We investigate the formation of spin gap in one-dimensional models characterized by the groups with hidden symmetries. We introduce a new class of Hamiltonians for description of spin staircases - the spin systems intermediate between 2-leg ladders and S=1 spin chains. The spin exchange anisotropy along legs is described by the angle of spiral twist. The properties of a special case of spin rotator chain (SRC) corresponding to a flat 1-leg ladder is considered by means of fermionization approach based on Jordan-Wigner transformation. The influence of dynamical hidden symmetries on the scaling properties of the spin gap is discussed.