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 (α) and
the out-of-plane inclination angle (β). 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
α 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 β enables true
directional stiffness decoupling: increasing β 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.
