Impulsive problems for mechanical systems subject to kinematic constraints are discussed in this paper. In addition to the applied impulses, there may exist suddenly changed constraints, or termed impulsive constraints. To describe the states of the system during the impulsive motion, three different phases, i.e., prior motion, virtual motion, and posterior motion, are defined which are subject to different sets of constraints, and thus have different degrees-of-freedom. A fundamental principle, i.e., the principle of velocity variation, for the constrained impulsive motion is enunciated as a foundation to derive the privileged impulse-momentum equations. It is shown that for a system with no applied impulse, a conservation law can be stated as the conservation of the virtual-privileged momenta. The proposed methodology provides a systematic scheme to deal with various types of impulsive constraints, which is illustrated in the paper by solving the constrained impulsive problems for the motion of a sleigh.
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