The control of mechanical systems with constraints has been a topic of intense research in the control and dynamical systems community for the past two decades. In particular, systems with velocity and/or acceleration level constraints which appear in many applications like - robotics, spacecrafts, launch vehicles, underwater vehicles - have been studied intensively. This monograph is a self-contained exposition on a switched, finite-time, control strategy for this class of systems. Beginning with basic definitions and mathematical preliminaries, the monograph works its way up to the main control algorithm. Three well-studied applications are chosen to demonstrate the algorithm. Other facets of the algorithm and an alternate algorithm are also briefly touched upon. The monograph is intended for graduate students and researchers in the area of nonlinear control and dynamical systems.