/mm² and all α terms dimensionless.

FIG. 2.

Response of the Ogden model as fitted to the bilinear material with a crimp ratio of 0.3.

Table 1.

Parameters for the Three-Term Ogden Model of the Bilinear Material (μ terms in N\mm²)

Crimp ratio	μ₁	α₁	μ₂	α₂	μ₃	α₃
0.2	20.32	2.24	5.48 × 10⁻⁴	40.59	−19.08	2.38
0.25	5.20	15.68	1.18	0.20	−5.21	15.94
0.3	2.67	0.0224	1.013	0.052	6.233 × 10⁻⁷	39.09

The potential material models were limited to those already implemented in the software package used, Siemens NX 12. Three-term Mooney–Rivlin, Gent, and Yeoh models were also calibrated to the data and their goodness-of-fit values, calculated using R² as the indicator, were 0.592, 0.757, and 0.713, respectively, compared with the Ogden model with 0.779. The estimated strain transition point of the Ogden and Gent models was calculated to investigate their ability at capturing the strain-stiffening response of the material. The Ogden model predicted this strain transition point with an error of 2.84%, compared with experimental data, and the Gent model an error of 8.76%. The Ogden model was therefore chosen as the best performing material model.

Bimodal Actuator Design and Modeling

Design criteria

Silicone has a highly nonlinear deformation characteristic. Coupling this with the response of the bilinear paper, it becomes difficult to predict the shape of an SPA purely by intuition. Empirical methods and numerical tools offer solutions to deal with iterative design problems.

The basic design describing a slow Pneu-net (a type of SPA) by Mosadegh et al.¹ is used as a guideline for the morphology of the actuator in this work, where the inextensible layer referred to is replaced with the bilinear composite material. The slow Pneu-net is preferred over the fast variant due to the continuous and smooth surfaces all round required for attempting bimodal bending behavior at this stage. The profile of the slow Pneu-net allows the asymmetric stiffness that determines the bending direction to be embedded on both sides in which the actuator should bend. The one discontinuous side of the fast Pneu-net does not allow for this stiffness embedding as that side will always have a lower tensile stiffness due to discontinuity and therefore only one preferential bending direction. To this end, a base design was chosen to which sections of material could easily be added as needed. This baseline actuator is 157.5 mm long, 15 mm wide, and 17.5 mm high; has 15 connected inner voids; and is manufactured from Smooth-On Mold Star 15 (Fig. 3). The height of the actuator varies between different design objectives as additional Mold Star 15 or Smooth-On Smooth-Sil 950 strips are added to the top edge of the green silicone section to get the different modes.

FIG. 3.

Cross-sectional view of the bimodal actuator showing the different materials used. The crimped paper layer of the bilinear composite is visible. Color images are available online.

To get two distinctly different bending directions, it is required that the actuator be preprogrammed with two preferential bending directions, which are dependent on the strain in the model. The bilinear material layer should be incorporated such that it facilitates the second bending mode.

Therefore, the first bending mode should be such that the bilinear material is elongated while the SPA deforms. This first deformation mode should proceed until the elongation is large enough for the strain transition point of the bilinear material to be reached. Once this point is reached, the stiffness provided by the now decrimped paper layer dominates over the stiffness provided by the opposite edge of the deformed actuator. This swing in stiffness forces the deformed state to change direction as the internal pressure continues to increase.

The bilinear composite material has a thickness of 5 mm. The initial tensile response of the composite material is provided by the silicone matrix material as well as the interaction between silicone and the decrimping paper layer. For the actuator to have a variable preferential bending direction, it is required that the stiffness of the actuator should change as it deforms due to an increasing internal pressure. The decrimping paper layer in the bilinear composite material provides this required change. The actuator must therefore be designed such that the side on which the bilinear material is added initially is more compliant than the opposite side; this will create a preferential bending direction such that the paper layer decrimps while the actuator is inflated until it is fully decrimped, whereafter the bending direction will change. Figure 4 illustrates this requirement where region A is required to be more compliant than region B for the initial tensile loading.

FIG. 4.

Cross-sectional view indicating the two different stiffness requirements for a bimodal behavior. The black rectangle shows the position of the internal cavity. A and B are the stiffness regions above and below the internal cavity. Color images are available online.

It is possible to fine-tune the stiffness of region B such that the actuator undergoes different deformation modes. One such example is elongation followed by bending when the initial stiffness of region B is matched to that of region A. Another example of bimodal behavior is bending in one planar direction followed by bending toward the opposite planar if the stiffness of region B is increased to be initially stiffer than that of region A.

Physical model

Molds to manufacture the physical model were designed such that changes to the geometry were easily facilitated. Instead of casting different actuators with different sets of molds, the baseline geometry was rather used to which additional thin strips could be glued to achieve different results. These additional strips allowed the response to be rapidly changed without the delay of waiting for new molds and were available in 1-, 2-, and 3-mm thicknesses. Fused deposition modeling (FDM) was used to 3D print the molds. The bilinear material was made as a separate piece according to the steps detailed by Ellis et al.¹⁵ and was glued to the Mold Star 15 body using a thin uniform layer of Smooth-On Sil-Poxy. To prevent the base material of the bilinear composite, the soft Ecoflex 0030, from directly being subjected to high pressures, a 1-mm strip of Mold Star 15 was glued to the bilinear material at the interface to the main actuator body, visible in Figure 3. The Ecoflex would have bulged substantially if directly subjected to the pressure required for the actuator to function as designed.

The actuator was clamped at the base and inflated using a medical needle inserted through the base into the first void. During testing, it was hung down vertically to mitigate the effect of friction between the actuator and a flat surface. SPAs are susceptible to external loading, such as gravity, and the chosen testing orientation subjected each bending mode to a similar condition. A checkerboard pattern with blocks spaced 2.5 mm apart was used to quantify deformation. A camera was attached to a tripod and used to take photos while the actuator was inflated. The internal pressure was controlled using a manual pneumatic pressure regulator and photos taken at 5-kPa pressure increments. The tip displacement was calculated during postprocessing by counting the blocks between the deformed state and reference state of the actuator. The small number of samples tested favored this procedure over using computer vision to track the actuator's tip.

Numerical development

Mold Star 15 and Smooth-Sil 950 samples were tested according to ISO 37 (Ref.¹⁶) using dumbbell-shaped samples for tension and ISO 7743 (Ref.¹⁷) using round pucks for compression. A three-term Ogden material model was used to model the stress–strain response of the silicone. This model was calibrated using a direct method and experimental data from three replicates over the strain range of −30% to 200% strain. The Ogden parameters are shown in Table 2.

Table 2.

Parameters for the Three-Term Ogden Material Model of the Silicone Rubbers Used

Material	μ₁	α₁	μ₂	α₂	μ₃	α₃
Mold Star 15	−6.503 × 10⁻⁶	−21.32	0.2169	1.180	1.372 × 10⁻³	4.884
Smooth-Sil 950	−0.3062	−3.059	0.0283	4.597	6.596 × 10⁻⁹	17.69

The numerical model was developed as an FE model using Siemens NX 12 and the multistep, nonlinear kinematic solver SOL 402. A 3D model was constructed using linear hexahedral (brick) elements to best represent the actuator.

Results and Discussion

To demonstrate the use of the bilinear material and the extent to which that translates to a bimodal behavior, the three different bilinear crimp ratios available were used. These design parameters should allow actuators to have distinctly different modes depending on whether the internal pressure has exceeded the transition pressure or not.

A sequence of the response to a pressure increase is available in Figure 5. The actuator tip that was tracked during the incremental pressure increases is shown as a red dot in the sequence. The pressure was increased until rupture occurred. The motion of the actuator is toward the right at lower pressures, whereafter a change in preferential bending direction occurs at 40 kPa and the motion of the actuator tip proceeds toward the left.

FIG. 5.

Sequential steady-state images of the bimodal actuator as pressure is increased (crimp ratio = 0.3). (a) 15 kPa, (b) 20 kPa, (c) 25 kPa, (d) 30 kPa, (e) 35 kPa, (f) 40 kPa, (g) 45 kPa, (h) 50 kPa, (i) 55 kPa, (j) 60 kPa, (k) 65 kPa and (l) 70 kPa. The red dot indicates the tip position tracked during postprocessing. Color images are available online.

Figures 6 –8 show the numerical and physical results for each crimp ratio as the pressure increases. These results are shown for the actuator tip that was tracked in Figure 5 and given as the displacement of the tip and not its position relative to the base of the actuator. The y-axis is in line with the vertical actuator body and the x-axis tracks the horizontal direction. With the initial pressure increase in Figure 8, it is shown that the actuator undergoes a horizontal displacement (x-direction) to a maximum value of just over 70 mm at 40 kPa. At this point, the bilinear material has fully decrimped. This change in asymmetric stiffness necessitates that the bending direction should gradually change with a further pressure increase. This is shown by a decrease in the x-displacement and an elongation of the actuator in the y-direction as pressure increases to 65 kPa.

FIG. 6.

Tip displacement using a crimp ratio of 0.2 (incremental pressure values indicated in kPa next to each point).

FIG. 7.

Tip displacement using a crimp ratio of 0.25 (incremental pressure values indicated in kPa next to each point).

FIG. 8.

Tip displacement using a crimp ratio of 0.3 (incremental pressure values indicated in kPa next to each point).

In all three cases, the physical actuator has a preferential bending direction that changes according to the internal pressure. By varying the crimp ratio of the bilinear composite, it was further possible to alter the pressure at which this preferential direction changes as well as the magnitude of the maximum tip displacement achieved.

The 0.3 crimp ratio composite essentially has the longest strip of paper embedded of the three composites manufactured. This translates to the highest tip displacement of 71.25 mm in the initial bending. In comparison, the 0.2 crimp ratio has the shortest embedded paper layer, which translates to the lowest tip displacement in the initial bending direction of 17.5 mm, but the highest tip displacement in the secondary bending direction of 65 mm. The crimp ratio therefore has a large impact on the tip displacement possible for each of the bending directions for a given pressure.

The large discrepancies evident between physical and numerical models in terms of X–Y displacements and pressure magnitudes will need further investigation. Numerous possible causes exist, which primarily revolve around the bilinear material model and the chosen manufacturing methods. Three-term Mooney–Rivlin, Gent,¹⁸ Yeoh,¹⁹ and Ogden²⁰ material models were calibrated using the bilinear tensile test data. The Ogden model was able to match the response the best between the different constitutive models, but as shown in Figure 2, bilinear stiffening is not captured completely. With regard to experimental testing, parameters that are possible to be measured on a homogeneous sample of silicone, such as bulk modulus, are difficult to characterize on the bilinear material. A work-around to this could be to model the bilinear material in a similar way as was done by Ellis et al.,¹⁵ where the Ecoflex 0030 matrix material was modeled separately from the crimped paper layer. The method used proved to be computationally efficient and avoided adding a contact surface between the two materials. Including the two constituent materials of the bilinear composite separately enables established standards to be used while testing for their properties. The 3D printed molds used to cast the actuators' parts have a coarse dimensional tolerance relative to the wall thickness used in the silicone part. Current FDM technology has dimensional tolerances in the range of ±0.2 − ±0.5 mm. Ellis²¹ investigated the impact that manufacturing tolerances have on the inflated shape of an SPA and found that ±0.1 mm is sufficient to significantly affect the inflated shape. A manufacturing process with smaller dimensional tolerances is required to narrow the disparity between the numerical and physical models. With these known inaccuracies in the numerical model, the numerical model was still able to capture the bimodal behavior that was desired.

Conclusions

A means to exploit the trait of soft robots that allow designers to embed deformation characteristics directly into their architecture was sought in this research. One such method was devised by incorporating a material with a bilinear tensile response that activates at an adjustable and predictable strain threshold into an SPA as part of the strain-limiting layer.

Three different crimp ratios of this bilinear composite material were incorporated into an SPA. Physical and numerical models were created to investigate the response of the SPA to an increasing internal pressure. Both of these models showed the desired behavior where a preferential bending direction exists at lower pressures. As soon as the SPA has been inflated to a large enough pressure, such that the deformation is sufficient to strain the bilinear composite material beyond its strain transition point, a new preferential bending direction is created in the opposite direction. A disparity between the required pressures and displacement magnitudes was found between the physical and numerical models. Causes for this disparity were narrowed down to limitations of the constitutive equations used to model the bilinear material response as well as artifacts of the manufacturing process used. The manufacturing process used favored the turnaround time of new designs over accuracy and consistency.

Footnotes

Author Disclosure Statement

No conflicts of interest exist.

Funding Information

No funding was received.

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