Extended Data Fig. 2: Transducer array design and mechanical testing.

a, Schematic illustration of the mesh-reinforced regions of the adhesive layer. b, Integration of the array with skin using the adhesive layer. c, Layer-by-layer fabrication of the adhesive coupling, schematic illustrations and photographs. d, Photograph of two transducer units positioned inside the controller module and schematic illustrations demonstrating how each modular interconnect layer routes signals through the hexagonal array. During assembly, the internal contacts fold into the core, in which they can be soldered to the coil. e–k, Mechanical response testing for the array. e, Model geometry for mechanical simulation of strain under a unit actuator during skin bending (50 mm radius). f, Simulated strain using a substrate without mesh. g, Simulated strain with a mesh-reinforced substrate. h, Photograph of the haptic array under 20% lateral stretching. i, Numerical simulation of strain within the Dragon Skin/mesh adhesive layer, polyimide interconnects (fracture strain, >7%; ref. ³⁸) and copper traces (fracture strain, >1%; ref. ³⁹) of the array during 20% lateral stretching. j, Photograph of the haptic array under 50-mm bending radius. k, Numerical simulation of strain within the Dragon Skin/mesh adhesive layer, polyimide interconnects and copper traces of the array during bending (50 mm radius). l, Transducer resonance measured across the array periodically by the embedded inductance measurement unit during cyclic deformations of stretching and bending (mean across 19 transducers; bars, standard deviation). m, Torsion angle induced by a kirigami structure (8.5 mm initial height) on a skin phantom (E = 31 kPa) measured periodically during cyclical translation of the top panel by 3 mm (setup shown in inset).