Experimental investigation on attachment properties of dry adhesives used in

climbing robots

Matthew W. Powelson

Tennessee Technological University

Dept. of Mechanical Engineering

Cookeville, Tennessee, 38505

United States of America

mwpowelson42@students.tntech.edu

Matthew Powelson received his B.Sc. degree in Mechanical Engineering in 2016 from Tennessee Technological University in Cookeville, TN, where

he is currently pursuing a M.Sc. in Mechanical Engineering. His current research interests

include mobile robotics, dry adhesives, micro-manufacturing, climbing robot technology, and

machine learning.

Stephen L. Canfield

Tennessee Technological University

Dept. of Mechanical Engineering

Cookeville, Tennessee, 38505

United States of America

SCanfield@tntech.edu

Stephen Canfield is a Professor in the Department of Mechanical Engineering at Tennessee Tech University. He received his Ph.D. from Virginia

Tech.

Keywords: Regabond-S, Suction Cup Tape, Dry Adhesive, Climbing Robots, Vytaflex, micro suction, elastomeric adhesion, van der Waals

Abstract

Mobile climbing robots commonly use magnets or active suction as their adhesive elements, but dry elastomer adhesives and particularly bio-inspired patterned elastomer adhesives are an area of increasing interest in robotics research. However, these patterned elastomer adhesives are not widely available. As a result, the authors propose the use of a commercially-available micro suction tape known as Regabond-S as the adhesion mechanism for climbing robots. In order to be useful in design, the performance of the adhesive must be understood. The authors propose a model for micro suction tapes that relates preloading with the maximum sustainable adhesion. The model suggests that the adhesion comes from a combination of van der Waals and suction forces, and its performance falls between unpatterned and patterned elastomers. The model is then experimentally verified and compared with other elastomer adhesives on acrylic, brushed aluminum, and steel surfaces. These results are then demonstrated on a track-based climbing mobile robot.

1. Introduction

Mobile climbing robots provide an alternative to bring automated manufacturing or inspection operations to a range of applications where it could prove dangerous or undesirable for humans to be directly in

contact with the task (Schmidt & Bernes, 2013). Further, robotic mechanization can lead to improved operation in some highly-repetitive tasks. For these reasons, mobile climbing robots have been proposed and developed by researchers to do tasks such as vessel inspection (Alkalla, et al., 2017; Canfield, et al., 2017), welding (Wu, et al., 2013; Shang, et al., 2008), cleaning (Zhang, et al., 2007), and power plant assessment (Lee, et al., 2013). Since the mobile climbing robot must generate the forces for equilibrium (these include gravity and dynamic forces) while moving over a climbing surface, the adhering technique and distribution of adhering forces are two vital parameters to be considered when designing these robots, and an effective adhering strategy to generate adhering forces is the starting point. Thus, proper selection of the adhering technique is a crucial step toward designing a climbing robot with high efficiency. Some of the primary adhesion methods suggested for mobile climbing robots are magnetic (Lee, et al., 2013; Tavakoli, et al., 2016), suction (Wang, et al., 2010; Lee, et al., 2015), mechanical grasping (Liu, et al., 2015; Palmer III, et al., 2015; Carpenter, et al., 2016), patterned and unpatterned dry adhesives, (Hawkes, et al., 2013; Li, et al., 2016; Gorb, et al., 2007) (Unver & Sitti, 2010; Seo & Sitti, 2013; Murphy & Sitti, 2007; Liu, et al., 2016), wet adhesion (He, et al., 2014; Miyake & Ishihara, 2007), thermoplastic adhesion (Wang & lida, 2013; Osswald & Iiad, 2013), and electrostatic adhesion (Liu, et al., 2013). While each adhering method has different characteristics that make them well suited for specific applications (Longo & Muscato, 2008), the class of dry-adhesives have several beneficial characteristics such as an applicability to a range of materials and passive actuation (no need to generate sucking forces). These are an area of interest in robotics research, with the majority of the current research in adhesives for climbing robots focusing on the use of bio-inspired patterned elastomer dry adhesives. Patterned elastomer adhesives demonstrate some of the highest performance, and a review of these bio-inspired adhesives is available (Li, et al., 2016). However, these adhesives are generally expensive to reproduce and currently are not commercially available.

Alternatively, Unver and Sitti (Unver & Sitti, 2009) performed a study of an unpatterned elastomer (a urethane casting rubber, Vytaflex-10A from Smooth-On Inc.) for climbing robots and characterized its adhering properties. The main feature of the elastomer is that it is readily available and can be cast into any desired shape. However, another dry adhesive known by the trade name as Regabond-S (Exel Trading Co., LTD) has been commercially available for some time. This adhesive has been cited in several US patents but no general modeling or characterization of Regabond-S has been published to the authors’ knowledge. As a result, the authors propose the use of this commercially available off the shelf (Inventables.com, Part #20543-11) micro suction tape known as Regabond-S as the adhesion mechanism for climbing robots – an adhesive which appears to offer a dual-mode approach to generating adhesion: micro suction and elastomeric dry adhesion (van der Waals forces). This paper will provide a model for Regabond-S and compare this to other unpatterned elastomer adhesives. The model is proposed based on a dual-mode adhesive mechanism. A series of empirical tests are performed to provide performance characteristics under various loading and unloading conditions that may be common in robot design as well as use on various climbing surfaces. The use of this data is then demonstrated in the design of a track-type climbing robot. A prototype of this robot is shown, and its basic performance is evaluated. Finally, the paper concludes with remarks related to longer-term application of Regabond-S to climbing robot applications.

2. Adhesive Modeling of the Regabond-S

2.1 Overview A model is presented to characterize the adhering properties of a dry adhesive that makes use of vacuum

or suction generated on the climbing surface through a large number of miniature or micro voids (see Fig.

1). A commercial version of this material, commonly called suction cup tape, is Regabond-S. Regabond-S

is an acrylic foam which has microscopic voids thought to act as suction cups during the adhesion process.

This foam is low cost, readily available, and relatively durable. While it has become common in consumer

applications (e.g. cell phone mounts), this adhesive does not appear to be widely studied or quantified.

The adhesive nature of the suction cup tape is theorized to be generated from two modes of action: the

suction created from the deformation of the voids in the foam when forces are applied and the van der

Waals forces typical of flat elastomer dry adhesives. A model is proposed here to characterize this micro

suction tape material for application in climbing robot systems.

2.2 Suction Cup Model The suction tape is created from an acrylic foam material in which interior closed-cell voids are introduced

and distributed throughout the material during the manufacturing process. The closed cells are generally

impermeable to air and the surface is sufficiently elastic to deform to the surface contour. A schematic of

a cross-section of the suction cup tape is presented in Fig. 2.

When a region of the foam is pressed against a surface, deformation and contouring to the surface

features generates suction forces in the voids (see Fig. 2). Assuming that the resulting void makes an

effective seal with the surface, the suction forces are directly related to change in air volume under an

ideal gas assumption. Given the small diameter of the hemispheres and the symmetric nature of the test

piece, elongation due to Poisson’s Effect is neglected when the foam is deformed (see Fig. 2). Thus, the

change in volume of the hemispheres can be modeled as a compression of spheres into spheroids

(compressed in one dimension only). Assuming a linear-elastic model for the foam, the new normal

dimension of the spheroid under preload is,

𝑧𝑛𝑒𝑤 = 𝑧0 (1 +𝜎

𝐸𝑒𝑓𝑓𝑒𝑐𝑡𝑖𝑣𝑒) (1)

where 𝑧𝑛𝑒𝑤, 𝑧0 are shown in Fig. 2, 𝜎 = 𝐹/𝐴 with 𝐹 as the exterior applied preload force and 𝐴 as the

cross-sectional area of the test specimen, and 𝐸𝑒𝑓𝑓𝑒𝑐𝑡𝑖𝑣𝑒 is the effective elastic modulus of the material in

the interface region. Note that 𝐹, 𝐴, and 𝜎 are gross values across the entire adhesive piece ignoring any

microscopic features, and compressive pressures and forces are negative. Parameter 𝑧𝑛𝑒𝑤 is now used to

complete the equation of the spheroid,

𝑥2+𝑦2

𝑎2 +𝑧2

𝑐2 = 1 (2)

where 𝑎 = 𝑅, the radius of the undeformed hemisphere, and c is the deformed hemisphere height (𝑐 =

𝑧𝑛𝑒𝑤, Eq. 1) evaluated at 𝑧0 = 𝑅. Therefore, the volume, 𝑉, of the hemisphere after preloading is,

𝑉 =2

3𝜋𝑎2𝑐 =

2

3𝜋𝑅3 (1 +

𝜎

𝐸𝑒𝑓𝑓𝑒𝑐𝑡𝑖𝑣𝑒). (3)

Using this description of deformed volume, the pressure can now be calculated using the ideal gas law.

The adhesive should be considered at two states: the deformed preload state and the deformed adhesion

state. During the preload state (when the force applied is negative), the air is assumed to fully escape as

the suction cups are compressed allowing the pressure to remain at 1 atm. As a positive load is applied,

the volume of the suction cup is increased. This causes a decrease in pressure below 1 atm and results in

adhesion. Applying the ideal gas law yields an equation for the adhesion pressure inside of a void,

𝑃𝑎𝑑ℎ𝑒𝑠𝑖𝑜𝑛 = 1 𝑎𝑡𝑚 ∗𝑉𝑝𝑟𝑒𝑙𝑜𝑎𝑑

𝑉𝑎𝑑ℎ𝑒𝑠𝑖𝑜𝑛 (4)

with 𝑉𝑝𝑟𝑒𝑙𝑜𝑎𝑑, 𝑉𝑎𝑑ℎ𝑒𝑠𝑖𝑜𝑛 calculated from Eq. 3 using associated preload and applied loads. Converting this

pressure to gage pressure and multiplying by the exposed area and the void density (𝑣𝑜𝑖𝑑𝑠

𝑚2 ), 𝐷, gives an

equation for the gross adhesion pressure, 𝜎𝑠𝑢𝑐𝑡𝑖𝑜𝑛,

𝜎𝑠𝑢𝑐𝑡𝑖𝑜𝑛 = (1 𝑎𝑡𝑚 − 𝑃𝑎𝑑ℎ𝑒𝑠𝑖𝑜𝑛) ∗ 𝜋𝑅2 ∗ 𝐷. (5)

2.3 Elastomeric Adhesion Effect The second adhesion effect from surface contact is based on the empirical model for dry adhesion due to

the elastomeric nature of the acrylic foam. Low durometer rubbers and other soft elastomers have long

been modeled analytically using the principles of contact mechanics. However, while these models

typically show the maximum adhesion as being independent of the preloading conditions, it has been

shown empirically that for rough surfaces and contact patches in the size needed to support climbing

robots, increasing preload can affect an increase in adhesive force for a finite amount of time (Unver &

Sitti, 2010). It is theorized that this is true in conditions where the no-load contact adhesion forces do not

allow for complete surface contact at either the macroscopic or microscopic level and is due to a

combination of viscoelastic effects and the interaction between the adhesive and the surface asperities

that would not otherwise be contacted. This is supported by the work of Gorb (Gorb, 2001) on modeling

the adhesion of an unpatterned elastomer hemisphere of radius, 𝑟6, with respect to the preload. Gorb

proposed that the maximum adhesive force is proportional to the contact area at separation. Gorb then

proposed that the deformation of the pad, and thus the area, could be described using Hertz theory for

low preloads with a saturation being reached when the pad was completely flattened. Thus, Gorb

described the force of adhesion, 𝐹𝑎𝑑ℎ𝑒𝑠𝑖𝑜𝑛 as,

𝐹𝑎𝑑ℎ𝑒𝑠𝑖𝑜𝑛 = 𝐾6𝐴 = 𝜋 (𝑟6

𝐾6)

2/3𝐾6𝐹𝑝𝑟𝑒𝑙𝑜𝑎𝑑

2/3 (6)

for forces below the saturation force, where 𝐾6 is constant.

For flat elastomer adhesives, Unver and Sitti (Unver & Sitti, 2010) (Unver & Sitti, 2009) and Murphy and

Sitti (Murphy & Sitti, 2007) suggest a similar model. Based on experimental observation, they also suggest

a power fit, in the form

𝜎𝑎𝑑ℎ𝑒𝑠𝑖𝑜𝑛 = 𝐾7,1(𝜎𝑝𝑟𝑒𝑙𝑜𝑎𝑑)𝐾7,2 (7)

with the constant parameters 𝐾7,1 and 𝐾7,2 being determined experimentally for a specific elastomer/test

surface pair and a given set of test conditions (preload speed, loading time, etc.). Unfortunately, since

Regabond-S is an off the shelf product, testing the adhesive without the suction cup voids is not possible;

therefore, the elastomeric adhesive properties of the suction cup tape are assumed to be similar to that

of other elastomeric dry adhesives. For comparison, the authors evaluated Shore 10A silicone sheet

rubber (McMaster-Carr part # 5963K11) and a Shore 10A urethane casting rubber (Vytaflex-10A from

Smooth-On Inc), mirroring the work of Unver and Sitti (Unver & Sitti, 2010). While Unver and Sitti

suggested a power fit for data of this kind (Unver & Sitti, 2009) (Murphy & Sitti, 2007), upon evaluation it

was observed that the curve profiles of the adhesion with respect to preload for these cases were better

approximated with an equation of the form,

𝜎𝑒𝑙𝑎𝑠𝑡𝑜𝑚𝑒𝑟𝑖𝑐 = 𝐺 ∗ log10 (𝜎𝑝𝑟𝑒𝑙𝑜𝑎𝑑

1 𝑘𝑃𝑎) + 𝐾 (8)

with G and K constants that define the curve. Eq. 8 better captures both the low preload region and the

high preload saturation region proposed by Gorb (Gorb, 2001). Therefore, through a series of response

curves, the elastomeric adhesive properties of each are modeled as logarithmic functions of preload given

a set of conditions including adhesive preload application time, attachment/detachment speed, surface

roughness, and adhesive thickness. A representative case of this is presented in Appendix A-1 and the

findings for each case are detailed in Section 4.3 (Tables 2-4).

2.4 Combined Adhesion Model Application The suction and adhesion models are then combined to yield a two-part adhesion model of the Regabond-

S calculated as

𝜎𝑡𝑜𝑡𝑎𝑙 = 𝜎𝑠𝑢𝑐𝑡𝑖𝑜𝑛 + 𝜎𝑒𝑙𝑎𝑠𝑡𝑜𝑚𝑒𝑟𝑖𝑐 = 1 𝑎𝑡𝑚 ∗ (1 −(1−

𝜎𝑝𝑟𝑒𝑙𝑜𝑎𝑑

𝐸𝑒𝑓𝑓𝑒𝑐𝑡𝑖𝑣𝑒)

(1+𝜎𝑙𝑜𝑎𝑑

𝐸𝑒𝑓𝑓𝑒𝑐𝑡𝑖𝑣𝑒)

) ∗ 𝜋𝑅2 ∗ 𝐷 + (𝐺 ∗ log10 (𝜎𝑝𝑟𝑒𝑙𝑜𝑎𝑑

1 𝑘𝑃𝑎) + 𝐾). (9)

Successful adhesion is considered to occur when the total available adhesion from all sources is greater

than the load pulling on the adhesive (𝜎𝑡𝑜𝑡𝑎𝑙 > 𝜎𝑙𝑜𝑎𝑑). Therefore, the maximum adhesion value is found

when 𝜎𝑙𝑜𝑎𝑑 = 𝜎𝑡𝑜𝑡𝑎𝑙. Note that since the adhesion due to suction is dependent on the load applied, the

maximum adhesion must be solved by applying a load, calculating the volume and pressure, and

comparing that resulting adhesion force to the pulling force. Solving this equation using the MATLAB

symbolic toolbox yields the closed form solution for the maximum adhesion shown in Appendix A-2.

The parameters defining the adhesion equation can now be determined experimentally using a

representative case of 0.8mm thick black Regabond-S. It was initially characterized using a 75x optical

microscope as shown in Fig. 1. The voids in the foam were confirmed to be approximately hemispherical

at the adhesion interface. A manual visual characterization process using the measurement tools in the

software ImageJ yielded a range of void radii, R, from 1-100 um with 15 m an approximate average value,

and a density of D = 90e6 voids/m2 for new adhesive. This corresponds to a total surface coverage,

𝐶𝑂𝑏𝑠𝑒𝑟𝑣𝑎𝑏𝑙𝑒, of approximately 10%. However, it was theorized that some of the voids that affect the

suction adhesion may actually be mostly unobservable using a microscope as they reside just below the

surface, covered only by a thin film. These would correspond to the small white specks observed in Fig. 1

where only a thin film separates the void from the interface surface, to be broken upon preload.

Therefore, the manually observed density value was multiplied by a factor, 𝜅, to yield the total effective

density of the voids (voids/m2),

𝐷 = 𝜅𝐶𝑂𝑏𝑠𝑒𝑟𝑣𝑎𝑏𝑙𝑒

𝜋𝑅2 (10)

The gross elastic modulus across the entire thickness of the acrylic foam, 𝐸, was found experimentally to

be 450 kPa. Due to the closed cell nature of the acrylic foam, 𝐸𝑒𝑓𝑓𝑒𝑐𝑡𝑖𝑣𝑒 must then be found due to the

effect of the air contained in the internal voids not at the contact surface (De Vries, 2009). Further, this

also accounts for any change in cross-sectional area at the contact surface and allows the bulk area, 𝐴, to

be used. These effects were accounted for by multiplying by a factor, α as shown in Eq. 11.

𝐸𝑒𝑓𝑓𝑒𝑐𝑡𝑖𝑣𝑒 = 𝛼 ∗ 𝐸 (11)

Since the curve shapes from the flat elastomer adhesives are the same across all of the adhesives and

surfaces tested, it was assumed that the elastomeric adhesive properties of the Regabond-S could also be

described using a logarithmic function of the form of Eq. 8. It was then observed that neither the suction

component nor the elastomeric adhesion models alone match the adhesion profile of the suction cup tape

as seen in Fig. 3.

3. Experimentation

3.1 Experimental Procedure An experimental procedure was developed based on the example of Unver and Sitti (Unver & Sitti, 2009;

Unver & Sitti, 2010) and Murphy and Sitti (Murphy & Sitti, 2007) to experimentally determine the adhesive

properties of the three materials considered. The model presented in Section 2 provides a relation

between maximum adhesion and preload; however, Unver and Sitti (Unver & Sitti, 2010) show that the

adhesion is also a function of preload application time, attachment/detachment speed, surface

roughness, and adhesive thickness. In order to gain a more intuitive understanding of the materials and

to verify that the suction cup tape performs similarly to the unpatterned elastomer adhesives, these

parameters are also considered.

Tests were performed on a one-degree-of-freedom, translating test apparatus with position and force

feedback incorporated into control of the linear axis. The adhesive was mounted on a calibrated force

sensor and attached to the translating plate, while the climbing surface was held stationary. The adhesive

was moved into contact with the test surface at a fixed speed until the desired preload normal force was

achieved. The adhesive was then held in that position for the designated preload application time before

being removed at a constant speed until the adhesive failed and contact between the adhesive and test

surface was lost.

Three adhesives were considered across three test surfaces. Shore 10A Vytaflex was chosen for

comparison with the results from Unver and Sitti (Unver & Sitti, 2010). It was prepared according to the

standard preparation instructions and cast into 1.59 mm thick test pieces. Shore 10A silicone was added

as an ideal test case as it is widely available in highly uniform sheets and was expected to perform similarly

to the Vytaflex 10A due to its similar durometer. The two adhesives were used to validate the test

procedure and expand upon the results available in the literature. 0.8mm black Regabond-S was selected

for testing over the thinner varieties available to increase the conformance of the adhesive and reduce

the effect of any misalignment in the tester. The adhesives were cut into 2.54 cm by 2.54 cm squares for

testing in order to observe the macroscopic properties of the adhesive that might only be observable on

samples of the size that could be used for climbing robots. These samples were then attached to a rigid

polycarbonate backing material. The test surfaces selected were opaque black cast acrylic (TAP Plastics),

weld-prepped brushed aluminum, and unprepared steel. All experiments were conducted at room

temperature and ambient humidity. Table 1 summarizes the test schedule which describes the range of

tests performed. The last column of Table 1 identifies the section of this paper in which the results are

discussed.

Table 1

ADHESIVE TEST

SURFACES

PRELOAD SPEED

(MM/S)

REMOVAL SPEED

(MM/S) PRELOAD TIME (S)

PRELOAD FORCE

(N) TOTAL RUNS

PAPER SECTION

1.59 MM

VYTAFLEX

10A

3 0.1:0.1:2.5 0.1:0.1:2.5 2 30 75 4.1

3 0.1 0.1 0:5:60 30 39 4.2

3 0.1 0.1 2 0:1:50 600 4.3

1.59 MM SILICONE

10A

3 0.1:0.1:2.5 0.1:0.1:2.5 2 30 75 4.1

3 0.1 0.1 0:5:60 30 39 4.2

3 0.1 0.1 2 0:1:50 1781 4.3

0.8 MM

REGABOND-

S

3 0.1:0.1:2.5 0.1:0.1:2.5 2 30 75 4.1

3 0.1 0.1 0:5:60 30 39 4.2

3 0.1 0.1 2 0:1:50 600 4.3

3.2 Experimental Setup

The experimental setup is shown in Fig. 4. The setup consists of two NEMA 17 stepper motors and two parallel M5 threaded rods to drive the motion. The adhesive was mounted to a bidirectional bending beam load cell which was read with a 24-bit HX711 analog to digital converter. Maximum travel speed of the setup is approximately 2.5mm/s when under test loading. Moreover, the tester was found to have an approximate elasticity of 48.7 N/mm in the test regime. Therefore, 120 N/s was the theoretical maximum force application speed with the actual maximum force application speed being lower due to the added elasticity of the test sample.

4. Results and Discussion The overall pressure profiles defining the adhesion of the tested materials were found to be consistent

with the past information reported in the literature. The three adhesives all exhibit behaviors with three

distinct regions as shown in Fig. 5: first a region of preloading during which the tester applies a constant

velocity input until the desired preload is achieved, second a relaxation region where the adhesive

conforms to the surface over time, and finally the removal region where the adhesive is displaced at a

constant velocity until adhesive failure. The preload pressure and adhesive failure pressure were then

recorded for each case for analysis in later sections.

4.1 Adhesion vs Speed As discussed in Section 2, elastomeric dry adhesives have time-dependent behavior that is not easily

quantified analytically. The most obvious effect of this is the relation between the maximum adhesion

exhibited and the speed with which the adhesive is removed. This can be seen in Fig. 6. For these tests,

the preload was set to 46.5 kPa (30N on a 6.54 cm2 test sample) and the preloading time was set to 2 s.

The preloading and removal speeds were then varied from 0.1 mm/s to 2.5 mm/s. This represents a test

scale an order of magnitude larger than Unver and Sitti (Unver & Sitti, 2010), but the tests show

reasonable agreement between the datasets. Importantly, the Regabond-S exhibits the same behavior as

the elastomeric adhesive tests. They both increase in a nonlinear fashion as the speed is increased and

appear to have similar curve profiles. This is important for robot design particularly in the case of track-

based systems. In a track-based system, the driving speed is directly related to the application and removal

speed. From these findings, it can be observed that a climbing robot utilizing these adhesives must be

robust to increasing adhesion forces. Further, considering an equilibrium model like the one presented by

Powelson and Canfield (Powelson & Canfield, 2017), these findings show that a robot could actually

sustain higher external loading when traveling at high speeds. This could become increasingly important

when considering the case of dynamic loading. Higher speeds could result in larger dynamic forces, but

since the adhesive will have greater adhesion potential, the robot has the possibility of remaining stable

across a larger design space.

4.2 Adhesion vs Wait Time The second time-dependent behavior observed in the adhesive is the dependence on the preload time.

These tests were carried out at a speed of 0.1mm/s with a preload of 46.5 kPa. The tests were carried out

between 0 and 60 seconds in steps of 5 seconds. This expanded on the range tested by Unver and Sitti,

and the results for the Vytaflex adhesive were comparable. As expected, the adhesive performed better

at higher preload times, with each adhesive seeming to increase by the same amount regardless of the

test surface. This is important for legged climbing robots and track based systems alike. For legged robots,

the designer must build the robot in such a way that the legs are preloaded for a long enough time to

achieve strong adhesion. However, the finding is even more significant for track-based systems when

considering the findings of Section 4.1.

In track-type climbing robots, the adhesive is generally preloaded for a small percentage of the track (see

for example (Powelson & Canfield, 2017)). When considering a robot traveling at speed, the time over

which the adhesive is preloaded will be a function of the robot speed, increasing as the robot drives

slower. However, as discussed in Section 4.1, the maximum adhesive pressure increases the faster the

adhesive is removed. Therefore, the optimal driving speed for a track based climbing mobile robot will be

the intersection of two curves both dependent on driving speed – one defined by the preload time and

one defined by the removal speed. While the exact profile of these curves will be scaled by the lengths of

the preload and removal regions of the tracks respectively, they will be of the shape shown in Fig. 6 and

Fig 7.

4.3 Adhesion vs Preload The adhesives were tested across a range of preloads from 1 to 50N in steps of 1N at a speed of 0.1mm/s

and a preload time of 2 s. These tests were carried out in a random order with between 200 and 1000

tests being run for each dataset. The tests show reasonable agreement with the findings of Unver and

Sitti (Unver & Sitti, 2009) for Vytaflex tests on acrylic. Intuitively, these adhesives adhere better the harder

they are applied, with some saturation eventually being reached. This adhesion to preload relationship

forms an important design requirement for climbing robots as will be demonstrated in Section 5. This

relationship is demonstrated in Figs. 8-10 for acrylic, steel, and aluminum climbing surfaces respectively.

As this finding provides the basis for most climbing robot designs, it is necessary to have a model of this

relationship as presented in Eqs. 8 and 9. Fitting the constant parameters associated with these equations

for Vytaflex and Silicone yields Tables 2 and 3. Combining the elastomeric model with the suction model

as detailed in Section 2.4 yields Table 4. In Table 4, the parameters 𝐸𝑒𝑓𝑓𝑒𝑐𝑡𝑖𝑣𝑒, 𝑅 and 𝐷 are constants

associated with the material while 𝐺 and 𝐾 represent behavior characteristics on specific test surface. The

measurements of the Regabond-S properties discussed in Section 2.4 above serve as a starting point to

find the material properties that best describe behavior under empirical tests.

Table 2 – Parameters for 1.59 mm Silicone at 0.1 mm/s

VARIABLE UNITS ACRYLIC ALUMINUM STEEL

𝑮 kPa 10.191 2.623 3.366 𝑲 kPa 11.219 2.903 7.807

APPROX. MAX 𝝈 kPa 29 5 14

Table 3 – Parameters for 1.59 mm Vytaflex at 0.1 mm/s

VARIABLE UNITS ACRYLIC ALUMINUM STEEL

𝑮 kPa 12.483 12.933 22.846 𝑲 kPa 3.199 -0.421 -3.297

APPROX. MAX 𝝈 kPa 26 25 40

Table 4 – Parameters for the 0.8 mm Suction cup tape at 0.1 mm/s

VARIABLE UNITS ACRYLIC ALUMINUM STEEL

𝑬𝒆𝒇𝒇𝒆𝒄𝒕𝒊𝒗𝒆 kPa 658.2 658.2 658.2

𝑹 𝜇m 20 20 20 𝑫 voids/m2 5.80e8 5.80e8 5.80e8 𝑮 kPa 40.27 24.65 22.61 𝑲 kPa -15.36 -11.83 -12.80

5. Application of Model to Tracked Robot Design This section will present an example application of the Regabond-S adhesion model to the design of a

track-type climbing robot. An advantage of robots with tracks is the extended area for adhesion with the

climbing surface relative to wheeled or legged robots with discrete foot pads. Further, the use of a force

distributing suspension could couple the track to the chassis in a way that distributes the forces needed

for equilibrium in an optimal manner (see for example (Powelson & Canfield, 2017)). Alternatively, the

climbing robot could employ a simple track drive without a suspension but with an additional trailing

moment arm (tail) to provide all the forces needed to satisfy equilibrium in climbing (see for example

the robot demonstrated in (Unver & Sitti, 2010)). This example will consider, in a simplified manner, a

robot similar to the later of these where the robot is modelled as having four distinct pressure regions –

a compressive preloading region (𝑤1), a no-load region, a region that is either compressive or tensile

depending on the loadings (𝑤2), and a tensile removal region (𝑤3). Fig. 11 shows a schematic of the test

robot while Table 5 summarizes its primary design parameters. This robot is intended for climbing in

vertical configurations on glass, plastic, or smooth metal surfaces.

The first robot parameter that must be determined is the size of the pressure regions 𝑤1, 𝑤2, and 𝑤3.

These can be estimated by considering the deformation in the track during those regions. The robot will

utilize a properly tensioned stiff belt coated in the Regabond-S, and therefore the track is assumed to

make contact along the region from the center of the leading sprocket to just behind the trailing sprocket

(for a peeling angle approaching 0). Selecting an off the shelf belt (McMaster-Carr #6484K752), the

distance, L, is estimated to be 225 mm and the width, 𝑏, is estimated to be 50.8 mm. Considering Fig. 12,

the contact region under the trailing sprocket (𝑙2 + 𝑙3) resulting from deformation in the adhesive, ℎ,

given in terms of the sprocket radius, 𝑟, and deformation angle, as,

ℎ = 𝑟 − 𝑟 ∗ 𝑐𝑜𝑠(𝜃) (12a)

and

𝑙3 = 𝑟 ∗ sin (𝜃) (12b)

or,

𝑙3 = 𝑟 ∗ sin (arccos(−ℎ

𝑟+ 1)) = 𝑟 ∗ √1 − (−

ℎ

𝑟+ 1)

22

. (13)

Assuming negligible deformation of the adhesive during pull-off, it can then be assumed that 𝑙2 = 𝑙3 by

symmetry and 𝑙1 = 2 ∗ 𝑙3 since the preloading can occur across the entire wheel. Assuming a deformation

of 0.4 mm (half of the adhesive thickness) and a radius of 25.4mm, the lengths can be estimated as 𝑙2 =

𝑙3 = 4.5 mm and 𝑙1= 9 mm for the subsequent calculations.

With the size belt chosen by the designer and the pressure regions calculated, the only remaining

parameter to choose is the moment applied by the tail. For this analysis, the length of the tail 𝑙𝑇𝑎𝑖𝑙 is

chosen to be 127 mm and 𝐹𝑇𝑎𝑖𝑙 is generated by deformation of a linear spring; however, in actual practice

the designer may choose to use a constant torque spring in which case the length of the tail is arbitrary,

effecting only the resultant friction at the tail’s point of contact. Regardless, a formulation could proceed

as follows. Taking the sum of the moments about the center of the bottom axle yields

(𝑤1𝑙1 ∗ 𝐿 + 𝑤2𝑙2 ∗𝑙2

2+ 𝑤3𝑙3 ∗

𝑙3

2) ∗ 𝑏 − 𝐹𝑇𝑎𝑖𝑙 ∗ 𝑙𝑇𝑎𝑖𝑙 = 0 (14)

since 𝑙2 and 𝑙3 are small relative to 𝑙𝑇𝑎𝑖𝑙 and 𝐿, the compressive pressure (𝑤1) can be a function of the

length of the robot, L, and the moment applied by the tail, 𝐹𝑇𝑎𝑖𝑙 ∗ 𝑙𝑡𝑎𝑖𝑙. Specifically,

𝑤1 ≅𝐹𝑇𝑎𝑖𝑙∗𝑙𝑇𝑎𝑖𝑙

𝑙1𝐿∗𝑏 (15)

Referring to Fig. 8, a preload pressure of 𝑤1 = 40 𝑘𝑃𝑎 seems a reasonable choice. Since the length of the

tail is selected as 𝑙𝑇𝑎𝑖𝑙 = 127 𝑚𝑚, 𝐹𝑇𝑎𝑖𝑙 is then calculated to be 32.4 N. Since this example design is

intended for smooth surfaces (that tend to have low coefficients of friction), this value is considered

acceptable.

With the tail tension calculated, the designer can now consider the time-dependent properties of the

adhesive. The robot travel speed, 𝑣𝑟𝑜𝑏𝑜𝑡, is expected to be 20 mm/s, so this is used to calculate the time

a discrete piece of adhesive will be in each pressure region, 𝑡𝑖, as

𝑡𝑖 =𝑙𝑖

𝑣𝑟𝑜𝑏𝑜𝑡. (16)

This yields 𝑡1 = .45 𝑠 and 𝑡2 = 𝑡3 = .225 𝑠. Since the normal distance displaced is estimated to be

0.4mm, the normal removal speed of the adhesive can then be calculated as 0.4 𝑚𝑚

.225 𝑠= 1.78

𝑚𝑚

𝑠. This can

then be used to compare to Fig 6. While this data cannot be used quantitatively due to the fact that it was

collected with a different preload pressure and speed, it can be qualitatively seen that the designer can

expect an increase in removal pressure (𝑤3) of 20-50%. Further, by comparison to Fig. 7 it can be observed

that the preload time, 𝑡1, is significantly short that the effect of the preload time is nearly negligible and

would most likely only have an effect in climbing robots of a different topology (eg. legged robots or track-

based robots with a force distributing suspension). The final design is pictured climbing on an acrylic

surface in Fig. 13. Table 5 provides a summary of the key design parameters and their method of selection.

The robot demonstrated the ability to climb a distance of at least three body lengths (the approximate

length of the test surface)

Table 5: Design parameters for example robot

DESIGN PARAMETER ASSOCIATED VARIABLE VALUE METHOD OF SELECTION

TOTAL TRACK LENGTH 𝐿 225 mm Design Choice REGION 1 LENGTH 𝑙1 9 mm Eqns. 14, 15 REGION 2 LENGTH 𝑙2 4.5 mm Eqns. 14, 15 REGION 3 LENGTH 𝑙3 4.5 mm Eqns. 14, 15 TRACK WIDTH 𝑏 50.8 mm Design Choice TAIL LENGTH 𝑙𝑇𝑎𝑖𝑙 127 mm Design Choice TAIL FORCE 𝐹𝑇𝑎𝑖𝑙 30.9 N Eqns. 16, 17

6. Conclusions This paper has investigated the use of Regabond-S, a commercially-available micro suction tape, as an

adhesion mechanism for mobile robots. A model-based design approach for climbing robots requires

predictive models for all components including adhesion elements. An example of this process is found

in Powelson and Canfield (Powelson & Canfield, 2017). An analytical model that combines the effects of

van der Waals and suction forces for the micro suction tape was developed and demonstrated. The van

der Waals forces are modeled based on an approximation of empirical data in an approach similar to

Unver and Sitti (Unver & Sitti, 2010). In a practical sense, the authors find that a logarithmic fit is a

better approximation of the empirical data than the power fit demonstrated by Gorb (Gorb, 2001)

because it captures both the low-pressure Hertzian deformation region as well as the saturation region

of the material. The suction forces are represented through a model that describes the system as locally

deforming spheres and assumes that the deformation is linearly distributed through the thickness of the

adhesive. The model is experimentally verified and compared with tests of two unpatterned elastomer

adhesives and data from the literature. The materials were tested in a different regime than that

demonstrated literature, particularly in terms of the application speeds and times; however, the tests

were consistent with the literature in the overlapping regions. Use of the results from this model and

tests were demonstrated in the design and testing of a track-based climbing mobile robot using the

Regabond-S.

The Regabond-S performed significantly better than the un-patterned elastomers in most loading

applications. The one exception was when climbing on steel, in which case the Vytaflex and Regabond-S

performed similarly. In most cases, the Regabond-S adhering force was approximately twice as large or

more at higher preloads. The model for the Regabond-S is useful for design and simulation purposes and

is based on a combination of material properties and parameters representing log fit to external effects

(climbing surface). The material properties incorporated into the model are the modulus of elasticity,

void size, and void density – each measured first through visual observations of the material and then

corrected by a fit of these parameters to empirical data. The measured observations served as a starting

point for the fit and, in general, were within the range of what was visually observed, except for the

total surface coverage (𝐶𝑂𝑏𝑠𝑒𝑟𝑣𝑎𝑏𝑙𝑒, Eq. 10). This was visually measured to be approximately 10% but

empirically found to be greater than 50%, implying far more voids acting to provide adhesion in the

material than could be seen. Alternatively, this difference could imply that the suction force in adhesion

is much greater than that predicted by the model. Some assumptions that may lead to this inaccuracy

are the spherical nature of voids or the linear behavior of the modulus. The model as shown is accurate

but corrections to make the surface coverage more consistent with that observed is a basis for future

work.

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Appendix

A-1 A representative case comparing a log fit to a power fit where G = 10.19 kPa and K = 11.22 kPa.

FIGURE A1 – COMPARISON OF LOG AND POWER FITS OF EXPERIMENTAL DATA FOR SILICONE ON ACRYLIC

A-2

𝜎𝑚𝑎𝑥,1 = ((𝐸2 ∗ 𝑙𝑛(10)2 + 𝐵2 ∗ 𝐾2 ∗ 𝑙𝑛(10)2 + 𝐵2 ∗ 𝐺2 ∗ 𝑙𝑜𝑔(𝜎𝑝𝑟𝑒𝑙𝑜𝑎𝑑)2

+ 2 ∗ 𝐵 ∗ 𝐸 ∗ 𝐾 ∗ 𝑙𝑛(10)2 + 2 ∗ 𝐵

∗ 𝐸 ∗ 𝐺 ∗ 𝑙𝑛(10) ∗ 𝑙𝑛(𝜎𝑝𝑟𝑒𝑙𝑜𝑎𝑑) + 2 ∗ 𝐵2 ∗ 𝐺 ∗ 𝐾 ∗ 𝑙𝑛(10) ∗ 𝑙𝑛(𝜎𝑝𝑟𝑒𝑙𝑜𝑎𝑑) + 𝐷2 ∗ 𝑅4 ∗ 𝑎𝑡𝑚2

∗ 𝜋2 ∗ 𝑙𝑛(10)2 − 2 ∗ 𝜋 ∗ 𝐷 ∗ 𝐸 ∗ 𝑅2 ∗ 𝑎𝑡𝑚 ∗ 𝑙𝑛(10)2 + 4 ∗ 𝑝𝑖 ∗ 𝐷 ∗ 𝑅2 ∗ 𝑎𝑡𝑚 ∗ 𝜎𝑝𝑟𝑒𝑙𝑜𝑎𝑑

∗ 𝑙𝑛(10)2 + 2 ∗ 𝜋 ∗ 𝐵 ∗ 𝐷 ∗ 𝐾 ∗ 𝑅2 ∗ 𝑎𝑡𝑚 ∗ 𝑙𝑛(10)2 + 2 ∗ 𝜋 ∗ 𝐵 ∗ 𝐷 ∗ 𝐺 ∗ 𝑅2 ∗ 𝑎𝑡𝑚 ∗ 𝑙𝑛(10)

∗ 𝑙𝑛(𝜎𝑝𝑟𝑒𝑙𝑜𝑎𝑑))

12

− 𝐸 ∗ 𝑙𝑛(10) + 𝐵 ∗ 𝐾 ∗ 𝑙𝑛(10) + 𝐵 ∗ 𝐺 ∗ 𝑙𝑛(𝜎𝑝𝑟𝑒𝑙𝑜𝑎𝑑) + 𝜋 ∗ 𝐷 ∗ 𝑅2 ∗ 𝑎𝑡𝑚

∗ 𝑙𝑛(10)) / (2 ∗ 𝑙𝑛(10))

𝜎𝑚𝑎𝑥,2 = (𝐾 ∗ 𝑙𝑛(10)

− (𝐸2 ∗ 𝑙𝑛(10)2 + 𝐾2 ∗ 𝑙𝑛(10)2 + 𝐺2 ∗ 𝑙𝑛(𝜎𝑝𝑟𝑒𝑙𝑜𝑎𝑑)2

+ 2 ∗ 𝐸 ∗ 𝐾 ∗ 𝑙𝑛(10)2 + 2 ∗ 𝐸 ∗ 𝐺

∗ 𝑙𝑛(10) ∗ 𝑙𝑛(𝜎𝑝𝑟𝑒𝑙𝑜𝑎𝑑) + 2 ∗ 𝐺 ∗ 𝐾 ∗ 𝑙𝑛(10) ∗ 𝑙𝑛(𝜎𝑝𝑟𝑒𝑙𝑜𝑎𝑑) + 𝐷2 ∗ 𝑅4 ∗ 𝑎𝑡𝑚2 ∗ 𝜋2 ∗ 𝑙𝑛(10)2

− 2 ∗ 𝜋 ∗ 𝐷 ∗ 𝐸 ∗ 𝑅2 ∗ 𝑎𝑡𝑚 ∗ 𝑙𝑛(10)2 + 4 ∗ 𝜋 ∗ 𝐷 ∗ 𝑅2 ∗ 𝑎𝑡𝑚 ∗ 𝜎𝑝𝑟𝑒𝑙𝑜𝑎𝑑 ∗ 𝑙𝑛(10)2 + 2 ∗ 𝜋 ∗ 𝐷

∗ 𝐾 ∗ 𝑅2 ∗ 𝑎𝑡𝑚 ∗ 𝑙𝑛(10)2 + 2 ∗ 𝜋 ∗ 𝐷 ∗ 𝐺 ∗ 𝑅2 ∗ 𝑎𝑡𝑚 ∗ 𝑙𝑛(10) ∗ 𝑙𝑛(𝜎𝑝𝑟𝑒𝑙𝑜𝑎𝑑))

12

− 𝐸 ∗ 𝑙𝑛(10)

+ 𝐺 ∗ 𝑙𝑛(𝜎𝑝𝑟𝑒𝑙𝑜𝑎𝑑) + 𝜋 ∗ 𝐷 ∗ 𝑅2 ∗ 𝑎𝑡𝑚 ∗ 𝑙𝑛(10)) / (2 ∗ 𝑙𝑛(10))

where 𝑎𝑡𝑚 = 1 𝑎𝑡𝑚 = 101325 𝑃𝑎. Depending on the parameters and 𝜎𝑝𝑟𝑒𝑙𝑜𝑎𝑑, one of the above curves

will be real. 𝜎𝑚𝑎𝑥 is the real answer.

Figures

FIGURE 1 – OPTICAL MICROSCOPE IMAGE OF MICRO SUCTION CUP TAPE. SIZING BAR IS 500 𝝁m

FIGURE 2 – CROSS SECTION VIEW OF SUCTION CUP MODEL

FIGURE 3 – COMPARISON OF SUCTION MODEL TO EXPERIMENTAL DATA FOR REGABOND-S ON ACRYLIC

Undeformed Deformed F

𝑧𝑛𝑒𝑤 𝑧0

FIGURE 4 – SCHEMATIC OF EXPERIMENTAL SETUP: (a) STEPPER MOTORS, (b) LEAD SCREWS, (c) GAUGED BEAM LOAD CELL, (d) ADHESIVE, (e) TEST SURFACE, (f) FLEXIBLE COUPLINGS

FIGURE 5 – TYPICAL PRESSURE PROFILE FOR TEST WITH CONSTANT SPEED PRELOAD, PRELOADING TIME, AND CONSTANT SPEED REMOVAL REGIONS LABELED

v v a b

c

d

e

f

Constant Speed

Preload Preloading Time Constant

Speed Removal

Failure

Preload

Pressure

FIGURE 6 – ADHESION VS APPLICATION/REMOVAL SPEED FOR SILICONE, VYTAFLEX, AND SUCTION CUP TAPE ON ACRYLIC, BRUSHED ALUMINUM, AND UNPREPARED STEEL

FIGURE 7 – ADHESION VS PRELOAD TIME FOR SILICONE, VYTAFLEX, AND SUCTION CUP TAPE ON ACRYLIC, BRUSHED ALUMINUM, AND UNPREPARED STEEL

FIGURE 8 – ADHESION VS PRELOAD ON ACRYLIC FOR SILICONE, VYTAFLEX, AND SUCTION CUP TAPE AT 0.1 mm/s

FIGURE 9 – ADHESION VS PRELOAD ON STEEL FOR SILICONE, VYTAFLEX, AND SUCTION CUP TAPE AT 0.1 mm/s

FIGURE 10 – ADHESION VS PRELOAD ON ALUMINUM FOR SILICONE, VYTAFLEX, AND SUCTION CUP TAPE AT 0.1 mm/s

FIGURE 11: SCHEMATIC OF TRACK-BASED CLIMBING ROBOT UTILIZING A TAIL AS A MOMENT TRANSFER DEVICE

𝑤1

𝑤3

𝐹𝑇𝑎𝑖𝑙

𝑤2

𝐿

𝑥𝑐𝑚

FIGURE 12: DIAGRAM OF THE REAR SPROCKET OF THE CLIMBING ROBOT SHOWING THE 𝒍𝟐 and 𝒍𝟑 PRESSURE REGIONS

ℎ

𝑟

𝑙2 𝑙3

𝜃

FIGURE 13: PHOTOGRAPH OF PROTOTYPE TRACKED ROBOT