Hamiltonian-path based constraint reduction for deployable polyhedral mechanisms

Gu, Yuanqing; Zhang, Xiao; Wei, Guowu; Chen, Yan

Abstract

Most of the deployable polyhedral mechanisms (DPMs) are multi-loop overconstrained mechanisms that causes barriers for their applications due to the issues in assembly, operation and control. Yet, constraint reduction for these multi-loop overconstrained mechanisms is extremely challenging in kinematics. In this paper, by introducing the Hamiltonian path to investigate the 3D topological graphs of a group of Sarrus-inspired DPMs, we propose a systematic method for constraint reduction of multi-loop overconstrained DPMs. We demonstrate that through the removal of redundant joints with the assistant of tetrahedral Hamiltonian path, one equivalent simplest topological graph of tetrahedral mechanism is identified as a reduction basic unit. Subsequently, one simplest form of Sarrus-inspired cubic mechanism is obtained by investigating two Hamiltonian paths of its dual octahedron and sequentially arranging basic units. Furthermore, a total of nineteen simplest forms of Sarrus-inspired dodecahedral mechanisms are identified from seventeen Hamiltonian paths of its dual icosahedron. The overconstraints in each simplest Sarrus-inspired DPM are greatly reduced while preserving the original one-degree-of-freedom (DOF) motion behavior. The method proposed in this paper not only lays the groundwork for further research in wider deployable polyhedrons, but also inspires the reduction of other multi-loop overconstrained mechanisms, with potential applications in the fields of manufacturing, architecture and space exploration.

Citation

Gu, Y., Zhang, X., Wei, G., & Chen, Y. (in press). Hamiltonian-path based constraint reduction for deployable polyhedral mechanisms. Mechanism and Machine Theory, 193, 105563. https://doi.org/10.1016/j.mechmachtheory.2023.105563

• Journal Article Type: Article
• Acceptance Date: Dec 6, 2023
• Online Publication Date: Dec 14, 2023
• Deposit Date: Jan 4, 2024
• Publicly Available Date: Jan 4, 2024
• Journal: Mechanism and Machine Theory
• Print ISSN: 0094-114X
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 193
• Pages: 105563
• DOI: https://doi.org/10.1016/j.mechmachtheory.2023.105563