Mechanics for vibratory manipulation

Vibratory manipulation is any mode of manipulation involving repeated impacts due to a striker which follows some periodic motion. In this paper, we study vibratory manipulation in the context of tapping planar objects which slide on a fixed support surface. We are interested in the behaviors an object exhibits under such excitation. There are two distinct types of tapping that can result: continuous tapping, in which the object is always in motion, and intermittent tapping, in which the object comes to rest between taps. We first examine vibratory manipulation in one dimension, adapting results from related work to find conditions for stable periodic motion. The general two dimensional case is closely related to our previous work in impulsive manipulation which examined the mechanics of a sliding rotating object. In fact, vibratory manipulation is an approximation to the limiting cases of impulsive manipulation. We develop the limiting cases for intermittent and continuous tapping for rotationally symmetric objects and conclude with some examples.