Abstract: A clamping or chucking apparatus is provided wherein the cutter blades or cutters, for the grinding thereof, are mounted in a cutter head. The cutter head is rotatable in the clamping apparatus about a cutter head axis, and further, is pivotably arranged for pivotable movement about a pivot axis. To provide a clamping apparatus having compact external dimensions and which, during adjustment of the cutter blades, requires very little freedom of movement room or space, and also possesses a good adjustment accuracy, the pivot axis is inclined and arranged at an acute angle with respect to the cutter head axis, such that the smallest spacing between the pivot axis and the cutter head axis is located externally of the clamping apparatus.