A new design scheme of a robotic gripper for rotational family parts is presented and analyzed in the paper. The third or first class lever type of coupled fingers located from contrary sides of common longitudinal axis of symmetry of the gripper are used so that no less than two fingers from each side of the symmetry axis create an artificial centering prism. Distance of a centerline of the prisms, so the centerline of the part being handled, from the basic surface of the gripper is kept constant at changing diameter of the parts. Fingers are driven by a motion of sliders assembled inside of carriageways inclined to some angle to the symmetry axis of a gripper hand. It is shown that by keeping some rates of dimensions of mechanism elements straight lined finger surfaces will be kept tangent to the cylindrical surface of handled parts. Mathematical equations defining these rates are derived.