Omnidirectional bending sensor with three-fold structural symmetry enables decoupling of bending angle and direction.

Abstract

Accurate shape sensing requires simultaneous quantification of bending angle (φ) and bending direction (θ). Yet existing bending sensors remain confined to uniaxial or discretized modes, relying on tedious, non-generalizable calibration procedures. Here, we present a snowflake-shaped omnidirectional bending sensor that achieves complete and linear decoupling of φ and θ through a three-fold rotationally symmetric arrangement of strain-sensitive resistors. By harnessing geometric symmetry as a physical prior, we establish a closed-form analytical model and signal projection framework that transform calibration from an empirical process into a simple, quantitative, universal procedure. The sensor is compatible with standard flexible printed circuit board (FPCB) fabrication on polyimide (PI) and polyethylene terephthalate (PET) substrates, ensuring scalability and integration. We demonstrate real-time reconstruction of multidirectional surface deformation and in situ correction of ultrasound imaging artifacts during bending. This symmetry-guided approach redefines the design principles of deformation sensing, providing a general platform for dynamic shape reconstruction and opening avenues for self-adaptive and self-aware electronic systems.