This paper deals with the controllability of a class of nonsmooth complementarity mechanical systems. Due to their particular structure they can be decomposed into an “object” and a “robot”, consequently they are named juggling systems. It is shown that the accessibility of the “object” can be characterized by nonlinear constrained equations, or generalized equations. Examples are presented, including a simple model of backlash. The main focus of the work is about linear jugglers.