Mathematical Modeling of Rigid Folding in Hamiltonian Circuits Using Denavit-Hartenberg Parameters

Abstract The aerospace industry places significant emphasis on designing deployable mechanisms that optimize both stow volume and deployed surface area. This paper introduces a novel approach leveraging Denavit-Hartenberg (DH) parameters to mathematically characterize the folding process of interconnected tiles, forming a Hamiltonian circuit. This circuit serves as a blueprint to ensure rigid foldability from a planar configuration into a double stack. The research outlined in this paper accomplishes several key objectives. Firstly, it delineates the fundamental components required to establish a Hamiltonian circuit for a set of tiles, outlining a folding pattern conducive to a double-stack configuration. Second, it identifies tile pairs suitable for occupying the top and bottom positions within the folded stack, optimizing the arrangement for efficient deployment. Last, the paper meticulously defines DH parameters tailored to the specific circuit under consideration. The proposed methodology is applied and validated using both square and hexagon tiles, demonstrating its versatility across different geometries. By employing this mathematical model, researchers and engineers can effectively assess and ensure the rigid foldability of deployable structures, offering an accurate and effective means of design evaluation within the aerospace industry. Through this innovative approach, advancements in deployable mechanism design can be achieved, contributing to enhanced performance and functionality in aerospace applications.