Tuning the Morphology of Suction Discs to Enable Directional Adhesion for Locomotion in Wet Environments

Abstract

Reversible adhesion provides robotic systems with unique capabilities, including wall climbing and walking underwater, and yet the control of adhesion continues to pose a challenge. Directional adhesives have begun to address this limitation by providing adhesion when loaded in one direction and releasing easily when loaded in the opposite direction. However, previous work has focused on directional adhesives for dry environments. In this work, we sought to address this need for directional adhesives for use in a wet environment by tuning the morphology of suction discs to achieve anisotropic adhesion. We developed a suction disc that exhibited significant directional preference in attachment and detachment without requiring active control. The suction discs exhibited morphological computation—that is, they were programmed based on their geometry and material properties to detach under specific angles of loading. We investigated two design parameters—disc symmetry and slits within the disc margin—as mechanisms to yield anisotropic adhesion, and through experimental characterizations, we determined that an asymmetric suction disc most consistently provided directional adhesion. We performed a parametric sweep of material stiffness to optimize for directional adhesion and found that the material composition of the suction disc demonstrated the ability to override the effect of body asymmetry on achieving anisotropic adhesion. We modeled the stress distributions within the different suction disc symmetries using finite element analysis, yielding insights into the differences in contact pressures between the variants. We experimentally demonstrated the utility of the suction discs in a simulated walking gait using linear actuators as one potential application of the directional suction disc.

Introduction

Reversible adhesion, the ability to attach to and detach from a surface in a controlled manner, has gained specific interest in the field of robotics, ranging from manipulation to locomotion.¹ In the area of robotic locomotion, adhesion can be advantageous for generating traction (i.e., for maintaining contact between a robot and a surface throughout a walking gait cycle). Reversible adhesion can therefore enable unprecedented locomotion capabilities, such as scaling glass walls.²

The adhesive strategies of animals have inspired a new generation of bioinspired adhesives to be paired with locomotion.³ Many organisms use adhesion to effectively locomote across a surface or to counter environmental disturbances. Animals ranging from lizards⁴ to insects⁵ use adhesive foot pads to walk on a wide variety of surfaces, including inverted surfaces.

By coupling adhesion and locomotion, animals can attain novel locomotion strategies while countering high disruptive forces. For instance, sea stars locomote using hundreds of tube feet to contact and chemically adhere to a substrate.⁶ This distribution of adhesion across a large quantity of attachment points allows echinoderms to locomote and remain attached to a substrate all the while countering wave surges, currents, and other marine disturbances. The coordination of a highly distributed network of actuators and adhesion allows sea stars to achieve a steady crawling locomotive gait.⁷ Our goal is to develop a directional adhesive that could in the future enable sea star inspired locomotion while minimizing the complexity of control.

Reversible adhesives developed for use in engineered systems include microstructured dry adhesives, interlocking devices, electroadhesives, magnetism, phase-change based adhesives, vibration-based adhesives, and negative static pressure devices (e.g., suction cups). Microstructured dry adhesives (i.e., gecko-inspired adhesives) take advantage of van der Waals forces to attach to a surface.⁸ Previous work has used these adhesives to endow robots with wall-climbing capabilities.^2,9

Roboticists have also explored the use of attachment devices composed of interlocking structures, ranging from rigid hooks¹⁰ to ex vivo shark skin,¹¹ on the foot pads of locomoting robots to provide greater frictional resistance to slippage while walking. Such interlocking devices may however limit the surface type to which locomotion would be successful.

Electroadhesion based on electrostatic attraction between two surfaces has been used to achieve robotic locomotion,¹² including on inverted and vertical surfaces.¹³ However, the presence of water generally leads to weak electrostatic adhesion due to Debye shielding.¹⁴ Adhesion using magnetism provides strong attachment during locomotion, yet is limited to ferromagnetic surfaces.^15,16

Adhesion mediated by a material such as gallium that changes phase from solid to liquid at a temperature just above the robot's normal operating temperature allows for switchable attachment dependent on temperature.¹⁷ Such adhesion occurs when a phase-change material partially covers and solidifies to an object once its temperature is decreased. Use of phase-change material to adhere requires control of its local temperature and may result in the deposition of residue.

In addition, adhesion generated by the vibration of a thin flexible membrane near a surface has recently been demonstrated for adhesion by mobile robots to curved, vertical, and inverted surfaces.¹⁸ This vibration-based adhesion functions by forming a low-pressure region in a lubricating air film beneath the vibrating disk. However, this form of adhesion requires constant energy expenditure to attach and remain adhered to a surface and has not been shown to work in incompressible fluids (e.g., underwater).

The use of suction has been explored in wall-climbing tasks in legged,¹⁹ tracked,²⁰ and soft, inchworm-inspired²¹ robots for use in air and underwater. However, suction discs currently used in locomoting robots are generally limited to use on smooth flat surfaces and require active control for attachment and detachment.²²

In addition to reversibility, controllability of an engineered adhesive is critical for robotic applications.^23,24 Control can be achieved by including an actuator to engage with and detach from a surface or by morphologically programming the structure of the adhesive. Active actuation requires an energetic input to achieve attachment and detachment, thereby adding complexity to a design that could potentially reduce the scalability of a design to smaller sizes or larger number of adhesion points.

An alternative form of adhesive control includes the use of morphological computation²⁵ to encode the conditions for attachment and detachment into the physical body of the adhesive. Morphological computation leverages the shape, design, and material composition to offload computational complexity into a physical structure of an object while producing a predictable behavior.^26–28

The use of morphological computation for adhesive control is not unique to engineered solutions but is also found in naturally occurring adhesive systems.^25,29 For instance, geckos utilize a dense array of branched anisotropic microstructures³⁰ to adhere using van der Waals forces.³¹ Moreover, the setae of the gecko demonstrate sensitivity to angle such that once a threshold in angle is reached, the setae detach with minimal pull-off force.^4,31,32

Similarly, gecko-inspired adhesives developed with anisotropic profiles, such as angled stalks or wedges, result in directional adhesion in artificial systems.^33,34 Pads expressing gecko-inspired adhesives can therefore be removed from a surface by peeling when adhesion is only required in one direction (e.g., in the case of climbing against gravity).³³ The morphological computation exhibited by these microstructures therefore creates controllable adhesion without necessitating additional methods of actuation to attach to and detach from a surface.²³

Directional microstructured adhesives which enable novel robotic locomotion are limited by the environment in which they are applied. Dry adhesives are most effective for adhering in dry environments and are significantly less effective in a wet environment. A thin lubricating layer has been reported to form between a substrate and the tip of a dry adhesive microstructure when submerged in water, leading to 50% lower pull-off forces.³⁵ Modifications of the dry microstructured adhesives, such as the use of polymer coatings,³⁶ changes to the material composition,³⁷ and incorporation of cupped terminations,³⁸ have been used to adapt the microstructures for wet environments. These advances in microstructured adhesives have yielded strong normal and shear adhesion in a wet environment, yet lack anisotropy for directional adhesion or a controllable mechanism for detachment.

Many underwater creatures use some form of reversible adhesion,³⁹ including the use of chemical secretions in echinoderms,⁶ mechanical interlocking in the remora,⁴⁰ and suction in the octopus⁴¹ and intertidal fish.⁴² Inspiration from these biological systems yields promising steps toward the development of successful engineered adhesives for use underwater.⁴³ Mechanical interlocking has been coupled with suction in the development of a biomimetic suction disc that is capable of withstanding high shear detachment forces.⁴⁴ Inspired by the clingfish, we have previously demonstrated the ability to modify the material composition of a suction disc to adhere to rough substrates.^45,46 Soft artificial suckers inspired by the octopus⁴⁷ and an array of vacuum-driven suckers have demonstrated the utility of suction for underwater manipulation and locomotion.⁴⁸

However, these previous approaches to suction-based adhesion necessitated a separate, actively controlled mechanism to reversibly attach to and/or detach from a surface. In these studies, detachment required a separately controlled set of actuators to disengage the suction disc from a surface.^49,50 For instance, detachment of the suction cups through peeling requires the outer perimeter of the disc to be lifted using tendons, thereby releasing the seal of the suction cup.¹⁹ Other works have explored actively controlling the shape of the suction cup²¹ or controlling pressure in a suction cup with a separate vacuum line for attachment and detachment, adding to the complexity of the pneumatic circuitry.⁵¹

In this study, we introduce a reversible suction disc that leverages morphological computation to detach at predetermined angles without necessitating a separate mechanism for detachment. Such a design would advance the field of directional adhesives, achieving anisotropic adhesion in a wet domain. We demonstrate that the detachment angle can be encoded into the body of the disc through a combination of factors—geometric asymmetry, disc margin morphology, and material stiffness. We generalized the types of design factors that yield directional adhesion in suction discs, and by applying the directional adhesives to linear actuators, we demonstrated their utility in sea star inspired walking. To the extent of our knowledge, this work presents the first directionally adhesive suction disc to be reported and demonstrated for use in multilegged robotic locomotion.

Results and Discussion

Testing two mechanisms for directional adhesion

We designed suction discs to achieve passive reversible adhesion with adhesive strength based on the angle of applied tensile loading. We considered a sea star inspired walking scenario in which we attached the disc to the end of a linear actuator which was mounted to a body constrained to move parallel to the surface (Fig. 1b). To achieve translation of the body, we desired high adhesion at what we defined as a negative angle of the tube foot-inspired actuator relative to the body (angle, <0°), corresponding to a tube foot that had reached out and engaged its suction disc with a horizontal surface. After pulling on the surface to move the body forward, causing the actuator to pass through the neutral axis (angle, 0°), we desired low adhesion allowing the suction disc to release at a positive angle of the tube foot relative to the body (angle, >0°).

FIG. 1.

Tuning morphology for directional adhesion. Design parameters of a suction disc cause an adhesive force that is highly dependent on the direction of loading. (a) Sea star inspired locomotion. Sea stars use an array of tube feet coupled with adhesive secretions to adhere and pull/push themselves along a surface. Inset: Image of the arm of a sea star, which can locomote across a variety of surface types. (b) Schematic demonstrating idealized, angle-dependent attachment and detachment conditions for sea star inspired locomotion. (c) Computer-generated rendering of suction disc, with key features labeled. (d) Model of the idealized performance of a suction disc with adhesion mechanically “programmed” as a function of the angle of an applied tensile load (relative to vertical). Color images are available online.

A suction disc was composed of a suction chamber that was lined by a disc margin (Fig. 1c), a design that we found previously to adhere well to surfaces with a variety of roughnesses in air and in water.⁴⁵ The disc margin was composed of silicone that was softer compared with the body cavity and served to seal the suction chamber against the substrate. A load was applied to the suction disc through a stem located at the top of the suction chamber. For all disc designs, the width of the disc (w) was twice the radius of the suction chamber (r), and the length of the disc (l) was four times the radius (Fig. 2a).

FIG. 2.

Experimental investigation into the morphological parameters for anisotropic adhesion. (a) Investigations into the first parameter, disc symmetry, on anisotropic adhesion. We tested three possible load placements for suction discs: discs A and B were asymmetric, with loads offset from the center, and discs C were symmetric, with a load applied to the center of the disc. (b) Effect of disc symmetry on adhesion, where adhesive stress (kPa) is plotted with respect to the angle of the surface. (c) Investigations into the second parameter, slits within the disc margin, on anisotropic adhesion. A schematic demonstrates the function of the slits. Top: Slits flare when the disc is pulled toward the heel, breaking the seal of the suction chamber. Bottom: Slits come together, forming a continuous seal, when the disc is pulled toward the toe. Representation of slit placement in the disc margin, angles with respect to the longitudinal axis. (d) Effect of slit angle on adhesion (body type, B), where adhesive stress (kPa) is plotted with respect to the angle of inclination of the surface. The discs with slits were compared to a disc without slits (N.S.). (e) Effect of material stiffness on adhesion for an asymmetric body type (A). Materials tested with platinum cured silicone with moduli of elasticity at 100% strain of 68.9 kPa (S1, light red), 338 kPa (S2), 593 kPa (S3), and 662 kPa (S4, dark red). (f) Effect of the magnitude of preload (N) on adhesion (kPa). Experiment performed on A and C body types (no slits). The angle of the surface relative to the discs was zero degrees for preload tests. All pull tests were performed in triplicate, error bars indicate standard deviation. Color images are available online.

To compare various approaches to achieve directional adhesion, we investigated the role of two parameters—symmetry and slits within the disc margin—to achieve anisotropic adhesion (Fig. 2a–d). We then performed a parametric sweep of the material stiffness of the disc to optimize anisotropic performance.

Parameter I: Symmetry for anisotropic adhesion

In the first set of prototypes, we varied the symmetry of the body of the disc. Symmetry was dependent on the location of the applied load, which we indirectly controlled with the position of the stem along the body of the disc. We then applied either a tensile or compressive load to the stem. We hypothesized that an uneven distribution of load across the body of the suction disc would adversely affect the seal around the disc margin for some (i.e., positive) angles of applied load relative to the surface, thereby reducing the adhesive stress. Accordingly, we hypothesized that a greater offset of the load would result in a more pronounced asymmetric performance of adhesion.

The load placement ranged from the center of the disc (Body Type C) to offset from the center (Body Types A and B). For body types A and B, a load was applied to the stem which was offset by a distance of half the radius, ( $r ∕ 2$ , Body Type B) or by one radius (r, Body Type A) from the center of the disc (Fig. 2a). We refer to the positions of the load as either symmetric, for the centered condition, or asymmetric, for the offset conditions, about the transverse axis. To evaluate how the adhesive force generated by the discs varied with the direction of the applied load, we performed pull tests with a universal mechanical testing machine across the sets of suction disc variants. We changed the angle of the substrate with respect to the direction of travel of the mechanical testing machine.

We found that the symmetry of the body significantly affected adhesive stress as a function of angle (Fig. 2b). At negative angles of inclination in which attachment was desired, all three disc body types (A–C) exhibited significant adhesion (>5 kPa), with only small differences in adhesive stress. All of the discs maintained adhesion across the neutral axis, perpendicular to the surface. However, the discs varied greatly on their performance at positive angles of inclination where detachment was desired.

The most asymmetric body type (A) with the largest offset had the largest difference in adhesive stress from attachment to detachment angles. Body Type A demonstrated nearly zero adhesive force in the angles associated with detachment. Conversely, the suction discs with a centered (Body Type C) and mildly offset load (Body Type B) maintained their adhesive strength (>4 kPa) in positive angles of inclination, corresponding to the desired detachment orientations. Overall, a high degree of asymmetry resulted in a dependence on the angle of the loading (i.e., in directional adhesion).

Parameter II: Slits in the disc margin for anisotropic adhesion

In the second set of disc variants, we evaluated the effect of slits in the disc margin to yield anisotropic adhesion. The incorporation of slits in the disc margin was inspired by the clingfish, an intertidal fish that uses a ventral suction disc to attach to rocky surfaces.⁴² The adhesive disc of the clingfish is formed by the union of the pelvic and pectoral fins, resulting in the formation of two bilateral slits in the disc margin. The clingfish can moderate the amount of suction by modifying the position of its fins,⁵² effectively changing the angle of the slits in its disc margin.

Inspired by the clingfish, we included two slits in the disc margin to passively achieve directional adhesion. The slits were intended to flare (Fig. 2c) thereby disrupting the seal of the disc margin when pulled or loaded from specific angles. We varied the angles of the slits with respect to the longitudinal axis of the disc from 15° to 90° for a moderately offset body type (B).

Similar to our tests of adhesion based on disc symmetry, we tested the discs with slits with a universal mechanical testing machine at a variety of angles of loading relative to the surface to determine whether the slits contributed to anisotropic adhesion. We hypothesized that the addition of slits would act as a valve to facilitate direction-dependent adhesion. To answer this hypothesis, we compared designs with slits (angles; 15°, 30°, 90°) to the design without slits (0°) for body type B (Fig. 2d).

Overall, we found that the addition of slits did not yield the intended directional adhesion. The disc variant with a 15° slit in the disc margin adhered in an angle-dependent manner, but opposite of the anticipated adhesive curves. We observed that while the slits (15°) flared as anticipated while experiencing a compressive load, they did not fully close when pulled to form a completely continuous disc margin in the attachment orientation.

The variant with slits of 15° exhibited directional adhesion, where the adhesive stress increased from 2.09 ± 0.12 kPa at −45° inclination to 3.98 ± 0.09 kPa at 0° and 45° inclinations. The magnitude of the dependency on the angle of the surface, however, was small. Thus while we were able to produce an anisotropic adhesive response in a disc with slits, the difference in adhesive stress between a negative and positive angle of the surface was lower than alternative disc variants (i.e., changing the symmetry of the disc).

The variant with a slit of 30° achieved lower adhesive stresses in comparison to the disc with slits of smaller angles (15°). The slits of 15° exhibited more overlap in the disc margin, in comparison to the 30° variant. Our interpretation of these results is that the greater amount of overlap corresponded to a better seal and thus higher adhesive stress. This trend continued for the suction disc with a slit of 90°, for which no adhesion was achieved across all angles of inclination. We attributed the ineffective adhesion of the 90° slits to the inability of the disc margin to seal the suction chamber.

The incorporation of slits was a less reliable design parameter than asymmetry and was therefore less practical for applications in locomotion. During detachment, the slits were intended to flare open, dependent on the angle and direction of the pulling force (Fig. 2c), thereby reducing adhesion. However, the slits were more sensitive to the initial loading conditions, such as the alignment of the disc with respect to the surface and with respect to the clamp from the load cell. Suction discs that were misaligned to the slope of the experimental substrate would result in an uneven flaring of the slits (Supplementary Fig. S1). This inconsistent behavior left slits either partially or fully closed, thereby keeping the suction chamber sealed during detachment.

We performed a quantification of the effect of misalignment on the overall adhesive stress of a disc (Body Type B) with slits (15°). This disc was either in-line (0°) or misaligned by 45° or 90° to the slope of the surface (Supplementary Fig. S1b). Given that the surface and the load cell were fixed in position, we created a misalignment by rotating the disc within the clamp of the load cell.

The degree of misalignment directly affected the adhesive stress, where a 45° misalignment resulted in up to a 31% drop in adhesive stress (2.77 ± 0.05 kPa), in comparison to the disc when in-line with the slope of the surface (4.04 ± 0.12 kPa). A 90° misalignment resulted in up to a 45% drop in adhesive stress (2.73 ± 0.07 kPa), compared to the disc in-line with the slope (4.99 ± 0.07 kPa). Thus, the adhesive performance of the discs with slits was highly dependent on its alignment with the slope of the surface.

We clarified how the performance of the disc was affected by its misalignment with respect to the clamp by testing against a flat surface without a slope (0°; Supplementary Fig. S1a). A misalignment (45° and 90°) of the suction disc relative to the clamp resulted in a ∼24% reduction in adhesive stress for the disc against a flat surface. We attributed this to an uneven distribution of compressive stress across the body of the disc caused by its misalignment with the clamp (Supplementary Fig. S1b). Misalignment would nonuniformly deform the suction chamber of the disc. We observed that this uneven distribution of stress caused by misalignment with the clamp resulted in an uneven flaring of the slits and therefore a reduced adhesive stress.

The considerable sensitivity of the slits to alignment made them less reliable for practical implementation in a locomoting robot. Future work could explore the use of different materials or geometries of the slits to yield more predictable flaring that is less sensitive to misalignment. We anticipate that we could modify the location of the slits and orientation (i.e., 180° to their current orientation) to help tune their anisotropic adhesive performance.

In conclusion, of the design parameters investigated (symmetry and slits), the modification of the symmetry of the suction disc yielded the most predictable, repeatable anisotropic adhesion. We therefore chose to use a suction disc with a large geometric asymmetry (Body Type A) without slits for further experiments.

Impact of stiffness on anisotropic adhesion

We investigated the impact of material stiffness of the suction chamber on adhesion of a highly asymmetric suction disc (Body Type A), in which the offset load has already demonstrated the ability to yield anisotropic adhesion (Fig. 2e). We hypothesized that increasing the stiffness of the body of the suction disc would help to maintain the integrity of the suction chamber when deformed, allowing for greater adhesive stresses to be achieved. We changed the stiffness of the suction chamber while maintaining a constant stiffness of the disc margin. The types of silicone used spanned across one order of magnitude of stiffness (moduli of elasticity at 100% of strain of 68.9 kPa for S1, 388 kPa for S2, 593 kPa for S3, and 662 kPa for S4).

We tested the discs of different stiffnesses on the universal mechanical testing machine by applying loads at different angles relative to the surface to determine how stiffness of the disc affects anisotropic adhesion. The relatively stiff elastomers, such as S4, adhered more strongly to a substrate in comparison to the softest elastomer tested (S1). However, stiff elastomers (S3 and S4) adhered with adhesive stresses greater than 5 and 2.5 kPa for negative and positive angles of the surface, respectively. We considered this behavior to be insufficient anisotropy as we desired minimal adhesion at positive angles with respect to the surface.

We found that by decreasing the stiffness of the suction chamber, the disc was able to preferentially directionally adhere. We found that an intermediate stiffness (S2) of 338 kPa (100% modulus) demonstrated adhesion that corresponded to the angle of the surface (Fig. 2e). S2 adhered with a high adhesive stress (>5 kPa) at negative angles and did not adhere (0 kPa) at positive angles, corresponding to the desired attachment and detachment orientations, respectively. However, we observed a limit to this trend as the disc composed of the softest of the silicones tested (S1) adhered with the lowest adhesive stress (<1 kPa) across all angles of the surface.

Thus, intermediate stiffnesses (0.38 MPa, S2) created directional adhesion, while the stiffest (>0.5 MPa, S3 and S4) and softest (<0.06 MPa, S1) elastomers did not produce both high adhesion at negative angles and low adhesion at positive angles. These results show that optimization of directional adhesion in suction discs requires a balance of material properties and geometric asymmetry.

We concluded that the differences in adhesive performances of the prototype variants resulted from the deformation experienced by the suction chamber. Decreasing the stiffness of the disc resulted in a reduced resistance to deformation and a low structural integrity that compromised the suction chamber, resulting in low adhesive stress at all load angles. In contrast, increasing the material stiffness of the disc reduced the deformation under the same compressive load, avoiding the collapse of the suction chamber.

This is consistent with previous work,⁵³ which found that increased stiffness of the suction chamber increased the adhesive force of the disc. However, to create directional adhesion, the disc must create minimal adhesive forces under certain loading conditions, dependent on the angle of the surface. A disc composed of high stiffness material would thereby create high adhesion forces at all angles of detachment. For predictable directional adhesion, the suction chamber must be of an intermediate stiffness to be compliant enough to collapse the front of the suction chamber during detachment while being stiff enough to maintain its integrity during attachment. We envision that additional optimizations of the structure of the discs could be used to combine the effects of shape and material stiffness on the directionality of the adhesion.

Impact of preload on symmetric and asymmetric discs

Finally, we tested the effects of preload on the adhesion of symmetric and asymmetric discs using a universal mechanical testing machine to first load the disc against a surface perpendicular to the axis of travel of the machine and then pull the disc away from the surface. The geometric asymmetry affected the amount of force that should be applied as a preload to achieve the maximum adhesive force (Fig. 2f).

The preload caused the disc to deform, which forced fluid out from the enclosed chamber and created a pressure differential responsible for adhesion. As the force of the preload increased, the adhesive stress increased until the disc was fully deformed and the maximum pressure differential was reached. After this point, a further increase to the preload resulted in a minimal increase of the adhesive stress, as demonstrated in the symmetric suction disc. Conversely, the increasing preload for the asymmetric disc led to a gradually decreasing slope, resulting in a point of inflection in the curve around 3 N.

We observed that the symmetric disc achieved an inflection point in the maximum adhesive stress at about half the preload required by the asymmetric disc (1.5 N for Body Type C, 3 N for Body Type A; Fig. 2f). We concluded that the reduced preload required by the symmetric disc was due to a more uniform deformation of the disc. Conversely, the asymmetric disc required a greater amount of force to fully evacuate the suction chamber as the shorter heel of the disc was more resistant to deformation.

Contact mechanics at discrete angles during loading

To understand why different discs demonstrated orientation-dependent adhesion, we imaged the contact made between the suction disc and a surface during preload and pull-off conditions using frustrated total internal reflection (FTIR; Fig. 3a and Supplementary Fig. S3). FTIR is a contact-visualization technique in which light is internally reflected within a sheet of acrylic.⁵⁴ Contact with the acrylic sheet allows light to escape, which can then be imaged by a camera and serves as an indicator of contact with a surface. However, FTIR does not provide the magnitude of the contact pressure, only whether or not there is contact with the surface.

FIG. 3.

Visualizing the contact between a suction disc and a surface. Visualization of the contact area of the asymmetric disc (Body Type A, top row) and symmetric disc (Body Type C, bottom row) for four angles of contact using FTIR. Column 1: a compressive load of 2 N was applied to the suction disc on a surface at an angle of −30°. Column 2: a compressive load of 2 N was applied to a disc perpendicular to a surface. Column 3: a compressive load of 2 N was applied to a disc at an angle of 30°. Column 4: the suction disc was then pulled away from the surface (angle, 30°), FTIR images correspond to the PoF, or the moment before the disc detached from the surface. For all FTIR images, the white regions indicate contact with the imaging surface. FTIR, frustrated total internal reflection; PoF, point of failure. Color images are available online.

During FTIR, both asymmetric (A) and symmetric (C) discs were imaged under a 2 N compressive load when the imaging surface was rotated to −30°, 0°, and 30° with respect to the suction disc. We then imaged the contact at the point of failure (PoF) of the suction disc when pulled from the imaging surface at a displacement rate of 150 mm/min.

As visualized during compressive trials using FTIR, the symmetric disc always maintained a seal between the disc margin and the substrate, irrespective of the angle of the surface (Fig. 3a). At both −30° and 30° rotations, a full preload of 2 N caused the outer perimeter of the disc margin to flare upwards, thereby reducing the area in contact with the imaging surface but still retaining the seal around the perimeter of the disc. This flaring behavior was not observed in the zero degree condition, suggesting a more uniform distribution of stress along the perimeter of the disc margin.

In addition, a compressive preload of 2 N caused the suction chamber to deform such that the inner surface of the top of the suction chamber (beneath the stem) contacted the imaging surface, shown as a circle in the frames from FTIR (arrow, Fig. 3; Supplementary Fig. S3b). We interpreted the contact of the top of the suction chamber with the imaging surface to be indicative of the strain in the disc; that is, a larger area of contact with the upper cavity implied a larger deformation of the disc.

The behavior of the asymmetric disc when in contact with the surface differed from the symmetric disc. At a negative angle of inclination, the asymmetric disc completely sealed its suction chamber. However, when loaded in compression from a positive angle (the low adhesion orientation), the asymmetric disc did not maintain a full seal.

When loaded by a compressive force in this orientation, the front of the disc lifted from the surface, while the heel was still in contact with the surface. As the suction disc was gradually pulled away from the surface in this orientation (first decreasing the magnitude of the compressive force to zero, then increasing the tensile load), the contact of the asymmetric disc would roll from heel to toe. Thus, at positive angles of inclination, the asymmetric disc did not adhere because the suction chamber was not sealed and hence did not maintain a pressure differential.

The FTIR results showed that a compressive preload concentrated about the heel of the asymmetric suction disc resulted in adhesion to a surface. However, as the compressive load changed to being centered about the toe, the front of the disc would lift and thereby break the seal of the suction chamber. We concluded that asymmetry resulted in an uneven distribution of stress across the disc, corresponding to reduced adhesion at angles associated with detachment in a locomotive gait cycle. In contrast, symmetry yielded high adhesion, irrespective of whether the load was centered over the heel or the toe.

Modeling mechanics and contact throughout a gait cycle

The FTIR results provided an understanding of the behavior of the discs when loaded at discrete angles against an imaging surface. However, when in use during a walking gait, the disc would be subjected to loading under a continuous change of angles relative to the surface (Fig. 1). To examine the behavior of the disc during a gait cycle, we used finite element analysis (FEA) to model the effects of body symmetry (Types A and C) on the mechanics due to loading while cycling from an angle of −30° to an angle of 30° (Fig. 4, Supplementary Figs. S4 and S6). To simulate the angle change, we loaded the suction discs to a virtual surface that rotated about an axis orthogonal to the stem and the long axis of the suction disc. The simulations neglected environmental conditions and effects of the fluid in the suction cavity and focused on how contact with the surface affected the mechanics of the disc.

FIG. 4.

FEA to model the mechanics of adhesion of a suction disc while attached at various angles of attachment and detachment. (a) Top panel: Visualization of the distribution of Von Mises stress (kPa) across a vertical cross-section through the center of suction discs A. Stress plotted when a load (2 N) was applied at an angle of −30°, 0°, and 30°. Bottom panel: Stress plotted for a symmetric suction disc C when a load (2 N) was applied at an angle of −30°, 0°, and 30°. (b) Plot of percent reduction in the internal volume within the suction chamber with respect to the internal volume for the case of no preload, as a function of the angle of the surface. Measurement of internal volume performed at seven angles during the simulation. (c) Plot of the contact pressure (kPa) of node II, located along the innermost perimeter of the disc margin, with respect to the angle of the surface. Measurement performed at seven angles during the simulation for both asymmetric (red) and symmetric (blue) discs. (d) Results from FEA visualizing contact pressure (kPa) of the suction disc with respect to angle of the surface. (e) Inset images of Node II for the asymmetric (top) and symmetric (bottom) discs. Node II was determined to be the location of lowest contact pressure for the asymmetric disc (see Supplementary Fig. S5 for details). FEA, finite element analysis. Color images are available online.

Distribution of stress within the body of the discs

The distribution of stress within the body of the suction disc differed between the body types (Fig. 4a). The symmetric disc (C) exhibited a symmetric distribution of stress with respect to the angle of the applied preload. Furthermore, the symmetric disc experienced a symmetric change in internal volume across angles tested in the simulation (Fig. 4b).

Conversely, the asymmetric disc (A) experienced a greater concentration of stress within the body (>175 kPa) during the angles associated with attachment (<0°) than in comparison to the angles associated with detachment (>0°). The stress was concentrated at the heel when loaded at −30°, which was distributed throughout the body of the suction disc when rotated. The asymmetric disc experienced the greatest reduction in internal volume at angles associated with detachment (>0°; Fig. 4b). A low internal volume corresponded to the collapse of the front of the asymmetric suction disc (>0°; Fig. 4a, Supplementary Fig. S4).

Distribution of contact pressure along the disc margin

We simulated the spatial distribution of contact pressure around the disc margin for the asymmetric (Body Type A) and symmetric (Body Type C) discs (Fig. 4c–e). The minimum contact pressure around the inner perimeter of the suction chamber provided a measure of the integrity of the seal of the suction chamber⁵³ (i.e., localized points of low contact pressure indicate a low adhesive strength).

The asymmetric disc experienced a contact pressure that was nonuniform across the inner perimeter of the disc margin. A compressive preload on the asymmetric disc generated a high contact pressure on the heel of the disc and lower contact pressure at the toe, which was a consistent trend across all angles tested (Fig. 4d). In contrast, the symmetric suction disc demonstrated a more uniform distribution of contact pressure across the inner perimeter of the disc margin for all angles of inclination of the surface.

To quantify the integrity of adhesion throughout the motion simulated, we probed five nodes along the inner perimeter of the disc margin, ranging in position from the toe to the heel (Supplementary Fig. S5). We found that the node along the arc transitioning from the toe to the middle of the suction disc (Node II) experienced the lowest contact pressure (0.9 kPa) for the asymmetric suction disc at 27° inclination of the surface (Fig. 4c).

Visually, this region of localized low contact pressure can be compared between the symmetric and asymmetric disc cases (Fig. 4e). The minimum contact pressure of the asymmetric disc dropped from 3.6 kPa at a 20° inclination to 0.9 kPa at 30° of inclination. In comparison, all nodes for the symmetric disc experienced a contact pressure that was greater than 5 kPa across all angles of inclination of the surface. The symmetric disc had a comparatively higher minimum contact pressure (5.6 kPA) across all angles of the simulation in comparison to the asymmetric disc, and most notably during positive angles of inclination. Overall, we concluded that angles of inclination of the surface >20° were shown through simulation to be predictive of low adhesion for the asymmetric disc due to localized points of low contact pressure.

Modeling to inform anisotropic adhesion

To successfully predict directional adhesion of a suction disc using a computational model, we found it important to characterize both the internal stresses and contact pressures of a disc rather than the change in internal volume. From our FEA model, we found that a change in volume, which is generally a predictor for adhesion using suction cups, was not a good indicator of directional adhesion. Adhesion of a suction cup is caused by a pressure differential between the internal suction chamber and the ambient fluid. The maximum limit of adhesion would correspond to when all the fluid is expelled from the internal chamber during preload. By this logic, a suction disc would adhere better given a larger decrease in internal volume during preload.

However, we found that this heuristic did not accurately predict adhesion due to directional loading. In our FEA model, the asymmetric suction disc had its greatest change of internal volume at angles that were experimentally determined to result in no adhesion to the surface. Predicting suction disc performance by the change in internal volume would oversimplify the mechanics involved in directional adhesion. As previously found, adhesion is also dependent on the contact pressure between an adhesive and a surface.⁵³ For a suction disc, contact pressure is a function of various parameters, including geometry, deformation due to preload, material stiffness, and size. Thus, investigating the differences in spatial distribution of contact pressure between the discs in simulation allowed us to better predict their behaviors.

From the combination of the results from FTIR, FEA, and pull test experiments, we concluded that a disc would detach when the minimum contact pressure along the innermost perimeter of the disc margin in contact with a surface dropped to near zero. As demonstrated by the asymmetric disc, although it underwent large internal changes in volume, the disc did not adhere due to a low contact pressure around the rim of the disc. Given that the quality of the seal is only as strong as its weakest point, when the contact pressure around the innermost perimeter of the disc margin dropped to near zero, this corresponded to a compromised seal, allowing the pressure of the fluid inside the suction chamber to equilibrate with the surrounding fluid.

An understanding of the changes in internal volume (determines theoretical maximum adhesion) coupled with changes in contact pressure distribution (determines ingress of fluid into the disc) was required to provide a more complete understanding of the anisotropy of adhesion. Using this information, we can design a disc to have a nonuniform contact pressure to design for greater directionality in suction discs.

Adhesion-enabled locomotion

To demonstrate sea star-inspired adhesion-based locomotion, we incorporated the directional suction discs into a proof-of-concept walking system. We attached a suction disc to the end of a pneumatic linear actuator (a syringe) attached by a rotational joint to a linear slider (with a counterweight to reduce the effects of friction on the slider). The syringe—which plays the role of the tube foot of the sea star (Fig. 1)—was free to rotate with respect to the slider and could be made to extend and contract with air pumped into/out of the syringe by an off-board programmable syringe pump.⁵⁵

To simulate sea star-inspired walking, we started the syringe at one end of the linear track with an initial angle, $θ$ , relative to the vertical (Fig. 5a). We then extended the syringe until the disc contacted and preloaded against a smooth acrylic surface, generating adhesion. Subsequent retraction of the syringe pulled the slider forward along the track (given sufficient friction at the disc to prevent the disc from slipping along the surface).

FIG. 5.

Using suction discs for sea star inspired adhesion-based locomotion. (a) Schematic of experimental setup. A suction disc attached to the end of a pneumatic linear actuator (a syringe) engaged with a surface, and upon contraction of the actuator, served as an anchoring point to pull the body forward. The translated distance ( $δ$ x) was measured from the initial position at the start of the linear track to its final position upon detachment of the suction disc. The tensile force ( $F_{t e n s i o n}$ ) was composed of the component of force in the direction of motion ( $F_{t r a c t i o n}$ ) and the component normal to the surface ( $F_{n o r m a l}$ ), dependent on the angle ( $θ$ ) of the actuator. (b) Bar graph of the distance traveled by the body ( $δ$ x) while varying the orientation of the suction disc. The suction disc was either oriented with the toe in the direction of motion (“Forw.”) or with the heel in the direction of motion (“Back.”). Asymmetric disc (A) shown in red; symmetric disc (C) represented in blue. Trials performed in triplicate, error bars represent standard deviation. (c) Images from the locomotion demonstration. An image of the initial position of linear actuator (i) was overlaid onto the image of its final position (f). Scale bar, 10 mm. Color images are available online.

We found that the symmetric suction disc and the asymmetric suction disc in the attachment orientation (toe facing the direction of desired locomotion) were both able to adhere to the surface and remain adhered to pull the slider forward (Fig. 5b) before detaching at approximately the same angle. As the angle $θ$ approached zero, the component of the tensile force in the direction of motion also approached zero ( $F_{t r a c t i o n} = F_{t e n s i o n} sin θ$ ), while the component normal to the surface increased ( $F_{n o r m a l} = F_{t e n s i o n} cos θ$ ), eventually leading to adhesion failure. However, when the asymmetric disc was attached in the reverse orientation (heel facing the direction of desired locomotion), the disc created negligible motion along the track before pulling off of the surface due to the directionality of the asymmetric disc.

We further demonstrated that this walking capability can be extended to take multiple steps with a second syringe mechanism (Supplementary Movie S1). With a single disc, subsequent extensions of the syringe to create a preload force also pushed the slider backward since it was no longer at the start of the track. However, if a second disc was adhered at the same time, the second disc could react with the preload force on the first disc. With the two disc-syringe pairs actuating out-of-phase, one disc was always adhered to the surface when the other was being preloaded, resulting in forward locomotion. Note that this locomotion gait bore some similarity to adhesion-based locomotion observed in sea stars, although sea stars typically walk using hundreds of tube feet (instead of two), using a gait in which each tube foot contracts only once per three steps of the sea star.⁵⁶

We demonstrated that the directionality of the adhesive disc is useful for creating a walking motion (Supplementary Movie S1 and Fig. 6). In this demonstration, we adhered one disc to the surface and used it to pull the slider forward on the track, stopping when the disc was about to detach from the surface (as described above) and the syringe was close to vertical. Then, without continuing to actuate the front syringe, we extended the rear syringe to adhere the rear disc to the surface and pulled the slider forward. This forced the front syringe to continue to rotate toward the vertical position while still in contact with the surface.

FIG. 6.

Demonstration of the use of directional adhesion in multilegged sea star inspired locomotion. (a) Schematic of a multilegged gait cycle where locomotion is aided by the programmed detachment of the suction disc. (Stage 1) The front disc is preloaded against a surface, resulting in attachment. The front actuator pulls on the disc, resulting in forward translation. (2) After the front actuator has been pulled forward, a second disc attached to the rear actuator is preloaded against the surface. The rear actuator is retracted, causing the body to move forward and eventually detach. (3) The rear actuator is extended again to engage the suction disc with the surface, pulling the body forward for the second step. This second step pulls the front actuator into the preprogrammed detachment angle. (4) The front disc disengages from the surface and allows for retraction of the front actuator, restarting the walking gait cycle. (b) Image sequence of the multilegged gait cycle for the asymmetric disc. The front suction disc detached from the surface in stage 4, returning to its initial position at the start of the gait cycle. (c) The image sequence of the multilegged gait cycle for the symmetric disc. The front suction disc did not detach from the surface in stage 4, given the same degree of retraction as the asymmetric disc (i.e., more effort, or active control of adhesion, would be required to reset the front actuator to its original position). Scale bar, 10 mm. Color images are available online.

We took two steps with the rear syringe to ensure that the front syringe was rotated to the detachment angle. We ended the rear step just before the rear disc detached from the surface and slightly retracted the front syringe. This slight retraction was enough to pull the asymmetric disc from the surface to restart the gait cycle, while the symmetric disc remained attached to the surface, inhibiting further motion.

The overall locomotion speed of the robot during the demonstrated gait cycle was 0.98 mm/s with the asymmetric discs and 0.94 mm/s with the symmetric discs, both with a 2.5 mm/s retraction speed of the syringe.

We further demonstrated similar performance of these discs in a locomotion scenario where the discs were submerged in 1.5 inches of water (Supplementary Movie S2 and Supplementary Fig. S7).

This demonstrated that the asymmetric disc was beneficial for sea star inspired legged locomotion because it can predictably detach from the surface with reduced effort compared to symmetric discs.

In robotics, when scaling the use of adhesion to a large array of actuators, control complexity becomes critical. By adding to an actuator a suction disc that can conditionally adhere, we have demonstrated that we can offload part of the complexity required to control the system into the morphology of the suction discs. Minimizing the force required for detachment places lower force requirements on the actuators that engage the discs with the surface. The use of directional suction discs is also scalable. Because the suction discs do not require additional actuators for adhesion, we can envision more easily scaling to arrays of many small suction discs controlled by many actuators to achieve locomotion similar to the sea star.

In addition, the size of the suction disc can be scaled down to be closer to the size to the tube foot of a sea star (Asterias rubens; diameter, ∼1300 μm; length, up to 20 mm⁶). Although the sea star uses chemical adhesion to attach to surfaces,⁶ we took inspiration from its large array of adhesive tube feet used to achieve locomotion. For a robot of many actuators, we can envision smaller discs with similar geometric ratios, appropriately scaled wall thicknesses, and analogous material stiffnesses to behave similarly to those discs presented in this work.

Large arrays of actuators have the potential to provide provocative abilities to locomoting walking robots in both wetted and submerged domains. For instance, a locomoting robot that will be subjected to directional flow may need to be stabilized to shear forces. Our current designs have not been optimized to withstand shear forces, yet such a goal may be achieved through an array of suction discs with appropriate coordination. Other environmental parameters, such as surface roughness, may be accounted for by the material softness of the disc margin, which has been demonstrated to allow for attachment to rough surfaces such as sandpapers.⁴⁵

While we are yet to fully characterize the walking performance of the robot over macroscale surface features, we anticipate that the discs would be effective against uneven, inclined, and coarse surfaces. We have demonstrated in previous work⁴⁵ that the use of a soft elastomeric layer on a suction disc allowed for high adhesion to irregular (i.e., concave) and rough surfaces (i.e., coarse sandpaper). Given that we have designed these anisotropic suction discs with a soft elastomeric layer in the disc margin, we would expect these discs to provide high adhesion to uneven and irregular surfaces.

Overall, the development of a directional suction disc can be applied to provide locomoting robots with traction in a wet environment, while minimizing actuation complexity.

Conclusion

Directional adhesives that exhibit morphological computation can reduce the complexity of control in robotic systems. In this article, we presented a way to design directional adhesives to adhere based on angle in a wet environment. We demonstrated that we can tune the performance of the suction disc by modifying the symmetry of the body, material composition, and incorporation of slits in the disc margin. Careful selection of body asymmetry, in coordination with material stiffness of the suction discs, produced the most successful and repeatable form of directional anisotropic adhesion.

By tuning the morphology of the adhesives, we incorporated behaviors (i.e., attachment/detachment at appropriate points in a gait cycle) into the body of the suction disc that would otherwise necessitate controlled actuation. We demonstrated that the suction discs can be applied to a linear actuator to achieve a pulling motion, helping to pull a body forward as mechanism for locomotion inspired by the sea star. Based on the approach and analyses presented here, future work could use these anisotropic suction discs to enable sea star inspired robots capable of robust locomotion in wetted and submerged environments to achieve traction and novel gaits with minimum system complexity.

Materials and Methods

Fabrication of the discs

We designed the suction discs using computer-aided design (Solidworks, Dassault Systems). We modified the disc symmetry, material stiffness, and presence of slits in the disc margin to determine which were successful in yielding directional adhesion. Across all prototype variants, the constraining dimensions of the body remained constant. The footprint of the suction chamber was an oval of 16 mm diameter, 28 mm length. The suction chamber was terminated by a disc margin that was 1 mm thick, 1.5 mm offset from the footprint of the suction chamber. The height of the suction chamber was 5.5 mm across all variants. We designed the discs to have cylindrical handles of 5 mm height and 6 mm diameter to provide a gripping surface during adhesive pull tests.

For experiments varying the symmetry of the discs, we fabricated two asymmetric discs (Body Type A and B) and a symmetric disc (Body Type C). The asymmetric discs varied by degree of asymmetry. Body type A had the largest degree of asymmetry, where the upper cavity was centered at one full radius from the center of the suction disc (Fig. 7c). The upper cavity of Body Type B was centered at one half the radius from the center of the suction disc. The upper cavity of Body Type C was located directly above the center of the suction disc.

FIG. 7.

Fabrication of the suction discs. (a) Molding process of the suction chamber using Dragon Skin 20. (b) Molding process of the disc margin, using EcoFlex 20. (c) Variations of the suction disc based on body type and angle of slits in the disc margin. Color images are available online.

We manufactured the suction chamber using a platinum cured silicone with an elastic modulus at 100% strain of 338 kPa (Dragon Skin 20; Smooth-On, Inc.), which we dyed with silicone pigment (Silc-Pig; Smooth-On, Inc.). The main body of the suction discs across all prototypes was composed of this silicone, except for those manufactured to test the impact of material stiffness on adhesion, in which case we fabricated a suction disc of Body Type A with a suction chamber composed of silicone of 100% modulus of 662 kPa (Mold Star 30; Smooth-On, Inc.), 593 kPa (Dragon Skin 30; Smooth-On, Inc.), 338 kPa (Dragon Skin 20; Smooth-On, Inc.), or 68.9 kPa (Ecoflex 00-20; Smooth-On, Inc.). Each silicone was dyed with a pigment corresponding to its stiffness.

Finally, we varied the presence and angle of slits in the disc margin. The slits were angled at 15°, 30°, or 90° with respect to the longitudinal axis.

For each disc variant, we fabricated the molds using a rigid, photocurable resin (VeroClear; Stratasys, Inc.) in a multimaterial 3D printer (Objet350 Connex3; Stratasys, Inc.). To ensure the parts were fully cured, we aged the molds in an oven at 40°C for 4 h. The molds containing uncured silicone were degassed in a vacuum chamber for 10 min and then fully cured in an oven for 1 h 30 min at 40°C (Fig. 7a). We then added a soft layer of silicone to the disc margin to provide a sealing layer, following the approach described in previous work.⁴⁵ To apply a soft layer, we first partially cured a mold of the elastomer (Ecoflex 00-30; Smooth-On, Inc.) at 40°C for 3 min, then applied the suction disc backing to the mold (Fig. 7b). We then fully cured the assembly for 1 h at 40°C.

Experimental evaluation of adhesion

We experimentally tested the adhesives at a fixed velocity. We conducted the pull tests using a universal tensile testing machine (force gauge, 100 N limit, 0.02 N resolution; M7–20, Mark-10 Co.). We mounted the handles of the discs into a clamp that was then held in the upper grips of the tensile testing machine. All pull tests were performed against an angled acrylic plate (angles; 0°, 15°, 30°, 45°) in a tank of water (Fig. 8).

FIG. 8.

Experimental setup for characterization of adhesion. (a) Schematic demonstrating that each adhesion test was performed in a water bath against an acrylic surface. H denotes heel, T denotes toe of the suction disc. (b) Image of experimental setup. Color images are available online.

We engaged the suction disc to the acrylic surface with a preload of 2 N. We performed the pull tests in triplicate, using a rate of retraction of 150 mm· min⁻¹ for all prototypes and trials. The adhesive stress was calculated by normalizing the adhesive force by the surface area of the footprint of the suction disc. We evaluated the effect of preload on the different body symmetries. We varied the preload between 0.25 and 3 N for body types A and C at angles of inclination of −30° and 0°.

Imaging contact

We imaged the contact of the suction disc with a surface using FTIR.⁵⁴ The setup of the FTIR station was custom built, where a 9.7 mm thick acrylic plate internally reflected the light emitted from diodes (natural white light-emitting diodes, 3528-24VDC; Super Bright LEDs, Inc.) that were mounted along the perimeter of the plate. The FTIR plate was statically angled at either −30°, 0°, or 30 to visualize contact throughout three distinctive phases of the gait cycle (Supplementary Fig. S2a).

To remove background noise, we dyed the suction discs black using silicone pigment (Silc Pig; Smooth-On, Inc.). We imaged the acrylic surface using a camera (1280 × 780 pixels, 140 pixels cm⁻¹, 40 frames per second, EXILIM EX-FH25; Casio Computer Co., Ltd.). The suction discs were engaged with the surface to a preload of 2 N, and the surface was wetted during the FTIR trials. When the surface was angled to 30° of inclination, we retracted the upper grip of the mechanical testing setup at a rate of 150 mm·min⁻¹, thereby pulling the suction disc from the imaging surface. The PoF was determined to be the last frame of the image sequence during which the suction disc was adhered to the imaging surface.

Modeling the mechanics of directional adhesion

FEA was performed using ANSYS Mechanical Version 2019R1. We experimentally determined the material properties of Dragon Skin 20 by performing a tensile test (3342; Instron, Inc.) and fitting the Yeoh 3rd order hyperelastic model to the experimental data. Parameters for the Yeoh 3rd order model (C10, C20, C30, D1, D2, D3) were 99 161 Pa, −1604 Pa, 1065.2 Pa, 0 Pa⁻¹, 0 Pa⁻¹, and 0 Pa⁻¹, respectively.

Due to the bilateral symmetry of the suction discs, we modeled half of the suction disc using symmetry boundary conditions in FEA to reduce the computation time. The suction discs were predominantly meshed using 20-node brick elements with an average element size of 0.5 mm. The suction discs were preloaded on an inclined steel plate to obtain a vertical reaction force of ≈0.28 N. Frictionless contact was assigned between the suction discs and the steel plate. We neglected the effects of the change in fluid pressure inside the cavity of the suction disc as the plate was rotated. We performed a quasi-static simulation and neglected the effects of surface energy and friction at the interface of the suction discs and the steel plate.

Simulating the attachment of the suction disc at a −45° angle of the plate, corresponding to the angle of the surface in the experimental setup, is complex due to the large-scale deformation, in addition to the contact and material nonlinearities required to model the physics of the suction disc. The simulation for the attachment of the suction disc at an angle of the plate of −45° was unable to converge in our case. Hence, we simulated the suction disc to attach to a plate that rotated from −30° (attachment) to 30° (detachment).

The angle of inclination for the steel plate was then varied from −30° to 30° with the horizontal (with +10° increments) and the response of the suction discs was recorded. The vertical reaction force, strain energy, Von-Mises stress, deformed shape, contact pressure, and contact status were recorded for variation in the angle of the steel plate between −30° and 30° with 10° increments. The volume of the internal cavity of the suction disc as the plate was rotated was calculated numerically. The internal surface of the suction disc cavity was extracted using Meshmixer 3.3. This extracted surface was then imported to Unity 5.6.7f1, and the volume enclosed by the cavity was numerically calculated.

We quantified the contact pressure of five nodes along the inner perimeter of the suction disc (Supplementary Fig. S5). We probed the contact pressure at the nodes along the plane of symmetry intersecting the inner perimeter (Supplementary Fig. S5, Node I and Node V), the node along the axis of rotation of the plate intersecting the inner perimeter (Supplementary Fig. S5, Node III), and the nodes where the geometry of the inner perimeter transitions from a straight line to a circular arc (Supplementary Fig. S5, Node II and Node IV).

Demonstration of locomotive application

The locomotion demonstrations were performed using a linear slider with Delrin surfaces sliding on an extruded aluminum rod. For the single-syringe demonstrations, a counterweight of 37 g on a pulley was attached to the slider to counteract friction between the slider and the rail. The syringe was driven using a fluid transmission from an off-board motor and lead screw (part number). The syringe was extended to the surface at 5 mm·s⁻¹ to preload the disc and then retracted at 2.5 mm·s⁻¹ to create the forward motion of the slider.

For the double-syringe demonstrations in air, the counterweight was increased to 47.3 g to account for the additional friction in the system. The second syringe was mounted on the slider free to rotate with respect to the slider and the first syringe and was driven by a second motor and lead screw. In this demonstration, the first syringe was extended and preloaded against the surface and then retracted. The second syringe was then extended and preloaded against the surface and retracted the same amount as the extension. The second syringe was then extended and preloaded again, retracted until the first syringe passed the crossover point, and then the first syringe was retracted a small amount to attempt to detach the disc from the surface.

For the submerged double-syringe demonstrations, the front syringe was extended and preloaded against the surface and then retracted to pull the body forward. The rear syringe was then extended and preloaded against the surface and retracted the same amount as the extension to again pull the body forward. The front syringe was then retracted a small amount more to attempt to detach the disc from the surface.

Footnotes

Data and Material Availability

Please contact J.A.S. or M.I. for data and other materials.

Acknowledgment

The authors thank N. Gravish for access to his FTIR setup.

Authors' Contributions

J.A.S., M.I., and M.T.T. conceived the project. J.A.S. designed and fabricated the suction discs. J.A.S., M.I., and S.H. performed experimental characterizations of the discs. S.J. performed the simulations. M.I. performed the locomotive demonstration. J.A.S. and M.I. prepared the initial draft of the article, and all authors provided feedback during revisions.

Author Disclosure Statement

No competing financial interests exist.

Funding Information

This work is supported by the Office of Naval Research grant numbers N00014-17-1-2062 and N00014-18-1-2277. J.A.S. is supported by the Gates Millennium Scholars (GMS) program. M.I. is supported by a National Defense Science and Engineering Graduate (NDSEG) fellowship.

Supplementary Material

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