The present invention aims at full-automatic adjustment apparatus for gripper-base height in regularly engaging condition without clutch means.Apparatus according to the invention comprises operation shaft 28 which is co-centered with cylinder axis 16 and is movable in the axial direction of cylinder; the shaft being equipped with rack portion 32 at optional position in the axial direction of cylinder and rotation engagement portion 36 at the extruded end from cylinder axis; adjustment shaft 54 which is rotary provided at the optional position in the axial direction of cylinder to the radial direction and is rotated upon receiving the force from the rack portion 32; the shaft 54 being connected by way of rotation displacement means 58 to gripper-base 22 which is adjustably provided in the radial direction; and drive means 44 which is connected to said rotation engagement portion 36 and moves said operation shaft 28 in the axial direction of cylinder.