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First published online August 30, 2006
Journal of Experimental Biology 209, 3558-3568 (2006)
Published by The Company of Biologists 2006
doi: 10.1242/jeb.02469

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Effective elastic modulus of isolated gecko setal arrays

K. Autumn^1,*, C. Majidi², R. E. Groff^2,, A. Dittmore¹ and R. Fearing²

¹ Department of Biology, Lewis & Clark College, Portland, OR 97219, USA
² Department of Electrical Engineering and Computer Science, University of California, Berkeley, CA 94720, USA

View larger version (67K): [in a new window]   Fig. 1. Structural hierarchy of the gecko adhesive system.

View larger version (23K): [in a new window]   Fig. 2. Schematic of compliance hierarchy of the gecko adhesive system (for reviews, see Autumn, 2006; Russell, 2002).

View larger version (25K): [in a new window]   Fig. 3. (A) Force-displacement relationship of an elastic rod for L=100 µm, R=2 µm, and E=2 GPa. As increases, the behavior transitions from cantilever bending to column buckling. (B) Normal force-displacement relationship of the full elastica model (black) and small-deflection, linearized approximation (gray) under differing shear loads for an elastic rod with L=100 µm, R=2 µm, E=2 GPa, =45°, and µ=0.25.

View larger version (17K): [in a new window]   Fig. 4. Schematic of testing platform. A servocontroller drove two closed loop DC servomotors attached to a 2-axis linear stage to produce µm scale displacements of setal arrays bonded to SEM stubs. A 3-axis piezoelectric force sensor measured the forces associated with deformation of setal arrays compressed against a PTFE substrate.

View larger version (11K): [in a new window]   Fig. 5. Testing protocol for setal arrays deformed along the natural path of drag (`with setal curvature', in the typical orientation that geckos use them to climb. In this protocol, the 2-axis micropositioner approached the substrate at 45° until the array was compressed to approx. 50% of its resting height, moved 100 µm parallel to the substrate, and then retracted at -45°.

View larger version (12K): [in a new window]   Fig. 6. Force vs time of representative trials. In all trials, shear velocity was 50 µm s-1. (A) Setal arrays compressed and relaxed vertically. (B) Setal arrays compressed and relaxed against the natural path of drag (`against setal curvature'), opposite to the usual direction for climbing in which they do not adhere. (C) Setal arrays compressed and relaxed along the natural path of drag (`with setal curvature', in the typical orientation that geckos use them to climb.

View larger version (14K): [in a new window]   Fig. 7. Force vs displacement of setal array loaded and unloaded vertically. The initial section of the curve represents preloading of the array, before full contact with the test surface was made. Following preload, the forces of deformation were statistically linear for deformations up to approx. 50% of array height. Solid and broken arrows indicate linear fits for loading and unloading, respectively.

View larger version (23K): [in a new window]   Fig. 8. Effective elastic modulus (Eeff) during deformation of isolated setal arrays. Horizontal labels denote direction of deformation relative to the curvature of the setae. Values are means ± s.e.m. Letters A,B denote significant ANOVA contrasts. Dotted line shows Eeff=100 kPa, the upper limit of Dahlquist's criterion for tack (Dahlquist, 1969; Pocius, 2002).

View larger version (15K): [in a new window]   Fig. 9. Young's modulus (E) of materials including approximate values of bulk ß-keratin and effective modulus (Eeff) of natural setal arrays (Geisler et al., 2005). A value of E100 kPa (measured at 1 Hz) is the upper limit of the Dahlquist criterion for tack, which is based on empirical observations of pressure sensitive adhesives [PSAs (Dahlquist, 1969; Pocius, 2002)]. A cantilever beam model [equation 5.3 (Sitti and Fearing, 2003)] predicts a value of Eeff near 100 kPa, as observed for natural setae and PSAs. It is notable that geckos have evolved Eeff close to the limit of tack. This value of Eeff may be tuned to allow strong and rapid adhesion, yet prevent spontaneous or inappropriate attachment.