In this paper, an impact model with possible stick between the two gears is proposed for gear transmission systems, which includes the piecewise backlash model and the traditional impact model for the first time. The new model presented in this paper possesses a time-varying boundary for two dynamical systems either to switch or to impact. Such a model can catch impacting chatter and stick phenomena in gear transmission systems. Based on the new model, periodic impacting chatter and stick in a gear transmission system can be investigated. For doing so, switching sets on the time-varying boundaries are introduced to define basic mappings. Mapping structures based on basic mappings are developed for characterizing motions in gear transmission systems, and from such mapping structures, periodic motions with impacting chatter and stick in such a gear transmission system are predicted analytically. Numerical simulations are performed for illustration of periodic motions with impacting chatter and stick phenomena.