A Study on the Minimum Folding Steps and Degrees of Freedom Required for Hamiltonian Cycle Paths

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.