<p>Variable-stiffness materials/structures are poised to optimize system performance in complex environments. Mechanical metastructures hold significant potential for smoothly and broadly tuning both linear and nonlinear properties. However, current tunable metastructures often exhibit asymmetric tension-compression stiffness and underutilize nonlinear tunability. Here we propose novel programmable metastructures with symmetrically tunable linear and nonlinear behaviors. Inspired from planetary gear systems, the tunable metacell comprises a circular slide rail and rotatable bidirectional pivots, enabling balanced stiffness under tension and compression, with a 30× tunable linear stiffness. Incorporating a subtle clearance within the metacell, we uncover a robust “clearance-lever” mechanism that enables a remarkable 10⁶× tunability of nonlinear stiffness, smoothly transitioning from linear to strongly nonlinear states. Beyond static properties, the metastructures present versatile tunability on both frequency and linear and nonlinear vibration response spectra. The dynamic metastructure designed based on this strategay offers tunable bandgap for elastic wave manipulation. Therefore, this work not only provides a new method for designing programmable metastructures, but also demonstrates its broad application sceneries for vibration isolation, absorption and wave manipulation.</p>