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WO2015167991A1 - Climbing device with dry adhesives - Google Patents

Climbing device with dry adhesives Download PDF

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Publication number
WO2015167991A1
WO2015167991A1 PCT/US2015/027729 US2015027729W WO2015167991A1 WO 2015167991 A1 WO2015167991 A1 WO 2015167991A1 US 2015027729 W US2015027729 W US 2015027729W WO 2015167991 A1 WO2015167991 A1 WO 2015167991A1
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WO
WIPO (PCT)
Prior art keywords
adhesive
load
degressive
tiles
tile
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Ceased
Application number
PCT/US2015/027729
Other languages
French (fr)
Inventor
Elliot W. HAWKES
David L. CHRISTENSEN
Eric V. EASON
Mark R. Cutkosky
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Leland Stanford Junior University
Original Assignee
Leland Stanford Junior University
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Filing date
Publication date
Application filed by Leland Stanford Junior University filed Critical Leland Stanford Junior University
Publication of WO2015167991A1 publication Critical patent/WO2015167991A1/en
Anticipated expiration legal-status Critical
Ceased legal-status Critical Current

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Classifications

    • CCHEMISTRY; METALLURGY
    • C09DYES; PAINTS; POLISHES; NATURAL RESINS; ADHESIVES; COMPOSITIONS NOT OTHERWISE PROVIDED FOR; APPLICATIONS OF MATERIALS NOT OTHERWISE PROVIDED FOR
    • C09JADHESIVES; NON-MECHANICAL ASPECTS OF ADHESIVE PROCESSES IN GENERAL; ADHESIVE PROCESSES NOT PROVIDED FOR ELSEWHERE; USE OF MATERIALS AS ADHESIVES
    • C09J7/00Adhesives in the form of films or foils
    • FMECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F16ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
    • F16FSPRINGS; SHOCK-ABSORBERS; MEANS FOR DAMPING VIBRATION
    • F16F1/00Springs
    • F16F1/02Springs made of steel or other material having low internal friction; Wound, torsion, leaf, cup, ring or the like springs, the material of the spring not being relevant
    • F16F1/021Springs made of steel or other material having low internal friction; Wound, torsion, leaf, cup, ring or the like springs, the material of the spring not being relevant characterised by their composition, e.g. comprising materials providing for particular spring properties
    • FMECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F16ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
    • F16FSPRINGS; SHOCK-ABSORBERS; MEANS FOR DAMPING VIBRATION
    • F16F15/00Suppression of vibrations in systems; Means or arrangements for avoiding or reducing out-of-balance forces, e.g. due to motion
    • F16F15/02Suppression of vibrations of non-rotating, e.g. reciprocating systems; Suppression of vibrations of rotating systems by use of members not moving with the rotating systems
    • F16F15/04Suppression of vibrations of non-rotating, e.g. reciprocating systems; Suppression of vibrations of rotating systems by use of members not moving with the rotating systems using elastic means
    • F16F15/06Suppression of vibrations of non-rotating, e.g. reciprocating systems; Suppression of vibrations of rotating systems by use of members not moving with the rotating systems using elastic means with metal springs
    • CCHEMISTRY; METALLURGY
    • C09DYES; PAINTS; POLISHES; NATURAL RESINS; ADHESIVES; COMPOSITIONS NOT OTHERWISE PROVIDED FOR; APPLICATIONS OF MATERIALS NOT OTHERWISE PROVIDED FOR
    • C09JADHESIVES; NON-MECHANICAL ASPECTS OF ADHESIVE PROCESSES IN GENERAL; ADHESIVE PROCESSES NOT PROVIDED FOR ELSEWHERE; USE OF MATERIALS AS ADHESIVES
    • C09J2301/00Additional features of adhesives in the form of films or foils
    • C09J2301/30Additional features of adhesives in the form of films or foils characterized by the chemical, physicochemical or physical properties of the adhesive or the carrier
    • C09J2301/31Additional features of adhesives in the form of films or foils characterized by the chemical, physicochemical or physical properties of the adhesive or the carrier the adhesive effect being based on a Gecko structure
    • CCHEMISTRY; METALLURGY
    • C09DYES; PAINTS; POLISHES; NATURAL RESINS; ADHESIVES; COMPOSITIONS NOT OTHERWISE PROVIDED FOR; APPLICATIONS OF MATERIALS NOT OTHERWISE PROVIDED FOR
    • C09JADHESIVES; NON-MECHANICAL ASPECTS OF ADHESIVE PROCESSES IN GENERAL; ADHESIVE PROCESSES NOT PROVIDED FOR ELSEWHERE; USE OF MATERIALS AS ADHESIVES
    • C09J2483/00Presence of polysiloxane
    • FMECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F16ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
    • F16FSPRINGS; SHOCK-ABSORBERS; MEANS FOR DAMPING VIBRATION
    • F16F2224/00Materials; Material properties
    • F16F2224/02Materials; Material properties solids
    • F16F2224/0258Shape-memory metals, e.g. Ni-Ti alloys
    • FMECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F16ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
    • F16FSPRINGS; SHOCK-ABSORBERS; MEANS FOR DAMPING VIBRATION
    • F16F2228/00Functional characteristics, e.g. variability, frequency-dependence
    • F16F2228/12Functional characteristics, e.g. variability, frequency-dependence degressive

Definitions

  • the present invention relates generally to dry adhesives. More particularly, the invention relates to a degressive load-sharing array of synthetic adhesive tiles.
  • the length scale of focus is the human scale, motivated by the challenge of human climbing with a gecko-inspired dr adhesive.
  • adhesive anchors capable of holding impressive loads have been created, but the scaling efficiency of these adhesion systems has not been reported.
  • a synthetic adhesion device includes a load plate, a load tendon, where the load tendon is connected to the load plate, an array of adhesive tiles, where each the adhesive tile includes adhesion microwedges, an array of degressive elastic elements, where each the degressive elastic element is configured to have a decreasing stiffness with an increasing displacement, where each the degressive elastic element includes a tile tendon, and an array of flexible pedestals, where each the flexible pedestal is connected to the load plate, where each the adhesive tile is connected to the flexible pedestal, where each the adhesive tile is further connected to the tile tendon, where each the degressive elastic element is connected to the load plate, where the array of adhesive tiles are configured for degressive load sharing to all the adhesive tiles.
  • the microwedges includes PDMS microwedges.
  • the degressive elastic element includes a nitinol degressive elastic element.
  • the load tendon is connected to the load plate in a configuration that does not apply moments to the array of adhesive tiles.
  • variations in displacement of the degressive elastic element are decoupled from variations in force applied to the degressive elastic element.
  • the adhesive tiles are elastically decoupled from each other.
  • the adhesive tiles include a rigid flat surface.
  • the array of degressive elastic elements are arranged in parallel.
  • the load tendon is connected to the load plate at an angle in a range of 0 to 7 degrees.
  • FIGs. 1A-1E show the effects of progressive and degressive elastic elements in load- sharing, where (FIG. 1 A) stress-strain curve of the skin of the tokay gecko, with a piecewise linear fit shown in dashed, and the ratio of ki to k ⁇ is 5, corresponding to a progressive elastic element; (FIG, IB) stress-strain curve of a strand of extruded nylon, with a k-i to ratio of 3, used as a progressive element for testing in the synthetic device; (FIG. 1C) stress- strain curve of a supereiastie nitinoi wire, with ratio of k2 to kl of 0.07, corresponding to a degressive elastic element; (FIG. 1 A) stress-strain curve of the skin of the tokay gecko, with a piecewise linear fit shown in dashed, and the ratio of ki to k ⁇ is 5, corresponding to a progressive elastic element; (FIG, IB) stress-strain curve of a
  • FIG. 2 shows visualizations of the synthetic adhesion system force-displacement data from FIG. IE at selected values of the total force, using either progressive or degressive load-sharing elements.
  • the CV equal to the ratio of the standard deviation to the mean (n ::: 24), remained constant at a moderate value (0.17-0.19) for the progressive elements as the load increased, but decreased significantly for the degressive elements (ending at 0.04).
  • Near maximum load the force distribution was non-uniform in the progressive case, with a few tiles carrying disproportionately high percentages of the load; on the other hand, the distribution became highly uniform in the degressive case near maximum load, with all of the tiles supporting nearly equal forces.
  • the degressive springs enabled the system to support a higher total force before exceeding the failure threshold of the tiles, according to the current invention.
  • FIGs. 3A-3C show a comparison of the branched network of tendons in a gecko toe
  • FIG. 3.4 a biomimetic branched design
  • FIG. 3B a biomimetic branched design
  • FIG. 3C the parallel network of tendons used in the synthetic adhesion system
  • FIGs. 4A-4B show (FIG. 4A) a scaling behavior of the synthetic adhesion system on a slightly curved (p ⁇ 200 m) acrylic surface (diamonds), where the area was adjusted by varying the number of adhesive tiles in the system, and adhesive performance data of single rigid adhesive tiles of different sizes on this surface are included for comparison (squares), where performance values are normalized relative to the force per unit area of the adhesive on flat acrylic; (FIG. 4B) an image of PDMS microwedges, according to one embodiment of the invention.
  • FIGs 5A-5C show an exemplary design of a climbing device and the synthetic adhesion system, where (FIG. 5A) climbing device: the load is transferred from the synthetic adhesion system through the load tendon into the rigid load member, which lies along the surface out of the way of the climber and supports the climber at the foot pivot. A rubberized roller prevents sideslip, and the foot pivot allows the ankle joint to be used. The foot pivot is located away from the wall, which allows the climber to move their center of mass closer to the wall than the foot pivot, negating any tendency to fal l backwards. (FIG 5B and FIG.
  • the current invention uses a concept referred to as degressive load-sharing.
  • degressive load-sharing elastic elements which have decreasing stiffness with increasing displacement support independent patches of adhesive and help equalize the load on all patches.
  • the synthetic adhesion system sustains adhesive stress with little decrease across four orders of magnitude of area, approximately following the power law ff max ex: A '1, 30 .
  • the system was found to resist catastrophic failure by preventing stress concentrations when a simulated failure was induced on a portion of the adhesive, and the system also requires little effort to attach or detach.
  • the synthetic adhesion system according to one embodiment of the current invention enables a human to ascend a vertical glass surface with a hand-sized area of adhesive.
  • the tendons are attached so that they do not apply moments to the tiles, and the tiles are made rigid to prevent deflection. Because rigid tiles cannot conform to large curvature, an array of smaller tiles performs significantly better than a single large tile on surfaces that are insufficiently flat. Therefore, in one exemplary embodiment, the adhesive is divided into 24 independent tiles to make the synthetic adhesive system functional on practical surfaces. This necessitates the use of a load-sharing mechanism to distribute the total load among the tiles.
  • load-sharing is accomplished by a suspension that applies forces to patches of adhesive.
  • this suspension is composed primarily of the stratum compactum of the skin of each lamella, which comprises taut elastin and coiled collagen fibers.
  • the stiffness of the skin increases as the collagen uncoils and bears load.
  • a progressive elastic element i.e. an element with tangent stiffness that increases with displacement
  • FIG. 1A a progressive element is not ideal for load-sharing. If some random variation in displacement exists among the patches of adhesive, the progressive stiffness curve will cause the subsequent variation in shear loads to become magnified as the displacements increase.
  • the synthetic adhesion system of the current invention uses degressive elastic elements. Unlike most materials, degressive elements become more compliant with extension while remaining elastic. Here, elements made of superelastic nitinol are used, which exhibit a roughly 15-fold decrease in stiffness over the range of extension, as shown in FIG. 1C. Using degressive elements as suspensions for patches of adhesive results in a decrease in the variation in adhesive loads as the displacements increase.
  • the elements In the low-stiffness regime, the elements produce a nearly-constant force over a large range of displacements, so variations in displacement are decoupled from variations in force. Unlike very soft, linear springs, degressive elements require only a small amount of total displacement to achieve an even load distribution. Additionally, as long as at least one element is still in its high- stiffness regime, the system exhibits high stiffness. Thus, the synthetic adhesion system 'feels' stiff, although many of the parallel elements are in a low-stiffness regime. If all the elements are in the lo w-stiffness regime, the overall stiffness of the system is much lower, but there is no instability, because the stiffness is still positive.
  • the degressive elements are tuned, so that they enter the low-stiffness (nearly-constant force) regime at a force just below the maximum force the PDMS microwedge adhesive on each tile can support as predicted by small-scale tests.
  • the synthetic adhesion system reaches maximum extension, the stress distribution over the adhesive area is both uniform and maximized, ensuring efficient scaling.
  • One method to inhibit crack propagation in peeling adhesive films is to attach the adhesive to a backing layer that is stiff in the loading direction. Another method is to array the adhesive material into eiasticaily coupled sections, whic tends to halt, divert and reinitiate the crack.
  • the synthetic adhesion system exhibited this stable behavior in tests.
  • An array of seven tiles was placed on a grid of force sensors and loaded to about 75% of the maximum load for the array.
  • one of the tiles was slowly unloaded, simulating a slip failure. This type of failure could be caused by a contaminated or damaged tile or surface.
  • the force it had been carrying w r as transferred to the two tiles that had been supporting less than 30 N of load whereas the force on the highly loaded tiles did not change significantly. Because the highly loaded tiles did not experience a substantial increase in force, they did not become overloaded and the failure did not propagate.
  • the superelastic nitinol degressive elements employed in one embodiment of the synthetic adhesion system have a hysteretic behaviour. This means that when a tile fails, less energy is released from its degressive element than was put in, resulting in a relatively smaller disturbance to the system than would occur with non-hysteretie elements.
  • the synthetic adhesion system has other design elements which are modified from the equivalent parts of the gecko adhesion system to improve performance.
  • the structure of the load-bearing tendons was modified.
  • the lateral digital tendons split into branches, each of which inserts into an individual lamella and loads an independent patch of adhesive (FIG. 3A).
  • Such a branched design allows the transfer of load solely through tension, without requiring compressive or bending elements, which could prevent a structure from conforming to non-flat surfaces.
  • any branch that is at an angle with respect to the external load vector has a component of tension that does not contribute to the external load.
  • the flatness of the adhesive patches was increased to improve adhesion on flat surfaces. If the shape of the adhesive surface is not identical to the shape of the adhered surface, non-uniform adhesive stresses are required to maintain contact across the entire area. In certain areas, these stresses may be above the adhesive limit causing the adhesive to detach. Spontaneous detachment was observed for portions of a tokay gecko toe on a flat surface, suggesting that the stresses required to flatten the adhesive surface are greater than the gecko's adhesive limit in certain areas of the toe. This is not ideal for adhesion on flat surfaces.
  • tokay geckos have been shown to perform wel l on slightly undulating substrates, and it is conjectured that the tokay adhesion system is adapted for use on non-flat surfaces, which may be more common in the tokay gecko's natural habitat.
  • the synthetic adhesion system was found to produce a nearly- imiform load distribution (FIG. 2) and a much more efficient scaling behavior than that of the gecko with little decrease in adhesive ability across four orders of magnitude of area ( max oc A "" ' bb ).
  • the synthetic adhesion system also exhibits good scaling on surfaces with some curvature (p ⁇ 200 m; FIG. 4A), in contrast to a simple single-tile mechanism.
  • the synthetic system with area of 100 cm z performs at just under 80% of the performance of a 6.5 cm" tile on a flat surface, whereas a 100 cm 2 single tile achieves only approximately 15%.
  • FIG. 4B shows an image of PDMS microwedges, according to one embodiment of the invention.
  • the inventors have shown that a synthetic adhesion system using degressive load-sharing elements distributes loads uniformly and robustly and allows efficient scaling of adhesives.
  • the feasibility of applying the synthetic adhesion system to human climbing was demonstrated.
  • the tile size is decreased at the expense of greater system complexity; and for rougher surfaces, the adhesion system is outfitted with one of the gecko inspired adhesive materials that have been developed for use on these surfaces.
  • the adhesion system is outfitted with one of the gecko inspired adhesive materials that have been developed for use on these surfaces.
  • the PDMS microwedge adhesive can be cleaned between steps by touching a material of higher surface energy (e.g. sticky tape), and it may be possible to achieve self-cleaning using an even lower-surface-energy, harder material, and by adopting finer terminal features.
  • Degressive load-sharing mvolves a trade-off between uniformity of the load distribution and robustness to failure. According to the current invention, maximum uniformity is achieved at maximum extension of the degressive elements, at which point a failure could potentially be catastrophic.
  • the failure-tolerant load redistribution behavior described below is only possible at less than maximum extension, when at least one of the adhesive loads is below maximum. While degressive load-sharing does not always ensure exactly equal loads, it does ensure that all loads are limited to a safe level as long as the entire system is not overloaded.
  • the load limits are determined by the low stiffness regime of the degressive elements. For degressive load-sharing to function correctly, these limits must be preset according to the maximum adhesion attainable on the intended combination of adhesive and adherend surface.
  • the synthetic adhesion system is suitable for other practical applications besides climbing.
  • the current system can support loads on a fixed vertical wail.
  • the load-sharing model used to create FIG. ID involves an array of identical nonlinear springs loaded in parallel, where the initial displacements of the springs are distributed over some range. Each spring follows the same force-displacement curve, iix - Q ).
  • P is the force on the h patch of adhesive
  • x is the displacement of the entire system
  • O is the relative displacement between the f h patch and the patch with the tautest tendon.
  • FIG. ID solid lines
  • the designs of one exemplary embodiment of the synthetic adhesion system and human climbing device are illustrated in FIGs, lOA-lOC.
  • the device is designed so that the climber's weight is supported by the leg muscles instead of the weaker upper body.
  • the climber's hands are used to place the adhesive on the wall, but the load is then transferred through a system of tendons and load members to the climber's shoes.
  • Each hand controls an independent 24-tile synthetic adhesion system which supports the corresponding foot during each stride.
  • This exemplary synthetic adhesion system contains 24 independent adhesive tiles in a staggered grid. Each tile is a 2.5 x 2.5 cm square and is attached to an independent degressive elastic element (FIGs. lOB-lOC).
  • the climbing device and synthetic adhesion system are designed so that the angle of the overall load on the synthetic adhesion system and the angles of the individual loads on the tiles remain between 0° and 7° from vertical. This improves the maximum load that the PDM8 microwedge adhesive can support.
  • the exemplary synthetic adhesion system creates a nearly-uniform load distribution across the whole adhesive area, improving upon the adhesive-bearing structures of a gecko's toe and enabling a human to climb vertical glass using an area of adhesive no larger than the area of a human hand.
  • degressive elements could be created by a coil constant-force spring, as found in a measuring tape.
  • the adhesives on the tiles could be any adhesive, not just PDMS microwedges.
  • degressive load sharing could be applied to any situation where load-sharing is desirable, like in the cables of a bridge. All such variations are considered to be within the scope and spirit of the present invention as defined by the following claims and their legal equivalents.

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  • Engineering & Computer Science (AREA)
  • General Engineering & Computer Science (AREA)
  • Mechanical Engineering (AREA)
  • Chemical & Material Sciences (AREA)
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  • Physics & Mathematics (AREA)
  • Acoustics & Sound (AREA)
  • Aviation & Aerospace Engineering (AREA)
  • Adhesives Or Adhesive Processes (AREA)

Abstract

A synthetic adhesion device is provided that includes a load plate, a load tendon, where the load tendon is connected to the load plate, an array of adhesive tiles, where each the adhesive tile includes adhesion microwedges, an array of degressive elastic elements, where each the degressive elastic element is configured to have a decreasing stiffness with an increasing displacement, where each the degressive elastic element includes a tile tendon, and an array of flexible pedestals, where each the flexible pedestal is connected to the load plate, where each the adhesive tile is connected to the flexible pedestal, where each the adhesive tile is further connected to the tile tendon, where each the degressive elastic element is connected to the load plate, where the array of adhesive tiles are configured for degressive load sharing to all the adhesive tiles.

Description

CLIMBING DEVICE WITH DRY ADHESIVES
FIELD OF THE INVENTION
The present invention relates generally to dry adhesives. More particularly, the invention relates to a degressive load-sharing array of synthetic adhesive tiles.
BACKGROUND OF THE INVENTION
Over a decade ago, scientists first reported the mechanism of adhesion in geckos. These animals exploit a complex hierarchical adhesion system, using nanoscale fibers, which produce adhesion through van der Waals forces and can be attached and detached by controlling the loading angle. Since then, researchers have created bioinspired adhesives using silicones, urethanes, plastics, carbon nanotubes and other materials; these materials boast impressive gecko-like properties such as reusability, self-cleaning ability, controllability, rough surface adhesion and the capability to produce large adhesive stresses. While the thrust of the research has been on developing and testing such properties in small-scale laboratory tests, in order to fully exploit these adhesives at different length scales, it is necessary to achieve efficient scaling, i.e. an increase in adhesive area without a significant decrease in adhesive capabilities.
The length scale of focus is the human scale, motivated by the challenge of human climbing with a gecko-inspired dr adhesive. There have been notable efforts to scale adhesives beyond small laboratory tests, but there has been little work dealing specifically with scaling efficiency. Researchers have created small robots that climb well with dry adhesives, yet these systems cannot support as large a load as predicted by their total area of adhesive. For instance, one attempt had an area of adhesive that should have supported 5 kg based on small-scale tests, but could only support 500 g owing to inefficient scaling. In other work, adhesive anchors capable of holding impressive loads have been created, but the scaling efficiency of these adhesion systems has not been reported.
Without scaling efficiency numbers in the literature, it is useful to set a scaling efficiency benchmark by turning towards the adhesion systems of geckos, as designers of dry adhesives have done previous!)' to judge the relative merits of their synthetic materials. In the tokay gecko (Gekko gecko), the adhesion decreases as the length scale increases from the seta-scale to the toe- and foot-scale. This adhesion system has been found to approximately follow a scaling power law, ffmax «: A1'4, where ffmax is the maximum shear stress supported by the adhesive and A is the adhesive area.
If the benchmark power law of the tokay gecko were applied to a PDMS microwedge adhesive, an impractical iy large area of more than 1200 cm' of adhesive per hand would be required to support a 70 kg human climber with no safety factor (a modern tennis racket is approx. 675 cm2). This is partly because the area of adhesive required for climbing increases disproportionately as the scale increases (even with perfectly efficient scaling) owing to the climber's surface area and mass following a square-cube law.
What is needed is a controllable synthetic adhesion system, which ensures that the load distribution across a large adhesive area is nearly uniform. SUMMARY OF THE INVENTION
To address the needs in the art, a synthetic adhesion device is provided that includes a load plate, a load tendon, where the load tendon is connected to the load plate, an array of adhesive tiles, where each the adhesive tile includes adhesion microwedges, an array of degressive elastic elements, where each the degressive elastic element is configured to have a decreasing stiffness with an increasing displacement, where each the degressive elastic element includes a tile tendon, and an array of flexible pedestals, where each the flexible pedestal is connected to the load plate, where each the adhesive tile is connected to the flexible pedestal, where each the adhesive tile is further connected to the tile tendon, where each the degressive elastic element is connected to the load plate, where the array of adhesive tiles are configured for degressive load sharing to all the adhesive tiles.
According to one aspect of the invention, the microwedges includes PDMS microwedges. In another aspect of the invention, the degressive elastic element includes a nitinol degressive elastic element.
In a further aspect of the invention, the load tendon is connected to the load plate in a configuration that does not apply moments to the array of adhesive tiles.
In yet another aspect of the invention, variations in displacement of the degressive elastic element are decoupled from variations in force applied to the degressive elastic element.
According to one aspect of the invention, the adhesive tiles are elastically decoupled from each other. In one aspect of the invention, the adhesive tiles include a rigid flat surface.
According to a further aspect of the invention, the array of degressive elastic elements are arranged in parallel.
In another aspect of the invention, the load tendon is connected to the load plate at an angle in a range of 0 to 7 degrees.
BRIEF DESCRIPTION OF THE DRAWINGS
FIGs. 1A-1E show the effects of progressive and degressive elastic elements in load- sharing, where (FIG. 1 A) stress-strain curve of the skin of the tokay gecko, with a piecewise linear fit shown in dashed, and the ratio of ki to k\ is 5, corresponding to a progressive elastic element; (FIG, IB) stress-strain curve of a strand of extruded nylon, with a k-i to
Figure imgf000005_0001
ratio of 3, used as a progressive element for testing in the synthetic device; (FIG. 1C) stress- strain curve of a supereiastie nitinoi wire, with ratio of k2 to kl of 0.07, corresponding to a degressive elastic element; (FIG. I D) a model based on identical nonlinear springs loaded in parallel with different initial displacements predicts the behavior of synthetic progressive springs (dashed) and synthetic degressive springs (solid) when used to load 24 adhesive patches, where the initial displacement offsets were measured from the synthetic adhesion system, where at the maximum displacement x ------- 4.6 mm, the spread in forces is predicted to be much larger for the progressive springs than for the degressive nitinoi springs, and the average forces avg are 74% and 97% of the maximum force Fmax for the two cases; (FIG. IE) force and displacement data from the synthetic adhesion system with progressive nylon springs (dotted) and degressive nitinol springs (solid) (electronic supplementary material, methods, force and displacement sensor), where at the displacement x = 4.6 mm, the average force Favg for the progressive springs was 70% of the maximum force Fmax, but 94% for the degressive nitinol springs.
FIG. 2 shows visualizations of the synthetic adhesion system force-displacement data from FIG. IE at selected values of the total force, using either progressive or degressive load-sharing elements. The CV, equal to the ratio of the standard deviation to the mean (n ::: 24), remained constant at a moderate value (0.17-0.19) for the progressive elements as the load increased, but decreased significantly for the degressive elements (ending at 0.04). Near maximum load, the force distribution was non-uniform in the progressive case, with a few tiles carrying disproportionately high percentages of the load; on the other hand, the distribution became highly uniform in the degressive case near maximum load, with all of the tiles supporting nearly equal forces. As a result, the degressive springs enabled the system to support a higher total force before exceeding the failure threshold of the tiles, according to the current invention.
FIGs. 3A-3C show a comparison of the branched network of tendons in a gecko toe
(FIG. 3.4), a biomimetic branched design (FIG. 3B) and the parallel network of tendons used in the synthetic adhesion system (FIG. 3C). Owing to the components of the tendon forces that are perpendicular to the external load, the biomimetic design would support only 82% of the external load that the parallel tendon design holds, solely considering tendon geometry differences, according to the current invention.
FIGs. 4A-4B show (FIG. 4A) a scaling behavior of the synthetic adhesion system on a slightly curved (p ~ 200 m) acrylic surface (diamonds), where the area was adjusted by varying the number of adhesive tiles in the system, and adhesive performance data of single rigid adhesive tiles of different sizes on this surface are included for comparison (squares), where performance values are normalized relative to the force per unit area of the adhesive on flat acrylic; (FIG. 4B) an image of PDMS microwedges, according to one embodiment of the invention.
FIGs 5A-5C show an exemplary design of a climbing device and the synthetic adhesion system, where (FIG. 5A) climbing device: the load is transferred from the synthetic adhesion system through the load tendon into the rigid load member, which lies along the surface out of the way of the climber and supports the climber at the foot pivot. A rubberized roller prevents sideslip, and the foot pivot allows the ankle joint to be used. The foot pivot is located away from the wall, which allows the climber to move their center of mass closer to the wall than the foot pivot, negating any tendency to fal l backwards. (FIG 5B and FIG. 5C) Synthetic adhesion system: the load is transferred from the adhesive tiles, through the tile tendons, into the degressive elastic elements, through the load plate and into the load tendon. The soft foam supports (or flexible pedestal) hold the adhesive tiles in place while in the swing phase, but are of negligible stiffness during the stance phase. The total area of the adhesive is 140 cm2 on each hand, divided into 24 independent tiles of dimensions 2.5 x 2.5 cm, according to the current invention.
DETAILED DESCRIPTION
The current invention uses a concept referred to as degressive load-sharing. In degressive load-sharing, elastic elements which have decreasing stiffness with increasing displacement support independent patches of adhesive and help equalize the load on all patches. The synthetic adhesion system sustains adhesive stress with little decrease across four orders of magnitude of area, approximately following the power law ffmax ex: A'1, 30. Furthermore, the system was found to resist catastrophic failure by preventing stress concentrations when a simulated failure was induced on a portion of the adhesive, and the system also requires little effort to attach or detach. Thus, with efficient scaling, robustness to failure and controllable adhesion, the synthetic adhesion system according to one embodiment of the current invention enables a human to ascend a vertical glass surface with a hand-sized area of adhesive.
To aid the comparison of the synthetic adhesion system and the adhesion system of the tokay gecko, a sensor was developed to take in vivo measurements of the stress distributions on gecko toes. The adhesion sensor data for a tokay gecko toe on a flat- surface showed that very little of the useful adhesive area was working at maximum capacity. Only a fraction of the adhesive area contacted the surface, and the load was not evenly distributed even in the areas that did make contact.
Similar results were also observed for a different species (crested gecko, Correlophus ciliatus). These results suggest that load-sharing in gecko adhesion systems may not be ideal, which motivates the development of a synthetic system with improved load-sharing. Turning now to degressive load-sharing, the human climbing synthetic adhesion system presented here retains several gecko-inspired design features, such as controllable adhesives, the separation of the adhesive into discrete elements (with the tiles in the synthetic adhesion system corresponding to lamellae in geckos) and a load-bearing structure that is compliant normal to the surface yet comparatively stiff in the loading direction. According to the current invention, each tile of adhesive is loaded using a tendon-like string. In order to ensure that the stress distribution is uniform over each tile, the tendons are attached so that they do not apply moments to the tiles, and the tiles are made rigid to prevent deflection. Because rigid tiles cannot conform to large curvature, an array of smaller tiles performs significantly better than a single large tile on surfaces that are insufficiently flat. Therefore, in one exemplary embodiment, the adhesive is divided into 24 independent tiles to make the synthetic adhesive system functional on practical surfaces. This necessitates the use of a load-sharing mechanism to distribute the total load among the tiles.
In general, load-sharing is accomplished by a suspension that applies forces to patches of adhesive. In the tokay gecko, this suspension is composed primarily of the stratum compactum of the skin of each lamella, which comprises taut elastin and coiled collagen fibers. During extension, the stiffness of the skin increases as the collagen uncoils and bears load. This is equivalent to a progressive elastic element (i.e. an element with tangent stiffness that increases with displacement), as shown in FIG. 1A. However, a progressive element is not ideal for load-sharing. If some random variation in displacement exists among the patches of adhesive, the progressive stiffness curve will cause the subsequent variation in shear loads to become magnified as the displacements increase. Using a model, it was predicted that a synthetic adhesive system with suitable progressive elements would result in an average adhesive force on all of the tiles that is only 74% of the maximum force on any of the tiles (FIG. ID, dashed lines). Instead of using a biomimetic load-sharing system with progressive elastic elements, the synthetic adhesion system of the current invention uses degressive elastic elements. Unlike most materials, degressive elements become more compliant with extension while remaining elastic. Here, elements made of superelastic nitinol are used, which exhibit a roughly 15-fold decrease in stiffness over the range of extension, as shown in FIG. 1C. Using degressive elements as suspensions for patches of adhesive results in a decrease in the variation in adhesive loads as the displacements increase. In the low-stiffness regime, the elements produce a nearly-constant force over a large range of displacements, so variations in displacement are decoupled from variations in force. Unlike very soft, linear springs, degressive elements require only a small amount of total displacement to achieve an even load distribution. Additionally, as long as at least one element is still in its high- stiffness regime, the system exhibits high stiffness. Thus, the synthetic adhesion system 'feels' stiff, although many of the parallel elements are in a low-stiffness regime. If all the elements are in the lo w-stiffness regime, the overall stiffness of the system is much lower, but there is no instability, because the stiffness is still positive.
With degressive load-sharing, the model now predicts an average adhesive force that is 97% of the maximum (FIG. ID, solid lines). Force and displacement measurements from the exemplary 24-tile synthetic adhesion system with progressive and degressive load- sharing elements (FIG. IE) show that the average adhesive forces at maximum extension were 70% and 94%.» of the maximum force on any of the tiles, in good agreement with the model The uniformity of the force distribution can be quantified by the ratio of the standard deviation to the mean, or coefficient of variation (CV), which was roughly constant for the progressive elements, but significantly decreased near maximum extension for the degressive elements (FIG. 2). The degressive elements are tuned, so that they enter the low-stiffness (nearly-constant force) regime at a force just below the maximum force the PDMS microwedge adhesive on each tile can support as predicted by small-scale tests. Thus, when the synthetic adhesion system reaches maximum extension, the stress distribution over the adhesive area is both uniform and maximized, ensuring efficient scaling.
Turning now to system stability with degressive load-sharing, while scaling efficiency is an important metric, for practical adhesion systems, the system stability and robustness to failure are equally important. If a small section of the adhesive detaches from the surface, does the entire system catastrophic-ally fail?
A similar question is considered in fracture mechanics, when a solid fails at a stress far below that predicted by ultimate strength after a crack is introduced. Accordingly, researchers have used Griffith crack theory to model the phenomenon that occurs when an elastic block adherend to a surface peels after a small section becomes unbonded, with the 'crack' at the interface between the elastic block and the adherend surface. This peeling phenomenon can cause an adhesion system to fail at a stress far below the theoretical maximum.
One method to inhibit crack propagation in peeling adhesive films is to attach the adhesive to a backing layer that is stiff in the loading direction. Another method is to array the adhesive material into eiasticaily coupled sections, whic tends to halt, divert and reinitiate the crack.
While both these methods are effective at decreasing the propensity of a crack to propagate, peeling still occurs in general, because the stress is concentrated along the crack front. On the other hand, a different situation occurs for a system of adhesive tiles loaded through independent degressive elements. If an adhesive tile fails, the combined load on the other tiles must increase to compensate for the decrease in area. However, this stress increase is not necessarily concentrated in the area surrounding the failure. The load is increased only on degressive elements that have not yet reached the nearly-constant- force regime. The loads on the other tiles do not increase, even if they are next to the tile that failed, because they are eiasticaily decoupled from each other owing to the low stiffness and independent nature of the degressive elements. Interestingly, the loads on the tiles remaining on the surface become more evenly distributed instead of more concentrated. This behavior continues as long as the load is not large enough to put all degressive elements into their neaiiy-constant-force regimes.
The synthetic adhesion system exhibited this stable behavior in tests. An array of seven tiles was placed on a grid of force sensors and loaded to about 75% of the maximum load for the array. Next, one of the tiles was slowly unloaded, simulating a slip failure. This type of failure could be caused by a contaminated or damaged tile or surface. As the tile was unloaded, the force it had been carrying wras transferred to the two tiles that had been supporting less than 30 N of load, whereas the force on the highly loaded tiles did not change significantly. Because the highly loaded tiles did not experience a substantial increase in force, they did not become overloaded and the failure did not propagate. As a final note on stability, the superelastic nitinol degressive elements employed in one embodiment of the synthetic adhesion system have a hysteretic behaviour. This means that when a tile fails, less energy is released from its degressive element than was put in, resulting in a relatively smaller disturbance to the system than would occur with non-hysteretie elements.
In addition to degressive load-sharing, the synthetic adhesion system has other design elements which are modified from the equivalent parts of the gecko adhesion system to improve performance. First, the structure of the load-bearing tendons was modified. In the tokay gecko, the lateral digital tendons split into branches, each of which inserts into an individual lamella and loads an independent patch of adhesive (FIG. 3A). Such a branched design allows the transfer of load solely through tension, without requiring compressive or bending elements, which could prevent a structure from conforming to non-flat surfaces. However, any branch that is at an angle with respect to the external load vector has a component of tension that does not contribute to the external load. Because it was know, a priori, that the intended climbing surface is relatively flat, compressive and bending elements were included to make all of the tendons parallel (FIG. 3C). Considering only tendon geometry, this parallel design can support 22% more load than a biomimetic branched design (FIG. 3B).
Second, the flatness of the adhesive patches was increased to improve adhesion on flat surfaces. If the shape of the adhesive surface is not identical to the shape of the adhered surface, non-uniform adhesive stresses are required to maintain contact across the entire area. In certain areas, these stresses may be above the adhesive limit causing the adhesive to detach. Spontaneous detachment was observed for portions of a tokay gecko toe on a flat surface, suggesting that the stresses required to flatten the adhesive surface are greater than the gecko's adhesive limit in certain areas of the toe. This is not ideal for adhesion on flat surfaces. As explanation for this behavior, it is noted that tokay geckos have been shown to perform wel l on slightly undulating substrates, and it is conjectured that the tokay adhesion system is adapted for use on non-flat surfaces, which may be more common in the tokay gecko's natural habitat.
With these design features, the synthetic adhesion system was found to produce a nearly- imiform load distribution (FIG. 2) and a much more efficient scaling behavior than that of the gecko with little decrease in adhesive ability across four orders of magnitude of area ( max oc A""'bb). The synthetic adhesion system also exhibits good scaling on surfaces with some curvature (p ~ 200 m; FIG. 4A), in contrast to a simple single-tile mechanism. On this curved surface, the synthetic system with area of 100 cmz performs at just under 80% of the performance of a 6.5 cm" tile on a flat surface, whereas a 100 cm2 single tile achieves only approximately 15%. Using this system, a human of mass 70 kg successfully ascended a 3.7 m vertical glass wall with 140 crcT of gecko-inspired dry adhesives in each hand. Hundreds of individual steps were tested on glass with the 70 kg climber and 140 cm2 of adhesive without failure. In addition, the maximum load for the exemplary system was tested five times, finding an average of 95.6 kg (938 N) and a standard deviation of 2.7 kg (26 N). Finally, it was found that the compressive force required to preload the device before loading is small (less than 1 N) and that the force required to release the device after unloading is also small (less than 2 N). Thus, the system retains the property of controllability from the adhesive material. FIG. 4B shows an image of PDMS microwedges, according to one embodiment of the invention. The inventors have shown that a synthetic adhesion system using degressive load-sharing elements distributes loads uniformly and robustly and allows efficient scaling of adhesives. In addition, the feasibility of applying the synthetic adhesion system to human climbing was demonstrated.
According to a further embodiment of the current invention, to adhere to surfaces with more curvature, the tile size is decreased at the expense of greater system complexity; and for rougher surfaces, the adhesion system is outfitted with one of the gecko inspired adhesive materials that have been developed for use on these surfaces. On contaminated surfaces, even geckos have trouble producing adhesion (van derWaals forces require intimate contact between the surface and the adhesive); however, gecko adhesive has been observed to self-clean when it becomes contaminated. In one embodiment, the PDMS microwedge adhesive can be cleaned between steps by touching a material of higher surface energy (e.g. sticky tape), and it may be possible to achieve self-cleaning using an even lower-surface-energy, harder material, and by adopting finer terminal features.
Degressive load-sharing mvolves a trade-off between uniformity of the load distribution and robustness to failure. According to the current invention, maximum uniformity is achieved at maximum extension of the degressive elements, at which point a failure could potentially be catastrophic. The failure-tolerant load redistribution behavior described below is only possible at less than maximum extension, when at least one of the adhesive loads is below maximum. While degressive load-sharing does not always ensure exactly equal loads, it does ensure that all loads are limited to a safe level as long as the entire system is not overloaded. The load limits are determined by the low stiffness regime of the degressive elements. For degressive load-sharing to function correctly, these limits must be preset according to the maximum adhesion attainable on the intended combination of adhesive and adherend surface.
In addition, the synthetic adhesion system is suitable for other practical applications besides climbing. The current system can support loads on a fixed vertical wail.
The load-sharing model used to create FIG. ID involves an array of identical nonlinear springs loaded in parallel, where the initial displacements of the springs are distributed over some range. Each spring follows the same force-displacement curve, iix - Q ). (A i) where P) is the force on the h patch of adhesive, is the force-displacement curve of the springs used, x is the displacement of the entire system, and O, is the relative displacement between the fh patch and the patch with the tautest tendon. The maximum force Fmax occurs for the patch with the tautest tendon (0,,-...,, ;= 0), and is given by equation (A2),
ΡΊτιακ j(x)', (A 2)
Assuming the function βΧ) is linear over the range of possible values taken by X = x - C¾, then
'.:* ,: = Fnm - kix)Qxv& (A3) where k(x) = άβάχ is the tangent stiffness of the springs at the displacement x (i.e. &2 for the piecewise linear fits in FIGs. 1A-1C). In order to compare the progressive and degressive springs, this model was used to calculate the maximum and average forces that would result from using the two types of springs in a 24-tile synthetic adhesion system. The force-displacement curves fix) of a degressive nitinol wire and a progressive strand of nylon fishing line were directly measured. The dimensions of these elastic elements were chosen, so that they produced the same force at x = 4.6 mm, which is the maximum displacement of the synthetic adhesion system. The initial displacements Q; were determined from the degressive-spring experimental data in FIG. IE by measuring the different values of x that resulted in each tile producing I O N. Using the progressive force-displacement curve of the nylon strand, equations (A2) and (A3) predict Fmax = 37 N and Favg = 27 N = 0.74 Fma?; (FIG, ID, dashed lines). With the degressive nitinol springs and with the same x and Qm , the model predicts max ~ 37 N and aVg ==: 36 N = 0.97 nax (FIG. ID, solid lines). The designs of one exemplary embodiment of the synthetic adhesion system and human climbing device are illustrated in FIGs, lOA-lOC. The device is designed so that the climber's weight is supported by the leg muscles instead of the weaker upper body. The climber's hands are used to place the adhesive on the wall, but the load is then transferred through a system of tendons and load members to the climber's shoes. Each hand controls an independent 24-tile synthetic adhesion system which supports the corresponding foot during each stride.
This exemplary synthetic adhesion system contains 24 independent adhesive tiles in a staggered grid. Each tile is a 2.5 x 2.5 cm square and is attached to an independent degressive elastic element (FIGs. lOB-lOC). The climbing device and synthetic adhesion system are designed so that the angle of the overall load on the synthetic adhesion system and the angles of the individual loads on the tiles remain between 0° and 7° from vertical. This improves the maximum load that the PDM8 microwedge adhesive can support. Considerable research has been dedicated to creating geckoinspired adhesives with desirable properties, but little work has been directed towards efficient scaling: scaling adhesives to large areas for practical applications with almost equal performance at all scales. The current invention provides a synthetic adhesion system that allows efficient scaling over four orders of magnitude of area. The exemplary synthetic adhesion system creates a nearly-uniform load distribution across the whole adhesive area, improving upon the adhesive-bearing structures of a gecko's toe and enabling a human to climb vertical glass using an area of adhesive no larger than the area of a human hand. These results show that gecko-inspired adhesives can be scaled from laboratory-scale tests to human- scale applications with little decrease in performance.
The present invention has now been described in accordance with several exemplary embodiments, which are intended to be illustrative in all aspects, rather than restrictive. Thus, the present invention is capable of many variations in detailed implementation, which may be derived from the description contained herein by a person of ordinary skill in the art. For example, degressive elements could be created by a coil constant-force spring, as found in a measuring tape. The adhesives on the tiles could be any adhesive, not just PDMS microwedges. More generally, the concept of degressive load sharing could be applied to any situation where load-sharing is desirable, like in the cables of a bridge. All such variations are considered to be within the scope and spirit of the present invention as defined by the following claims and their legal equivalents.

Claims

claimed:
A synthetic adhesion device, comprising:
a. a load plate;
b. a load tendon, wherein said load tendon is connected to said load plate;
c. an array of adhesive tiles, wherein each said adhesive tile comprises adhesion microwedges;
d. an array of degressive elastic elements, wherein each said degressive elastic element is configured to have a decreasing stiffness with an increasing displacement, wherein each said degressive elastic element comprises a tile tendon; and
e. an array of flexible pedestals, wherein each said flexible pedestal is connected to said load plate, wherein each said adhesive tile is connected to said flexible pedestal, wherein each said adhesive tile is further connected to said tile tendon, wherein each said degressive elastic element is connected to said load plate, wherein said array of adhesive tiles are configured for degressive load sharing to all said adhesive tiles.
2. The synthetic adhesion device of claim 1, wherein said microwedges comprises PDMS microwedges.
3. The synthetic adhesion device of claim 1, wherein said degressive elastic element comprises a nitinol degressive elastic element.
4. The synthetic adhesion device of claim 1, wherein said load tendon is connected to said load plate in a configuration that does not apply moments to said array of adhesive tiles.
5. The synthetic adhesion device of claim 1, wherein variations in displacement of said degressive elastic element are decoupled from variations in force applied to said degressive elastic element.
6. The synthetic adhesion device of claim 1, wherein said adhesive tiles are elastically decoupled from each other.
7. The synthetic adhesion device of claim 1, wherein said adhesive tiles comprise a rigid flat surface.
8. The synthetic adhesion device of claim 1, wherein said array of degressive elastic elements are arranged in parallel.
9. The synthetic adhesion device of claim 1, wherein said load tendon is connected to said load plate at an angle in a range of 0 to 7 degrees.
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