Energy Flow in Multibody Limb Models: A Case Study in Frogs

A frog jump is both simple and difficult to comprehend. The center-of-mass (COM) follows a two-dimensional (2D) path; it accelerates diagonally upward, then traces a predictable arc in flight. Despite this simplicity, the leg segments trace intricate trajectories to drive the COM both upwards and forwards. Because the frog sits crouched with sprawled legs, segments must pivot, tilt, and twist; they solve a long-recognized problem of converting non-linear 3D motion of the leg segments to linear 2D motion of the COM. I use mathematical approaches borrowed from robotics to address: How do frogs manipulate the flow of kinetic energy through their body to influence jump trajectory? I address (1) transfer of motion through kinematic transmission and (2) transfer of motion through dynamic coupling of segment mass-inertia properties. Using a multi-body simulation, I explore how segment acceleration induces rotations at neighboring segments (even without accounting for bi-articular muscles). During jumps, this inertial coupling mechanism is likely crucial for modulating the direction of travel. The frog case study highlights a useful computational framework for studying how limb joints produce coordinated motion.

The dynamic role of the ilio-sacral joint in jumping frogs

A striking feature among jumping frogs is a sharp pelvic bend about the ilio-sacral (IS) joint, unique to anurans. Although this sagittal plane hinge has been interpreted as crucial for the evolution of jumping, its mechanical contribution has not been quantified. Using a model based on Kassina maculata and animated with kinematics from prior experiments, we solved the ground contact dynamics in MuJoCo enabling inverse dynamics without force plate measurements. We altered the magnitude, speed and direction of IS extension (leaving remaining kinematics unaltered) to determine its role in jumping. Ground reaction forces (GRFs) matched recorded data. Prior work postulated that IS rotation facilitates jumping by aligning the torso with the GRF. However, our simulations revealed that static torso orientation has little effect on GRF due to the close proximity of the IS joint with the COM, failing to support the ‘torso alignment’ hypothesis. Rather than a postural role, IS rotation has a dynamic function whereby angular acceleration (i) influences GRF direction to modulate jump direction and (ii) increases joint loading, particularly at the ankle and knee, perhaps increasing tendon elastic energy storage early in jumps. Findings suggest that the pelvic hinge mechanism is not obligatory for jumping, but rather crucial for the fine tuning of jump trajectory, particularly in complex habitats.

The adaptation to standing long jump distance in parkour is performed by the modulation of specific variables prior and during take-off

The present study aimed at investigating different variables that can be manipulated prior to and during take-off, to execute a specific standing long jump (SLJ) distance, according to jump expertise in parkour practitioners (= traceurs). Fourteen healthy young traceurs were included and separated into two groups: beginners (BEG) and experts (EXP). Firstly, classical vertical jump battery was used to characterize participants arm use and leg efficiency. Secondly, standing long jump (SLJ) performances were analyzed at four distances: 70, 80, 90, and 100% of each participant’s maximal SLJ distance. The force-time curves of the ground reaction forces (GRF) and the center of pressure (CoP) trajectory were measured with a force platform during the jump impulses. Take-off speed, angle and jump trajectory were estimated. For all of the participants, take-off speed and angle, power output, and vertical GRF during jump preparation (counter movement) varied with distance. The EXP group exhibited greater backward CoP excursion, greater arm participation, greater take-off velocity and a greater modulation of take-off angle than BEG group. When comparing jumps of similar distance, EXP exhibited a more curvilinear trajectory with a higher peak than BEG. To conclude, different motor strategies can be adopted based on the jump distance, and these strategies can evolve as parkour experience increases.

Dynamics and stability of directional jumps in the desert locust

Locusts are known for their ability to jump large distances to avoid predation. The jump also serves to launch the adult locust into the air in order to initiate flight. Various aspects of this important behavior have been studied extensively, from muscle physiology and biomechanics, to the energy storage systems involved in powering the jump, and more. Less well understood are the mechanisms participating in control of the jump trajectory. Here we utilise video monitoring and careful analysis of experimental directional jumps by adult desert locusts, together with dynamic computer simulation, in order to understand how the locusts control the direction and elevation of the jump, the residual angular velocities resulting from the jump and the timing of flapping-flight initiation. Our study confirms and expands early findings regarding the instrumental role of the initial body position and orientation. Both real-jump video analysis and simulations based on our expanded dynamical model demonstrate that the initial body coordinates of position (relative to the hind-legs ground-contact points) are dominant in predicting the jumps’ azimuth and elevation angles. We also report a strong linear correlation between the jumps’ pitch-angular-velocity and flight initiation timing, such that head downwards rotations lead to earlier wing opening. In addition to offering important insights into the bio-mechanical principles of locust jumping and flight initiation, the findings from this study will be used in designing future prototypes of a bio-inspired miniature jumping robot that will be employed in animal behaviour studies and environmental monitoring applications.

Variability in escape trajectory in the Trinidadian stream frog and two treefrogs at different life-history stages

Most studies investigating anuran jumping behaviour have examined the relationship between body size and parameters such as jump distance, velocity, and force; however, few have investigated jump trajectory. We constructed an arena to determine escape trajectories in relation to the direction of an artificial stimulus in the aromobatid Mannophryne trinitatis (Garman, 1888) and two treefrogs, Trachycephalus venulosus (Laurenti, 1768) and Hypsiboas geographicus (Spix, 1824). Three categories of M. trinitatis (i.e., tadpole-transporting males, nontransporting males, and females) and three ontogenetic stages of the treefrogs were compared. Mannophryne trinitatis escaped in a broadly predictable trajectory away from the stimulus, although jump trajectories were highly variable, suggesting a degree of unpredictability. No systematic differences were found between categories of M. trinitatis, adding to the findings of previous studies that larval transport incurs no measurable locomotor costs on antipredatory jumping behaviour with regards to jump angle and distance. The treefrogs showed similar patterns of escape trajectory and unpredictability. There were no consistent differences between life-history stages and no relationship between distance jumped and angular deviation. In M. trinitatis and H. geographicus, there was some evidence of bimodality in escape trajectory. The results are discussed in the context of other work on escape trajectories and the concept of “protean” defence strategies.