Kinematics and energetics of the desert locust (Schistocerca gregaria) when jumping from compliant surfaces

Abstract

Animals often leap from substrates that give way under them, such as leaves, soft ground or flexible branches. This provides an added complexity for latch-mediated spring-actuated (LaMSA) jumping animals because the spring-loaded system often works so quickly that neural feedback cannot adjust for errors caused by a yielding substrate. We studied a LaMSA jumper, the grasshopper, to determine how the mechanical properties of a substrate giving way under them would affect the kinematics of the jump. We measured this by allowing grasshoppers to leap from two diving boards, a long one that could generate a whole range of relative stiffnesses, and a shorter, much lighter, but stiffer board. Substrate stiffness was manipulated by then placing the grasshopper on different locations on that diving board, presenting from 30% of the grasshopper's leg stiffness to 200 times the grasshoppers leg stiffness. For platform stiffnesses that were less than that of the grasshopper, take-off velocity and kinetic energy were reduced, but jump elevation (the jump trajectory) was unaffected. For stiffnesses that were greater than that of the grasshopper, there was no effect on take-off velocity and kinetic energy. When jumping from an extremely light and stiff substrate, recoil of the surface allowed the grasshopper to recover some of the lost energy. Consequently, when jumping from substrates that are less stiff than they are (such as floppy leaves), grasshoppers must contend with lower take-off velocities, but jump direction is unaffected.

Keywords: Biomechanics; Energy; Jumping; LaMSA; Locomotion; Locust.

Fig. 1.

Experimental set-up for recording of jumps. (A) Top view. (B) Camera view. The platform (2) was fixed with Blu-tack to the fixed elevated box (8), allowing the platforms to be changed throughout the course of the experiment. For a scaled illustration of the platforms, see Fig. S1.

Fig. 2.

Example still images from a high-speed video of a control grasshopper jump. (A) Example of a control grasshopper pre-jump with a calibration to 1 cm (blue bar in A) of film. Close-up images from a grasshopper control jump (B) at the last frame of tarsi–platform contact (0 ms) and (C) 10 frames later (10 ms), displaying the plot points at the same coxa–body joint at 0 and 10 ms.

Fig. 3.

Relative velocity across different platforms and platform stiffnesses. The horizontal grey line marks 1, where below this line shows velocity decrease compared with the control jumps. The vertical grey bar shows the mean grasshopper stiffness (3.42 N m⁻¹). Asterisks indicates data points significantly differing from 1.0 (where v_g=mean v_c). Trendlines were generated based on output from linear mixed effect regression analysis of the data (see Table 1). Values are means±s.e.m. of n=40 [n=21 for platform A (red) and n=19 for platform B (black)].

Fig. 4.

Relative kinetic energy density across different platforms and platform stiffnesses. The horizontal grey line marks 1, where below this line shows a decrease in kinetic energy density compared with the control jumps. The vertical grey bar shows the mean grasshopper stiffness (3.42 N m⁻¹). Asterisks indicate data points significantly differing from 1.0 (where KED_g=mean KED_c). Trendlines were generated based on output from linear mixed effect regression analysis of the data (see Table 1). Values are means±s.e.m. of n=40 [n=21 for platform A (red) and n=19 for platform B (black)].

Fig. 5.

Relative acceleration across different platforms and platform stiffnesses. The horizontal grey line marks 1, where below this line shows acceleration decrease compared with the control jumps. The vertical grey bar shows the mean grasshopper stiffness (3.42 N m⁻¹). Trendlines were generated based on output from linear mixed effect regression analysis of the data (see Table 1). Values are means±s.e.m. of n=40 [n=21 for platform A (red) and n=19 for platform B (black)].

Fig. 6.

Relative power density across different platforms and platform stiffnesses. The horizontal grey line marks 1, where below this line shows a decrease in power density compared with the control jumps. The vertical grey bar shows the mean grasshopper stiffness (3.42 N m⁻¹). Trendlines were generated based on output from linear mixed effect regression analysis of the data (see Table 1). Values are means±s.e.m. of n=40 [n=21 for platform A (red) and n=19 for platform B (black)].

Fig. 7.

Energy recovery from a compliant platform. (A) A grasshopper jumping from a compliant substrate of 24 N m⁻¹, platform B. 0 ms was prior to any metathoracic leg extension, 25 ms was at maximum platform displacement (i.e. displaced to its lowest point) and 28 ms was at take-off. The purple marker was a fixed point on the platform that was tracked across the jump. (B) A graphical representation of the displacement of the purple tracked point on the platform. Between 0 and 25 ms, energy is dissipated to the platform as it is moved in a downward direction. Between 25 and 28 ms, the platform moved in an upward direction while the grasshopper remained in contact with it, allowing the grasshopper to recover energy from the recoiling platform during this 3 ms period.