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. 2022 Aug 9;13:4456. doi: 10.1038/s41467-022-32123-4

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© The Author(s) 2022

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.

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Fig. 3 — a Lorentz forces acting on the various parts of the liquid metal coils in the external magnetic field ( $B$ ), top view; current ( $I$ ) is indicated by the counterclockwise arrows. The force pairs ( $F_{1 A}$ , $F_{1 B}$ ) and ( $F_{2 A}$ , $F_{2 B}$ ) are perpendicular to the bending direction and cancel. The central pair ( $F_{1 L}$ , $F_{2 R}$ ) also cancels in the overall balance. b Free-body diagram of curved SEMR with the remaining relevant loading Lorentz forces ( $F_{1 R}$ , $F_{2 L}$ ), side view. Gravity force ( $G$ ) is applied to the center of mass (COM); the normal supporting forces ( $F_{s 1}$ , $F_{s 2}$ ) and frictional forces ( $F_{f 1}$ , $F_{f 2}$ ) are indicated as well. c Running mechanism of the SEMR TST on an asymmetrically structured substrate. d Key stages for the walking SEMR TST driven by a square-wave current (0.3 A, 1 Hz). e Snapshots of the running SEMR TSTS driven by square-wave currents (0.3 A, 55 Hz and 0.5 A, 45 Hz), as indicated. The time between the snapshots is 0.05 s. The bottom sequence corresponds to the maximum speed of 70 BL/s. f Running mechanism of the SEMR with the L-shaped feet. g Key stages for the walking SEMR TST driven by a square-wave current (0.2 A, 1 Hz). h Snapshots of the running SEMR TL driven by square-wave currents (0.3 A, 40 Hz and 0.4 A, 30 Hz), as indicated. The time between the snapshots is 0.05 s. The bottom sequence corresponds to the maximum speed of 35 BL/s. i Maximum speed of the SEMR TST driven by square-wave currents as a function of frequency at different amplitudes (0.3 A, 0.4 A and 0.5 A). j Maximum speed of the SEMR TL driven by square-wave currents as a function of frequency at different amplitudes (0.2 A, 0.3 A and 0.4 A). k Maximum running speed of SEMR TL on different substrates, including various sandpapers (Sp-p80, p180 and p400), elastomer (PDMS), paper, wood, metal, plastic and glass (Supplementary Movie 3). All error bars represent the standard deviation of four measurements. All snapshots are from different parts of Supplementary Movie 3.