This paper uses concepts in multibody dynamics, together with a collision detection algorithm to study the dynamics of collision avoidance. Obstacle avoidance of a mechanical system in motion is expressed in terms of distances, relative velocities and relative accelerations between potentially colliding bodies. The generalized control forces (constraint forces) used to adjust the system dynamics are based on an n-timestep collision avoidance algorithm. Constraint violations resulting from sudden changes in motion direction are compensated for by feeding back the errors of position and velocity constraints to assure asymptotic stability. The procedures developed are illustrated through a maneuver in space of a robotic manipulator used for grasp and deployment.