Hamiltonian-path based constraint reduction for deployable polyhedral mechanisms

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.