Meeting Abstract
A frog jump is both simple and difficult to comprehend. The centre-of-mass (COM) follows a 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-recognised problem of converting non-linear 3D motion of the leg segments to linear 2D motion of the COM. We use mathematical approaches borrowed from robotics to address: How do frogs manipulate the flow of kinetic energy through their body to influence jump trajectory? We address: 1) Transfer of motion through kinematic transmission and 2) transfer of motion through dynamic coupling of segment mass-inertia properties. We used a quaternion-based approach to explore how non-linear leg motions convert to nearly linear/planar torso motion for effective jumping. We found that segment rotations follow nearly linear paths not in Euclidean space, but in 4D unit quaternion space. The shank acted as a steering rod to transmit motion from hip and ankle joints to influence upward versus forward motion of the torso. Additionally, we developed a multi-body simulation to explore how segment acceleration induces rotations at neighbouring segments (without bi-articular muscles). Frogs famously extend their back early in jumps. We found that this ilio-sacral joint rotation causes counterbalancing torques which are potentially used to tune the extent and timing of elastic energy storage-release in tendons. Thus, this inertial coupling mechanism is likely crucial not only for fine-tuning the flow of kinetic energy among segments, but also for modulating the direction of travel.
