A Modified 2-DoF Wave Buoy with an Embedded Tunable Magnetic-Spring Electromagnetic Energy Harvester: Concept, Dynamic Modeling and Numerical Analysis

This paper presents a modified two-degree-of-freedom wave buoy with an embedded tunable magnetic-spring electromagnetic energy harvester. The proposed device is modeled as a branched kinematic chain composed of a rotational–rotational buoy mechanism and a rotational–prismatic harvester branch sharing the first revolute joint. Two harvester orientations are considered and compared. The mathematical model is formulated using homogeneous transformations, velocity Jacobians and Lagrange equations. Particular attention is paid to the structure of the inertia matrix and to the way in which its inverse transmits generalized forces between the rotational coordinates and the translational motion of the moving magnet. The model is implemented in MATLAB/Simulink R2024b and evaluated under free-response, regular-wave, and bidirectional frequency-sweep excitation scenarios. Under regular-wave excitation, Config. 1 produces approximately 19.3 and 2.98 times greater average load power than Config. 2 for moving-assembly masses of 5 g and 268 g, respectively. The frequency-sweep results show that the preferred harvester orientation depends on the excitation frequency and moving-assembly mass. No resolved sweep-direction dependence is observed for 5 g, whereas for 268 g the identified hysteresis intervals are approximately 0.53 rad/s for Config. 2 and 0.64 rad/s for Config. 1. These results provide design guidelines for selecting the harvester orientation and moving mass in compact wave-excited buoy systems.