Programmable shape morphing and space deployment through graded derivatives of origami architectures

Real-time programmable mechanical features including shape morphing ability in metamaterials and metasurfaces can be crucial for a range of technologically demanding space applications such as deployable space structures and antennas, adaptive solar arrays, robotic arms, actuators and advanced robotic materials. This paper proposes second-order derivatives of spatially-varying Miura-based origami architectures like graded Arc Miura, inclined Arc Miura, and tapered Arc Miura for achieving a range of programmable shape-changing capabilities. The rigid foldability and motion behavior of the graded geometries are investigated thoroughly based on computational simulations and tabletop experiments using physical prototypes, leading to the evidence of on-demand shape morphing and target curvature attainment under limited actuation, and transitional deployment from 2D to 3D states. An efficient approach of kinematic mapping is developed based on idealized spherical 4R linkages involving Denavit-Hartenberg matrix notations, resulting in piece-wise spatially-graded tessellations for achieving programmed pre-defined symmetric and asymmetric curvatures with complex two and three-dimensional geometrical shapes. The fundamental mechanics of the proposed origami metamaterials being mostly scale-independent, this emerging class of deployable shape-changing architectures can be directly transferred for application in a range of milli-, micro-, and nano-metre-size space systems, essentially opening avenues for the design of various programmable structures and machines at multiple length-scales.