Mechanical Metamaterial Based on Non-Circular Planetary Gear Train with Continuously Tunable Mechanical Properties

The geometric degrees of freedom of non-circular gears provide a means for continuously tuning mechanical metamaterials. However, the relationship between pitch design and load-bearing and vibration responses still needs to be clarified. In this paper, we construct a mechanical metamaterial consisting of a fourth-order non-circular sun gear, a sixth-order non-circular ring gear, and four cylindrical planet gears, using the sun gear’s angular position as the configuration control variable. By using high-order elliptic pitch curves and enveloping-generated tooth surfaces, we transform the rotational input into changes in the ring gear's support positions and the effective bending span. Simulations of contact motion and finite element analysis jointly reveal the relationship between geometric encoding, support migration, and load path reconstruction. During combined compression and rotation, the equivalent compressive modulus in the gauge region varies between 5.15 and 117.96 GPa, with a tuning ratio of 22.9. The 2×2 and 3×3 finite arrays preserve configuration-dependent stress migration through shared walls and facilitate load sharing between unit cells. Modal and harmonic response analyses of fixed configurations indicate that the angle of rotation simultaneously alters the distribution of mode shapes as well as the positions of resonance peaks and anti-resonance troughs. These results link non-circular gear geometry with configuration-dependent mechanics, providing a design basis for continuous stiffness adjustment and vibration response control in load-bearing structures.