In this study, a multi-degree-of-freedom model is developed to investigate the vibration characteristics of a feed system with nonlinear kinematic joints. Linear guide, ball screw, and ball bearing are the main kinematic joints that connect and support the worktable of a feed system. Considering the contact behaviors of rolling balls, contact force is a piecewise smooth function of displacements of the multi-degree-of-freedom system. In terms of modeling, geometry and material parameters are determined according to the experimental feed system and the model is verified by a dynamic experiment. The motion equations of the system are derived to evaluate the effects of force excitation and screw-nut position on the vibration amplitude and stable state of the vibratory system. With the variation of screw-nut position, there exist jumping phenomena for displacement and deformation amplitude near the resonance frequency region. The hardening and softening type nonlinearity, super harmonic resonance, jumping phenomenon and chaotic motion are strongly attributed to the coupling vibrations. The application of the multi-degree-of-freedom model can supply information to suppress vibration and improve processing precision.