On periodic motions of an inclined impact pair

The dynamical behavior of an inclined impact pair is investigated by using the discrete maps theory of discontinuous dynamical systems. The mechanical model consists of a ball and a frame. The frame, in which there is an inclined slot, is harmonically excited, and the ball is constrained to move freely in the slot without friction. The analytical conditions for predicting the occurrence of period-1 motion of two impacts under N cycles are obtained, from which the corresponding results of the horizontal impact pair can be derived. Different from the horizontal impact pair, for any integer N, the symmetrical period-1 motions of two impact under N cycles do not appear for 0 < e < 1 , θ > 0 , and this result is more general than the previous work. For a better understanding of periodic motions, plots of mechanical model in relative coordinate of the ball are presented.