Higher-Order Derivatives of Origami Architectures for Reconfigurable Space Antenna Design

Origami-inspired metamaterials have garnered increasing attention for their ability to achieve real-time, programmable shape morphing. This has led to the emergence of a new interdisciplinary field in science and engineering that explores the transformation of two-dimensional preforms into complex three-dimensional structures through controlled folding. In the present study, we have proposed a higher-order origami derivative capable of on-programmable shape morphing. The rigid foldability and the motion dynamics of the Miura derivative are thoroughly examined through computational simulation, resulting in evidence of the on-demand programmable shape morphing capabilities. An efficient mathematical approach to kinematic mapping is developed based on idealising the Miura derivative as a 4R spherical linkage involving Denavit-Hartenberg matrix notations. This formulation enables the generation of piecewise tessellations that realise pre-defined shapes with single-degree-of-freedom programmable mechanics. The proposed origami-based metamaterial represents an innovative class of deployable hybrid structures tailored for reconfigurable antenna applications. The proposed geometries of higher-order origami derivatives enable dynamic control over shape, orientation, and operational parameters through a single degree of freedom kinematics. This seamless transition between the planar and three-dimensional configuration enhances the frequency tunability, radiation pattern and polarisation diversity, thereby offering significant potential in next-generation space applications.