The classification of constraints in mechanics and the various mechanical principles that apply to different types of constraints constitute a major area of research in the field of theoretical and applied mechanics. The sudden introduction of bilateral constraints into a mechanical process is blocking and its sudden removal is releasing. The sudden introduction and removal of bilateral constraints, which exist in a subset of the whole process time span, may induce impacts. An impulsive action integral is proposed for such mechanical processes. The projectors of the tangent space of the submanifold and the cotangent space are derived and the equations of motion in different constrained submanifolds are obtained by making use of the projectors. The questions of the uniqueness and the existence of the post-transition velocity are addressed.