Peking geckos (Gekko swinhonis) traversing upward steps: the effect of step height on the transition from horizontal to vertical locomotion

Abstract

The ability to transition between surfaces (e.g., from the ground to vertical barriers, such as walls, tree trunks, or rock surfaces) is important for the Peking gecko’s (Gekko swinhonis Günther 1864) survival. However, quantitative research on gecko’s kinematic performance and the effect of obstacle height during transitional locomotion remains scarce. In this study, the transitional locomotion of geckos facing different obstacle heights was assessed. Remarkably, geckos demonstrated a bimodal locomotion ability, as they could climb and jump. Climbing was more common on smaller obstacles and took longer than jumping. The jumping type depended on the obstacle height: when geckos could jump onto the obstacle, the vertical velocity increased with obstacle height; however, geckos jumped from a closer position when the obstacle height exceeded this range and would get attached to the vertical surface. A stability analysis of vertical surface landing using a collision model revealed that geckos can reduce their restraint impulse by increasing the landing angle through limb extension close to the body, consequently dissipating collision energy and reducing their horizontal and vertical velocities. The findings of this study reveal the adaptations evolved by geckos to move in their environments and may have applicability in the robotics field.

Appendices

Appendix

Modelling method

The landing behaviour of the gecko in the model is simplified as the collision of a straight rod with the obstacle, after which the two were combined as a whole without being bounced off. The effective extension lengths of the forelimbs and hindlimbs pointing toward the vertical landing surface were represented by a and b, respectively (Fig. 5a). The relationship between the calculated angle $\theta_{1}$, and the landing angle $\theta$ are provided by Eq. (A1), and Fig. 5c revealed the relationship between $\theta_{1}$ and θ under different effective leg lengths a:

$$ a\sin \theta_{1} = 0.5l\sin \left( {\theta - \theta_{1} } \right) $$

(A1)

where a is the effective length of the forelimbs and l is the length from the shoulder joint to the hip joint.

Through the collision model (Fig. 5b), the mechanism of the gecko to reduce the restraint reaction and improve the landing stability is analysed. The smaller the restraint impulse, the easier it is to achieve stable adhesion. The normal, tangential and rotational restraint impulse ($I_{X}$, $I_{Z}$, and $I_{\theta 1}$) received by point H in the model presented are given by Eqs. (A2–A4), respectively:

$$ I_{X} = m\frac{{3V_{X} {\text{sin}}^{2} \theta_{1} - 3V_{Z} {\text{sin}}\theta_{1} {\text{cos}}\theta_{1} + L\omega {\text{sin}}\theta_{1} - 4V_{X} }}{4} $$

(A2)

$$ I_{Z} = m\frac{{3V_{Z} {\text{cos}}^{2} \theta_{1} - 3V_{X} {\text{sin}}\theta_{1} {\text{cos}}\theta_{1} - L\omega {\text{cos}}\theta_{1} - 4V_{Z} }}{4} $$

(A3)

$$ I_{\theta 1} = - \hat{\lambda }_{1} L{\text{sin}}\theta_{1} + \hat{\lambda }_{2} L{\text{cos}}\theta_{1} $$

(A4)

where the value of L is half of the length of the rod HT, $\omega$ is the angular velocity at landing, and $V_{Z}$ and $V_{X}$ are the vertical and horizontal landing velocity, respectively.