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First published online August 30, 2006
Journal of Experimental Biology 209, 3569-3579 (2006)
Published by The Company of Biologists 2006
doi: 10.1242/jeb.02486

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Frictional adhesion: a new angle on gecko attachment

K. Autumn^1,*, A. Dittmore¹, D. Santos², M. Spenko² and M. Cutkosky²

¹ Department of Biology, Lewis & Clark College, 0615 SW Palatine Hill Road, Portland, OR 97219, USA and
² Department of Mechanical Engineering, Stanford University, Building 530, 440 Panama Mall, Stanford, CA 94305-3030, USA

View larger version (57K): [in a new window]   Fig. 1. Gecko adhesive system. (A) Micrograph of a single gecko seta assembled from a montage of five Cryo-SEM images (image by Stas Gorb and K. Autumn). (B) Nanoscale array of hundreds of spatular tips of a single gecko seta. Note that the field of spatulae forms a plane at an acute angle to the base of the setal shaft. Raising the angle of the shaft above 30° may cause spatular detachment (Autumn et al., 2000; Gao et al., 2005). (C) Ventral view of a tokay gecko (Gekko gecko) climbing a glass surface. (D) Array of setae are arranged in a nearly grid-like pattern on the ventral surface of each scansor. In this scanning electron micrograph, each diamond-shaped structure is the branched end of a group of four setae clustered together in a tetrad. (E) Toe peeling (digital hyperextension, DH) during detachment. Scale bars, 50 µm (D), 5 µm (A), 1 µm (B).

View larger version (88K): [in a new window]   Fig. 2. Apparatus used to measure the angle (*) at which gecko toes detach from a glass surface. We discovered that the normally aggressive and temperamental tokays (Gekko gecko) became docile when attached by a single toe to a glass surface. A soft pad of bubble wrap cushioned falls. Animals were suspended a distance of approx. 10 cm above the pad, and in nearly all trials we caught the animal by hand prior to contact with the pad. A thin strip of adhesive bandage tape acted as a muzzle to prevent bites.

View larger version (27K): [in a new window]   Fig. 3. Shear and normal forces in isolated gecko setal arrays on a glass surface. Motion in normal and shear axes was controlled at 50 µm s-1. (A) Setal array during load (1), drag (2) and pull (3) (LDP) against the curvature of the setal shafts exhibits Coulomb friction. Negative F|| represents the reaction forces during a drag to the left. However, no difference between static and kinetic friction was evident. Compression force F was approx. 3.2 times shear force F||. (B) Setal array during LDP with the curvature of the setal shafts compressed initially, and then was pulled into tension as the setal tips adhered. Positive F|| represents the reaction forces during a drag to the right. Adhesion was sustained during the 100 µm drag step (2). (C) Normal vs shear force during LDP against curvature of the setal shafts. F and F|| followed a path along the Coulomb friction cone (red broken line of slope 1/µ). (D) Normal vs shear force during LDP with curvature of the setal shafts. F and F|| followed a path that began initially along the Coulomb friction cone (red broken line of slope 1/µ). As adhesion developed, the forces converged on F=-F||tan*, where *30° (blue broken line).

View larger version (18K): [in a new window]   Fig. 4. (A) Adhesion (-F ) vs shear force (F||) at three scales: isolated setae (circles), isolated setal arrays (squares) and live gecko toes (triangles). For all scales, F=-F||tan*, where *30°. (B) Release angle (*) vs adhesion (-F ) at three scales: isolated setae (circles), isolated setal arrays (squares) and live gecko toes (triangles). For all scales, * was near 30°. Values of * differed minimally but significantly among seta, array and toe levels (Kruskal-Wallis, H=90.133; d.f.=2; P<0.001). Letters A and B denote significant Dunn's pairwise contrasts. Array and toe values of * were not significantly different from each other (rank=4.475; Q=0.273; P>0.05), and were significantly lower than * in setae, suggesting that the value of *=30° in single setae sets the upper limit for detachment angles at array and toe scales.

View larger version (16K): [in a new window]   Fig. 5. Comparison of frictional adhesion, JKR and Kendall peel models. We chose parameters such that a 2-D model of a 50 g gecko could adhere to inclined planes from 0° to 180°. Stability regions (shaded) and limits (borders) of each model are plotted in force-space (F||, F ) measured as a percentage of body weight. (A) Frictional adhesion given by Eqn 4, Eqn 5 and Eqn 6 along with current experimental results from setal arrays and toe detachment angles and previous results for single setae (Autumn et al., 2000). (B) JKR model for elastic spherical asperity in contact with flat substrate. Absolute values for adhesive and shear forces have been increased to comparable levels by assuming an array of contact asperities each contributing to overall adhesion and shear (Peressadko and Gorb, 2004). (C) Kendall peel model for thin adhesive films. Maximum force occurs at 0° (intersection with +F||-axis) and decreases as peel angle increases (measured below horizontal) towards 90° (intersection with-F -axis), eventually reaching a minimum finite value at 180°. Maximum shear for positive normal force is assumed to be independent of normal force and set at the Kendall peel model limits for 0° and 180°.

View larger version (16K): [in a new window]   Fig. 6. (A) Planar model of a gecko on a flat inclined surface. is the angle of inclination and ranges from 0° (flat) to 180° (inverted). Center of mass was 2 cm above the surface and centered between the front and rear feet. A distance of 10 cm separated front and rear feet. For static equilibrium, forces in y and z and moment about x (not shown) must balance to zero. (B) Graphical description of stability margin. Given a particular point in force-space, the stability margin is shown using the frictional adhesion model (d1) and the Kendall peel model (d2). For the JKR model, the point shown would violate stability criteria and result in a negative stability margin. Stability margin is the minimum distance in any direction to avoid violating a constraint.

View larger version (17K): [in a new window]   Fig. 7. The stability margin (top) and internal force (bottom) required for the gecko model to maintain a minimum stability margin of 25% body weight. Estimated force data from climbing house geckos, Hemidactylus garnotii (Autumn et al., 2006a), yielded a safety margin of approximately 36% body weight, assuming an * of 25°. Before point A, the frictional adhesion and Kendall peel models dictate the gecko orient its feet opposite of each other to maintain the specified stability margin. From point A to points B (frictional adhesion) and C (Kendall peel), the gecko model orients both feet with gravity since gravity naturally loads the contacts in their preferred adhesive direction and achieves greater than 25% stability margin (point D) without applying internal forces. As the surface becomes vertical and overhanging, the front foot must sustain more adhesion than the rear. In the JKR model, increasing adhesion is only possible by decreasing shear; thus, it is preferable for the rear foot to bear more shear load than the front. In the anisotropic models, the opposite is true. The front foot bears more shear load than the rear, because this tends to increase maximum adhesion. After points B and C, the respective anisotropic models only maintain the specified stability by reversing the rear foot and pulling inward with both feet. Point E indicates where both the peel and JKR models can no longer maintain the specified stability using any amount of internal force. This is in part due to the particular parameters chosen, but also due to the eventual decrease in adhesive forces when shear forces become too large.

View larger version (69K): [in a new window]   Fig. 8. Experimental climbing machine, `Stickybot' (A), for testing anisotropic adhesive structures and force control strategies. Inset (B) shows experimental measurements of normal vs shear forces in an anisotropic frictional adhesive inspired by gecko setae. We used the same methods as for isolated gecko setal arrays. The urethane microarrays demonstrated a similar frictional adhesion response to that of gecko setae (Fig. 3D). Data were taken on a patch with an area of 35 mm2. The area of each Stickybot toe is 431 mm2 (C) Magnified view showing angled contact surface of frictional adhesive microarray.