Abstract: The conventional pendulum tuned mass damper (PTMD) requires a substantial vertical space, and its alternative, the friction pendulum system tuned mass damper (FPS-TMD), struggles to balance sensitivity with high damping demands. The reliance on singular friction damping can undermine the control effectiveness and precision of TMDs. To overcome these challenges, this study introduces an eddy current-enhanced bidirectional rail pendulum tuned mass damper (ECBRP-TMD), develops a dynamic analysis model for the ECBRP-TMD utilizing Lagrangian equations, and investigates its nonlinear characteristics via the method of slowly varying parameters. Addressing detuning issues triggered by large sliding angles, an innovative periodic robustness design method is proposed and validated via shaking table experiments. Results indicate that the dual damping mechanism enhances the TMD's instantaneous energy dissipation capability and facilitates convenient damping adjustments. The cycloidal trajectory design significantly improves the damping performance of the ECBRP-TMD under high excitation amplitudes without increasing the mass ratio, compared to the circular arc trajectory.