Fig. 5: Actuations of the magneto-origami spring actuator.

a The spring actuator can contract when the magnet is placed in its axial direction. b The contraction ratio \(({L}_{0}-L)/{L}_{0}\) of the spring actuator plotted as a function of magnetic field strength up to 220 mT. c The spring actuator remains 93% of the original length \({L}_{0}\) after a 1000-cycle actuation (B ~220 mT). d Bending behaviors of the spring actuator. Panels show bending angles are 0°, 45°, 90°, 180°, respectively. e The 360° rotation behavior of a bent spring actuator by rotating the magnet surrounding the actuator. The yellow arrow represents the rotation direction of the rotating magnet. f Experimental demonstration of the rolling locomotion of the spring actuator by passing through several obstructions including stairs, obstacles, narrow path, and groove. The height of the stair, obstacle, and narrow path is 10, 10, and 12 mm, respectively. The width of the groove is 10 mm. Quantitative control schemes are provided in which rational angle \(\alpha \) (left axis, blue curve) and distance d between the magnet and magneto-origami spring actuator is plotted as a function of the magnet position.