A Study on the Minimum Folding Steps and Degrees of Freedom Required for Hamiltonian Cycle Paths
Year: 2026
Type: article
Abstract: Deployable grid structures are widely used in aerospace engineering due to their capability of compact storage and large-scale deployment. However, the design of efficient folding paths for thick-panel grid structures remains challenging because of the complex relationship between topology and mechanical performance. Hamiltonian cycles provide an effective approach for generating continuous and non-intersecting folding trajectories, but systematic evaluation and optimization of different grid configurations remain limited. This study proposes a topology optimization framework for Hamiltonian-cycle-based thick-panel folding structures. Three rectangular grids, including 4×4, 4×5, and 4×6 configurations, are investigated. A complete enumeration algorithm is developed to generate Hamiltonian cycles, followed by rotational and mirror symmetry elimination to obtain independent topologies. Thickness interference screening, degree- of - freedom (DOF) calculation, and minimum folding-step analysis are further introduced to evaluate folding feasibility and performance. Based on these criteria, optimal Hamiltonian cycle configurations are identified for different grid sizes. The proposed framework integrates graph-based topology generation with kinematic analysis, providing a systematic approach for the design and optimization of compact deployable folding structures.
Authors: Yuntong Chen, Rongning Fan, Haole Shen
Institutions: Fuzhou University, Shanxi Normal University
Language: English
Subfield: Civil and Structural Engineering
Field: Engineering
Domain: Physical Sciences
Open Access status: hybrid
OpenAlex ID: W7225739926