Geometry-controlled instability pathway selection in elastic helices enables fast, efficient robotic locomotion

Mechanical instabilities can convert slow actuation into rapid, amplified motion, but predicting whether a three-dimensional elastic structure buckles smoothly or snaps remains challenging. Here, we show that helix geometry and boundary loading jointly select continuous buckling or snap-through in elastic filaments. Combining nonlinear rod theory, simulations, and high-throughput robotic arm experiments, we establish a predictive pathway map and identify snap-through as a robust mechanism for repeatable motion amplification under simple boundary actuation. Guided by this map, we design a snap-actuated helical limb that converts small end rotations into rapid global reconfiguration and cyclic energy release. Integrated into an untethered robot, this limb enables sustained hopping across wood, cloth, acrylic, leather, grass, and sand, reaching 3.21 body lengths per second with an electrical cost of transport of 4.79. Controlled comparisons with a rigid-legged robot show that snap-through drives the gains in speed, efficiency, and terrain robustness. The same limb architecture also enables agile turning, repeated back-flips, and swimming.