Legged jumping robots generate highly dynamic motions through linkage rotations, making closed-form solutions difficult to obtain. To predict jumping performance, we used a Lagrangian-based model and analyzed the system through numerical simulation. We focused on the ground reaction force and its duration, since the results determine the robot’s takeoff momentum. In this context, I contributed to two projects:

(A) Leg compliance for improved energy utilization

Legged jumping robots can lose ground contact before the stored energy is fully released. Because the leg transmits the actuation force to the ground, appropriately tuned compliance allows the leg to deflect under load and delays liftoff, extending contact time so that the stored energy is more fully utilized—thereby improving jumping performance. We modeled compliant legs using a pseudo-rigid-body model (PRBM), conducted a Lagrangian-based parameter study, and validated it experimentally.

(B) Surface-tension–dominated water takeoff

On water, surface tension behaves like a spring up to a breakaway threshold; once this threshold is exceeded, the surface ruptures and the input energy can be lost to splashing rather than contributing to takeoff. Therefore, ground-like jumping on water requires keeping the reaction force below the threshold while extending force application time to generate sufficient momentum. We designed a torque-reversal mechanism with long compliant legs to regulate reaction force below the threshold. I conducted a Lagrangian-based parameter study, fabricated the robot, and performed experimental demonstrations.