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The primary objectives of the investigation are to analyze the dynamical behavior of a three-degree-of-freedom vibratory system and choose the suitable system parameters to obtain larger impact velocity or larger regions of periodic motions for engineering application. Stability and local bifurcations of one-impact periodic motion are analyzed by using Jacobian matrix of the Poincareacute mapping. Global bifurcations are used to optimize the system parameters. Based on theoretical analysis and numerical simulation, some unusual bifurcations are obtained, such as Neimark-Sacker bifurcation including torus doubling, discontinuous period doubling bifurcation including Neimark-Sacker bifurcation, or torus doubling, or grazing singularities. And their routes from periodic motions to chaos are discussed as well. Some methods of obtaining larger impact velocity or larger regions of periodic motions are presented too.