Fig. 1: Structural design and moving mechanism of the BHMbot.

a Optical photo of an untethered BHMbot integrated with a lithium battery and an onboard power and control circuit (a ruler is used to show the scale). b Three-dimensional model to show the structural details of the BHMbot. c Enlarged top view of the actuation mechanism composed of an electromagnetic actuator, a transmission and a front leg. L1, L2 and L3 represent three linkages of the transmission. The reciprocating linear motion of the electromagnetic actuator is transformed into the swing motion of the front leg. d, e High-speed images showing the motions of two front legs of the BHMbot (prototype #1) under two in-phase driving signals and two out-of-phase driving signals, respectively. f Diagrams illustrating the generation of the bouncing momentum for the BHMbot during an actuation cycle of the front leg. g Diagrams showing the bouncing movements of the BHMbot. h Series of high-speed images showing one bouncing cycle during the running process of the BHMbot (prototype #1), including initial, squatting, bouncing, aerial, and landing phases. All images are from different parts of Supplementary Movie 2. i Measurements of the vertical position of the rear and front feet of the BHMbot relative to the ground during one bouncing cycle. The gray dotted line represents the ground. When all the rear and front feet are off the ground, the BHMbot is in the aerial phase (shown as the blue area).