Finite-Stroke Magnetic Quasi-Zero-Stiffness Electromagnetic Harvester for Foot-Worn Sensors: Reproducible Numerical Design Under Public Foot-IMU Excitation.

Foot-worn electromagnetic harvesters are driven by irregular rigid-body motion, while their response is limited by mechanical stroke, coil geometry, mounting direction, and the electrical interface. This paper presents a reproducible numerical design study of a finite-stroke magnetic quasi-zero-stiffness (QZS) moving-magnet harvester. Two public three-axis foot-IMU records are processed with stated gyroscope-bias estimation, six-axis attitude estimation, gravity removal, residual-offset correction, filtering, and angular-acceleration calculation. Three explicit axes are used in the design screen, and the selected candidate is then evaluated over a 62-direction spherical grid. Rigid-body angular-acceleration and centripetal terms are included for specified sensor-to-harvester offsets. Two normalized magnetic force laws are compared. The electrical model uses position-dependent flux linkage, explicit series connection and polarity of coil sections, winding-derived resistance, and a position-dependent electromagnetic reaction force. A fixed-seed random screen evaluates 720 geometry-constrained candidates. The highest-ranked nominal candidate is a 150 mm external foot-worn module with a 40.6 g moving mass, a 30 mm hard half-stroke, 1649 turns in two series sections, and a 25.27 mm coil outer diameter. Across 72 design-screen cases formed from 12 five-second windows, three mounting axes, and two magnetic laws, this candidate remained hard-stroke- and design-stroke-safe. Its conditional ideal load-side power had a 10th percentile of 1.38 mW and a median of 2.03 mW. In the 62-direction check, all 1488 cases remained hard-stroke-safe; two opposite directions each produced one design-stroke exceedance, with a maximum displacement of 24.15 mm. Re-ranking all 30 Stage-2 candidates under coupling and magnetic-stiffness changes retained the long geometry family, although a 30% coupling reduction changed the highest-ranked candidate from 600 to 632. Soft-stop sensitivity, equation-level consistency, and multi-case Runge-Kutta convergence are also reported. The results support finite-stroke design screening, but they do not constitute prototype, finite-element, or delivered-power validation.