首先建立了落砂机系统周期运动的 Poincaré映射，考虑到在设计过程中经典的Neimark-Sacker分岔临界准则需要直接计算特征值带来的局限性，利用不直接依赖于特征值计算的显式临界准则，获得了系统发生 Neimark-Sacker 分岔的两参数区域图，所获得的参数区域图有助于主动设计系统的拟周期碰撞运动。然后应用中心流形正则形方法进一步分析了拟周期碰撞运动的稳定性。最后数值仿真表明在选定的系统参数处能产生稳定的拟周期碰撞运动。“,”The Poincarémap of periodic motion was established,and the bifurcation diagram of two pa-rameters was obtained by using an explicit critical criterion without using eigen values when the difficulties caused by the classical Neimark-Sacker bifurcation critical criterion described by the properties of eigenval-ues were considered.The bifurcation diagram helps to proactively design the quasi-periodic impact motion of the system.Then,the stability of the quasi-periodic impact motion was further analyzed by utilizing the center manifold and normal formal theory.Finally,numerical experiments verify that the stable quasi-peri-odic impact motion can be generated at chosen parameters points.