<p>The ability to design linear systems exhibiting non-reciprocal wave propagation would enable precise control of mechanical signals for filtering and vibration control. This study presents a macroscopic mechanical metamaterial with a time-varying radius based on crank-slider mechanisms. A hierarchical framework is established, formed by supercells, with each supercell comprising multiple subcells. Among configurations with varying numbers of subcells, the investigation focuses on a phase-modulated triatomic configuration designed to break time inversion symmetry to achieve non-reciprocity, which generates asymmetric bandgaps to selectively suppress wave propagation in positive wavenumber domains while permitting propagation in negative domains. The spatiotemporal field patterns with different modulation parameters are provided. Numerical simulations are also conducted to verify non-reciprocal wave propagation behavior. Furthermore, the influences of modulation amplitude, frequency, and initial phase on the bandgap structure are systematically examined, revealing their potential for precise asymmetric bandgap tuning wave propagation characteristics.</p>