Extended Data Fig. 3: Direct-actuated jumper simulations.

a, The produced energy specific to the jumper mass. b, The centre-of-mass kinetic energy, specific to the jumper mass. c, The acceleration time. d, The optimal fixed reduction, G, producing the highest acceleration velocity for each jumper scale. The simulations are performed (i) for biological jumpers with fixed reductions of 0.01, 0.1, and 1 (dotted lines), and (ii) for biological jumpers (blue solid) and engineered jumpers (red solid: no linkage; red dotted: with linkage) using variable reduction to operate at maximum power. Each fixed reduction is only possible up to a limiting scale, where the motor force balances the body weight. Biological jumpers operating at full power are also limited in scale, as the motor runs out of stroke. Consequently, biological energy production is always limited by the motor energy (black dashed line). Finally, when operating at the optimal fixed or full-power variable reduction, the acceleration time scales with a 2/3 power of size, reflected in the same scaling in energy and gear reduction.