Limiting Cases of Impulsive Manipulation

W. H. Huang and M. T. Mason

**Abstract **

Impulsive manipulation is the use of impulsive forces to manipulate
objects. In particular, we are studying how to manipulate a rigid planar
slider by tapping. In this paper, we focus on the limiting case --- where
the number of taps approaches infinity as the energy of each tap approaches
zero. This paper develops two definitions of the limiting case: for *intermittent
tapping*, where the object comes to rest between taps, and for *continuous
tapping*, where the object does not come to rest. For *intermittent
tapping*, we find that the motion obeys a simple scaling law, and for
*continuous tapping*, we find that there is a limiting case such that
the possible motions of the object are identical to those for pushing for
rotationally symmetric objects. We also explore analogous forms of *vibratory
manipulation*, where we take the striker behavior foremost and examine
the resulting object motion.