Topology-manifold-based parametric design of dual-spherical-4R chiral origami mechanisms

Chiral mechanisms are defined by their mirror-symmetric structural or motion properties, typically exhibiting a helical morphology. These mechanisms excel in folding capabilities, allowing structures to achieve compact configurations, and are characterized by programmable mechanical properties. Additionally, they enable transitions between linear and rotational motion, generating significant interest in their potential applications. Despite this, a systematic design methodology for such mechanisms remains underdeveloped. Topological manifolds provide a critical mathematical framework for describing origami mechanisms with chiral characteristics, forming the foundation for an effective design approach. This paper introduces a parametric design methodology inspired by origami and based on spherical manifolds for creating dual-spherical-4R chiral mechanisms. These mechanisms facilitate transitions among two distinct fully-folded configurations and a fully-deployed configuration. The proposed methodology capitalizes on the unique attributes of spherical manifolds, which operate independently of length scale constraints. It employs a single design parameter to define the dual-spherical-4R chiral mechanisms, enabling the adjustment of 2D planar profiles and 3D motion spaces. Furthermore, this paper investigates the coupling relationship between the design parameters of chiral origami mechanisms and the fully folded polygonal profiles represented by n-polygons. By uncovering the mathematical principles that govern the structural and motion properties of dual-spherical-4R chiral origami mechanisms, the study establishes a clear connection between design parameters and morphological profiles. This framework provides a foundation for developing reconfigurable modular chiral origami robots with diverse motion capabilities.