A motion transmission unit for a drive train of a hair cutting appliance includes an input shaft, an eccentric portion, a motion converter, and a tilting lever that engages a driving portion of a blade set. The motion converter is arranged between the input shaft and the tilting lever. The eccentric portion engages a motion converter input interface. A motion converter output interface engages the tilting lever input interface and includes a cylindrical portion defining a cylinder axis parallel to a swivel axis of the tilting lever. A tilting lever output interface includes a head portion defining a cylinder axis parallel to a swivel axis of the tilting lever. The cylinder axis of the head portion and the cylinder axis of the cylindrical portion are parallel to the swivel axis.