The invention relates to a clamping apparatus (1) for clamping a workpiece (100), which is or is to be toothed and has an axis of rotation, onto a spindle, which can be rotationally driven and has a spindle axis defining an axial direction (A), with a clamping mechanism (20), which converts an axial force (FA) transferred via a force transfer device (10) into a clamping force (Fg) directed radially to the spindle axis, wherein the force transfer device (10) has a first section (12) movably guided by a guide arrangement (30) in relation to a movement having an axial direction component, wherein the first section (12) is segmented into several transfer elements (12a, 12b, 12c, 12d) spaced apart from one another in a circumferential direction.