In this paper the simplified mechanical model for a machine-tool system is presented. The state and domains are defined with respect to the (contact and frictional force) boundaries in this system. The switching sets for this machine-tool will be defined for all the boundaries considered herein. The forces and force product components at the switching points are determined according to discontinuous systems theory. The forces and force product govern the passability of the machine-tool through the respective boundary. Mapping definitions and notations are developed through the switching sets for the boundaries. A mapping structure and notation for one type of intermittent cutting periodic motion is defined as an example.