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

To attach reliably on various inclined rough surfaces, many insects have evolved both claws and adhesive pads on their feet. However, the interaction between these organs still remains unclear. Here we designed an artificial attachment device, which mimics the structure and function of claws and adhesive pads, and tested it on stiff spheres of different dimensions. The results show that the attachment forces of claws decrease with an increase of the sphere radius. The forces may become very strong, when the sphere radius is smaller or comparable to the claw radius, because of the frictional self-lock. On the other hand, adhesive pads generate considerable adhesion on large sphere diameter due to large contact areas. The synergy effect between the claws and adhesive pads leads to much stronger attachment forces, if compared to the action of claw or adhesive pads independently (or even to the sum of both). The results carried out by our insect-inspired artificial attachment device clearly demonstrate why biological evolution employed two attachment organs working in concert. The results may greatly inspire the robot design, to obtain reliable attachment forces on various substrates.

Due to the contact friction between claw tips and spheres, the lateral forces increased, while the normal forces decreased continuously until the claw tips slipped off the spheres (Fig.S1). The adhesive pad stuck to the top of protrusions and bore shearing and peeling forces. When peeled vertically, two peak forces were observed, because the cohesive force of the adhesive pad was smaller than the maximum adhesive force. While sheared horizontally, friction forces initially increased and decreased later ( Fig.S2). In the tarsus consisting of both claws and adhesive pad, the measured forces curves were slightly similar to those obtained on the stiff claws except for the magnitudes and durations of peak attachment forces. However, the reaction forces did not vary linearly, because of the action of the adhesive pad (Fig.S3). It is worth noting that for all experiments, the reaction forces in fore-and-aft direction were slightly invariable, if compared with normal and lateral forces, indicating that interactions at the two claw tips were almost symmetric.

Supplementary B. Model of the contact between attachment devices and large protrusions
To establish the model, four assumptions were made as follow: (1) When attachment is stable, the configuration of the tarsus device does not change; (2) Friction Ff and the local support force FS at claw tips can be described by Ff =μsmax×FS; (3) The adhesive pad sticks to the top of large protrusions.
(4) The two claws are symmetrical and the center of the adhesive pad is coincident with the symmetry plane; Based on these assumptions, a model was established (Fig.S4 A). Fig.S4 B shows a sketch of the reaction forces.
P1, P2 and P3 are the contact centers of claw tips and adhesive pad, respectively. A coordinate system is set up and shown in Fig.S4. θ is the contact angle and γ is the vertically projected angle between lines (P1O and P2O) from the two claw tips to the sphere center. FS-l and FS-r are the local support forces at the two claw tips, while Ff-l and Ff-r are the corresponding friction forces; F F p , F L p and F N p are the 3D reaction forces at the adhesive pad which are correlated with the pressure and the pad itself. Then, the 3D reaction forces at the two tips can be expressed in the coordinate system as follow: γcan be calculated from Fig. S1 where δ is the gap between the two tips and R is the radius of protrusions. According to the assumption (1), δ is constant.
To simplify, the local support forces FS-r and FS-l are regarded to be equal, which is in agreement According to equation (S5), lateral forces F L c will decrease with the increase of contact angle, while the normal forces F N c will increase. Obviously, the equation (S5) is similar to our previous Dai-Gorb-Schwarz model 1 .
If we take the adhesive pad into consideration, the equation (S5) can be extended as s max s max 0 2 (cos sin ) cos 2 2 (sin cos ) Equation (S6) indicates that when the substrate protrusions are very large (i e. θ→90°), the action of claws will be enhanced significantly if the pad adheres well. While if the protrusions are small (i e. θ→0°), the inter-locking between claw and substrates are strong enough to prevent the device detach even the adhesive pad work poorly.
Supplementary Figure S4. A. 3D contact model. B. The sketch of 3D reaction forces of the biomimetic tarsus devices.