Design and analysis of mobile mechanism based on three-dimensional Hilbert curve

This paper introduces a mobile mechanism inspired by three-dimensional Hilbert curves, comprising the Hilbert first-order curve mobile mechanism (HFCM) and the second-order curve mobile mechanism (HSCM). The HFCM, a bipedal system, utilizes seven actuated telescopic joints to replicate the geometric expansion–contraction behaviour of the first-order Hilbert curve. Featuring an amoeba-like adaptive morphology, this mechanism demonstrates high manoeuvrability in confined environments such as narrow pipelines and rubble zones through sequential segment actuation. Stability analysis, kinematic modelling, and experimental validation confirmed its capabilities for static walking, rotational motion, and stair negotiation on planar surfaces. The HSCM, designed based on the second-order Hilbert curve, underwent comprehensive gait planning and dynamic stability evaluation. ADAMS simulations validated its planar translation and omni-directional rotation performance under uniform mass distribution. This research establishes a novel design framework for reconfigurable mechanisms, with future work focusing on developing higher-order Hilbert curve-based systems and exploring their applications in disaster response robotics.