A dynamic model for a new principle of percussive-rotary drilling is presented. This is a non-linear mechanical system with two degrees of freedom, in which friction-induced vibration is used for excitation of impacts, which influence the parameters of stick-slip motion. The model incorporates the friction force as a function of sliding velocity, which allows for the self-excitation of the coupled vibration of the rotating bit and striker, which tends to a steady state periodic cycle. The dynamic coupling of vibro-impact action with the stick-slip process provides an entirely new adaptive feature in the drilling process. The dynamic behaviour of the system with and without impact is studied numerically. Special attention is given to analysis of the relationship between the sticking and impacting phase of the process in order to achieve an optimal drilling performance. This paper provides an understanding of the mechanics of percussive -rotary drilling and design of new drilling tools with advanced characteristics. Conventional percussive-rotary drilling requires two independent actuators and special control for the synchronization of impact and rotation. In the approach presented, a combined complex interaction of drill bit and striker is synchronized by a single rotating drive.