In the following a percussion drilling machine is examined as an example for mechanical systems with unilateral contacts. It is characteristic for such systems that the number of degrees of freedom changes during motion. To avoid a description of each possible system state using different sets of minimal coordinates, the constrained motion is taken into account by algebraic relations. This method has the advantage that the motion of the system and simultaneously the constraint forces are available, which is necessary to obtain conditions for a change in the state of the system. Furthermore different combinations of constraints can be easily taken into consideration in this way.