The problem of nuclear rotation treated within the framework of the two-dimensional cranking and particles-rotor Hamiltonians is solved in the many-body space for a deformed single-j shell configuration with pairing. The properties of ``identical'' (twinned) bands in neighboring, in particular, odd and even systems are studied. It is shown that the twinned band mechanism is accompanied by a ``quantized alignment'' in the relative angular momentum (or incremental) alignments without involving any special dynamical symmetry as, e.g., pseudospin symmetry. Conditions for a nontrivial manifestation of the quantized incremental alignment together with the criteria of ``being identical'' found in the literature are discussed.