Fig. 1

Assembly and sensing mechanisms of the compliant m-MEMS platform. a Schematic structure of the m-MEMS platform. b Mechanisms of the touchless (proximity) and tactile (pressure) sensing modes. The GMR sensor is biased by the built-in magnetic field (yellow cloud; only the field on the sensor side is sketched) of a compliant permanent magnet with pyramid-shaped extrusions. The m-MEMS is exposed to an external magnetic field with the opposite polarity (blue cloud) to the one of the built-in magnet. c The m-MEMS platform unambiguously discriminates touchless and tactile interaction modes, as the corresponding signals are located at different ranges with respect to a safety window (orange-shaded stripe). Since the signals are not overlapping, this method does not depend on the history of the interaction process (Supplementary Figs. 7 and 11). Optical images of (d) a PDMS frame with a blind hole, (e) a compliant permanent magnet with pyramid-shaped extrusions on its top surface, and (f) a GMR sensor on a polymeric foil. (g) Optical microscopy image (with false color) of the cross-section of the m-MEMS platform. SEM images of the pyramid-shaped extrusions in (h) low and (i) high magnification. j Cross-sectional SEM image of a compliant permanent magnet. k Simulated magnetic field profile above the compliant permanent magnet with pyramid-shaped extrusions (magnetized in a field of 1.5 T, Supplementary Fig. 5). l Simulated magnetic field profile between a pyramid tip and the GMR sensor. m The experimentally measured change of the electrical resistance (ΔR/R₀) of the GMR sensor in response to an applied external magnetic field. ΔR = R₀−R, R₀ and R are the initial and real-time resistance of the GMR, respectively