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. 2021 Dec 16;11:24125. doi: 10.1038/s41598-021-03588-y

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© The Author(s) 2021

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 licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence 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 licence, visit http://creativecommons.org/licenses/by/4.0/.

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Magnetic-based transduction method of the MST Sensor. (A) A single three-layer block with integrated permanent magnet as stimulus, and magnetometer covered by a 3D printed holder. (B) Schematic cross-section of the single block. (C) The variation of the overall magnetic field with respect to the displacement of the permanent magnet in the top layer. (D) The variation of the $Δ B / B_{0}$ with respect to the permanent magnet displacement (left y-axis), linear fitting (red lines) at three locking stages (highlighted background in green, yellow, and red), and gradient of linear fitting (right y-axis) corresponding to $(Δ B / B_{0}) / Δ d$ . (E) The variation of the applied force with respect to the displacement of top layer (left y-axis) linear fitting (red lines) at three locking stages, and gradient of linear fitting (right y-axis), corresponding to the stiffness of different layers of the block ( $k = Δ F / Δ d$ ). (F) The variation of the $Δ B / B_{0}$ with respect to the applied force (left y-axis), linear fitting (red lines) at three locking stages, and gradient of linear fitting (right y-axis), corresponding to the multiple sensitivities of the MST sensor at different force sensing ranges ( $S = (Δ B / B_{0}) / Δ F$ ).