Directional Stiffness Decoupling in Meta-Wheels via Three-Dimensional Discrete Curved Spokes

<div>Meta-wheels—non-pneumatic wheels whose performance is governed by structural geometry rather than internal pressure—offer new opportunities for directional stiffness control. Yet achieving independent tuning of longitudinal, lateral, and vertical stiffness within a single wheel architecture has remained challenging due to the inherent coupling in conventional radial and planar curved spokes. In this study, we introduce a three-dimensional (3D) discrete curved-spoke design that provides explicit geometric control through two independent parameters: the in-plane curvature angle (<i>α</i>) and the out-of-plane inclination angle (<i>β</i>). Using spoke-level and full-wheel finite-element (FE) simulations, supported by a simplified cantilever-beam analytical model, we show that these two geometric parameters govern stiffness in fundamentally different ways. The curvature angle <i>α</i> serves primarily as a geometric softener, reducing stiffness in all directions while maintaining a high top-loading ratio (TLR) (>92%). In contrast, the inclination angle <i>β</i> enables true directional stiffness decoupling: increasing <i>β</i> substantially raises longitudinal stiffness and decreases lateral stiffness, while leaving vertical stiffness nearly unchanged (≈1.4% variation). Compared with conventional two-dimensional (2D) spoke designs, the proposed 3D architecture achieves stiffness characteristics approaching those of pneumatic tires, particularly higher longitudinal stiffness and lower lateral stiffness, without sacrificing vertical load-bearing capacity. Moreover, the combined simulation–analysis framework provides an efficient early-stage screening tool by mapping desired stiffness ratios directly to geometric parameters, narrowing the feasible design space before full-wheel FE verification. Overall, this work demonstrates that 3D discrete curved spokes present a practical and interpretable route toward stiffness-decoupled, directionally programmable meta-wheels for next-generation mobility platforms.</div>