Spring-Mass Runner: Leg-Stiffness Gait Dynamics (2D)

This 2D simulator is the running-gait companion to the 3D compass-gait walker, and it uses a genuinely different mechanism to get there: rather than a rigid leg rotating as an inverted pendulum, the leg here is modelled as a real one-sided damped spring, integrated as full two-dimensional Cartesian dynamics (not a single angle) with a fourth-order Runge–Kutta solver. During stance the compressing leg stores elastic energy exactly as an Achilles tendon or a running-blade prosthesis does, releasing it again as the leg extends; between stances the body is genuinely airborne, a true ballistic flight the rigid-leg walker never has. Two independent active-thrust controls — one regulating forward speed, one regulating hop height — replace the energy that a small tissue-damping term and each landing's touchdown braking remove every stride, the running-gait equivalent of the compass gait's push-off. Tune the touchdown angle, leg stiffness and thrust gain to watch the runner settle into an exact, repeating stride (or decelerate and stumble if the active thrust can't keep up) — the same elastic-recoil-versus-collision-loss trade-off that separates running-blade prosthetic design and exoskeleton-assist tuning from the rigid-leg walking case.