<p>We present a rotating mass-spring model with dry friction by introducing a circular conveyor belt. The classifications of all equilibrium states of this novel dry friction system are investigated by adjusting the conveyor belt speed. Note that the tangential friction force with irrational nonlinearity depends not only on relative angular velocity but also on angular displacement. When the conveyor belt is stationary, the implicit function expression between friction force and pressure force is derived. The relationship diagram between friction force and pressure force shows the loop shaped structure, eight shaped structure and horizontal linear structure. Based upon the Coulomb cone and relationship diagram, the split and merge among equilibrium sets of the dry friction system are demonstrated by adjusting the sliding friction coefficient, and all the phase portraits with equilibrium sets are displayed from planar to cylindrical analysis. The coexistence of the equilibria and multiple stick regions can be analyzed by changing the angular velocity of circular conveyor belt. The stabilities of equilibria are given by means of the potential function with dry friction. The effect of the stick region on the singular closed orbits can be discussed by adjusting the velocity of conveyor belt. Numerical simulations are carried out to detect the stationary and multiple stick–slip motions.</p>