This paper is concerned with the analysis of a class of impacting systems of relevance in applications: cam-follower systems. We show that these systems, which can be modeled as discontinuously forced impact oscillators, can exhibit complex behavior due to the detachment at high rotational speeds between the follower and the cam. We propose that the observed phenomena can be explained in terms of a novel type of discontinuity-induced bifurcation, termed as corner-impact. We present a complete analysis of this bifurcation in the case of a nonautonomous impact oscillator and explain the transition to chaos observed in a representative cam-follower example. The theoretical findings are validated numerically.