  We study mixed quantum spin chains consisting of two kinds of spins with
magnitudes, s_a and s_b. The spins are arrayed as s_a-s_a-s_b-s_b in a unit
cell and the exchange couplings are accordingly periodic with period 4. The
spin Hamiltonian is mapped onto a nonlinear $\sigma$ model based on the general
formula for periodic inhomogeneous spin chains. The gapless condition given by
the nonlinear $\sigma$ model determines boundaries between disordered phases in
the space of the exchange parameters. The phase diagram has a rich phase
structure characterized by the values of s_a and s_b. We explain all phases in
the singlet-cluster-solid picture which is an extension of the
valence-bond-solid picture.
