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.