Abstract: The invention relates to a tail stock device (10) for supporting a workpiece in a machine tool, for example a grinding machine. The tail stock device (10) comprises a tail stock arm (16) that is pivotally supported about a pivot axis (S), said tail stock arm having arranged on its outer end (16a) a centering tip (12) that is oriented parallel to the pivot axis (S). By means of a pivot drive (30) comprising a first pneumatic cylinder (31), the tail stock arm 16 can be pivoted between a working position (A) and a resting position (R). The movement of the piston (32) of the first pneumatic cylinder (31) is transmitted—via a first coupling arrangement (35)—to the tail stock arm (16).