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With excellent folding-induced deformability and shape reconfigurability, origami-based designs have shown great potentials in developing deployable structures. Noting that origami deployment is essentially a dynamic process, while its dynamical behaviors remain largely unexplored owing to the challenges in modeling. This research aims at advancing the state of the art of origami deployable structures by exploring the transient dynamics under free deployment, with the Miura-origami tube being selected as the object of study because it possesses relatively simple geometry, exceptional kinematic properties, and wide applications. In detail, a preliminary free deployment test is performed, which indicates that the transient oscillation in the transverse direction is nonnegligible and the tube deployment is no longer a single-degree-of-freedom (SDOF) mechanism. Based on experimental observations, four assumptions are made for modeling purposes, and a 2N-DOF dynamic model is established for an N-cell Miura-origami tube to predict the transient oscillations in both the deploying and the transverse directions. Employing the settling times and the overshoot values as the transient dynamic indexes, a comprehensive parameter study is then carried out. It reveals that both the physical and geometrical parameters will significantly affect the transient deploying dynamics, with some of the parameter dependence relationships being counter-intuitive. The results show that the relationships between the transient dynamic behaviors and the examined parameters are sometimes contradictory in the deploying and the transverse directions, suggesting the necessity of a compromise in design.