The synergy between the insect-inspired claws and adhesive pads increases the attachment ability on various rough surfaces

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1 The synergy between the inset-insired laws and adhesive ads inreases the attahment ability on various rough surfaes Yi Song 1, 2, Zhendong Dai 1, Zhouyi Wang 1, Aihong Ji 1 1, 3,*, and Stanislav Gorb 1 Institute of Bio-insired Struture and Surfae Engineering, anjing University of Aeronautis and Astronautis, 29 Yudao Street, , anjing, China 2 College of Mehanial and Eletrial Engineering, anjing University of Aeronautis and Astronautis, 29 Yudao Street, ,anjing, China 3 Deartment of untional Morhology and Biomehanis, Kiel University, Am Botanishen Garten 1 9, D Kiel, Germany * Corresonding Author: , zddai@nuaa.edu.n, sgorb@zoologie.uni-kiel.de 0. Sulementary A. ores measured on the three kinds of attahment devies When the stiff biomimeti tarsus with two laws interats with the large sherial rotrusions, the measured fores are aused by the ontat frition between law tis and shere surfae aserities. Due to the ontat frition between law tis and sheres, the lateral fores inreased, while the normal fores dereased ontinuously until the law tis slied off the sheres (ig.s1). The adhesive ad stuk to the to of rotrusions and bore shearing and eeling fores. When eeled vertially, two eak fores were observed, beause the ohesive fore of the adhesive ad was smaller than the maximum adhesive fore. While sheared horizontally, frition fores initially inreased and dereased later (ig.s2). In the tarsus onsisting of both laws and adhesive ad, the measured fores urves were slightly similar to those obtained on the stiff laws exet for the magnitudes and durations of eak attahment fores. However, the reation fores did not vary linearly, beause of the ation of the adhesive ad (ig.s3). It is worth noting that for all exeriments, the reation fores in fore-and-aft diretion were slightly invariable, if omared with normal and lateral fores, indiating that interations at the two law tis were almost symmetri.

2 Sulementary igure S1. The 3-d reation fores of the stiff law with two law tis on shere rotrusions with different radii. A. R = 7.00mm. B. R = 8.00 mm. C. R = 9.00 mm. D. R = mm. D. R = mm. D. R = mm. Sulementary igure S2. The eeling and shearing fores of emloyed adhesive on sherial rotrusions with different radii. A. Peeling, R = 8.00 mm. B. Peeling, R = mm. C. Peeling, R = mm. D. Shearing, R = 8.00 mm. D. Shearing, R = mm. D. Shearing, R = mm. The initial ressures are about 0.37 and there was no signifiant differene among the initial ressures (>0.05).

3 Sulementary igure S3. The 3-d reation fores of ombined tarsus devie onsisting of aired laws and adhesive ad on sherial rotrusions with different radii. A. R = 7.00 mm. B. R = 8.00 mm. C. R = 9.00 mm. D. R = mm. D. R = mm. D. R = mm. 1. Sulementary B. Model of the ontat between attahment devies and large rotrusions To establish the model, four assumtions were made as follow: (1) When attahment is stable, the onfiguration of the tarsus devie does not hange; (2) rition f and the loal suort fore S at law tis an be desribed by f =μsmax S; (3) The adhesive ad stiks to the to of large rotrusions. (4) The two laws are symmetrial and the enter of the adhesive ad is oinident with the symmetry lane; Based on these assumtions, a model was established (ig.s4 A). ig.s4 B shows a sketh of the reation fores. P1, P2 and P3 are the ontat enters of law tis and adhesive ad, resetively. A oordinate system is set u and shown in ig.s4. θ is the ontat angle and γ is the vertially rojeted angle between lines (P1O and P2O) from the two law tis to the shere enter. S-l and S-r are the loal suort fores at the two law tis, while f-l and f-r are the orresonding frition fores;, and are the 3D reation fores at the adhesive ad whih are orrelated with the ressure and the ad

4 itself. Then, the 3D reation fores at the two tis an be exressed in the oordinate system as follow: (os sin ) r S r s max (sin os ) r S r s max (os sin ) l S l s max (sin os ) l S l s max, (S1) Then the resultant fores an be written as ( r l )sin 2 ( r l )os 2, (S2) l r By submitting equation (S1) to (S2), we get: ( S r S l )(os smax sin )sin 2 ( S r S l )(os smax sin )os 2, (S3) ( )(sin os ) S r S l γan be alulated from ig. S1 B: smax PP, (S4) sin O 2 os 1P1 R where δ is the ga between the two tis and R is the radius of rotrusions. Aording to the assumtion (1), δ is onstant. To simlify, the loal suort fores S-r and S-l are regarded to be equal, whih is in agreement with our exeriments results. Thus, 0 2 s (os s max sin )os 2 2 (sin os ) s s max, (S5) Aording to equation (S5), lateral fores will derease with the inrease of ontat angle, while the normal fores will inrease. Obviously, the equation (S5) is similar to our revious Dai- Gorb-Shwarz model 1. If we take the adhesive ad into onsideration, the equation (S5) an be extended as

5 0 2 S (os smax sin )os 2 2 (sin os ) S smax, (S6) Equation (S6) indiates that when the substrate rotrusions are very large (i e. θ 90 ), the ation of laws will be enhaned signifiantly if the ad adheres well. While if the rotrusions are small (i e. θ 0 ), the inter-loking between law and substrates are strong enough to revent the devie detah even the adhesive ad work oorly. Sulementary igure S4. A. 3D ontat model. B. The sketh of 3D reation fores of the biomimeti tarsus devies. Referenes 1. Dai, Z., Gorb, S.. & Shwarz, U. Roughness-deendent frition fore of the tarsal law system in the beetle Pahnoda marginata (Coleotera, Sarabaeidae). J. Ex. Biol. 205, (2002).