  Following the work of Niu and Griffiths, in \emph{Phys.Rev.A 58, 4377(1998)},
we shall investigate the problem, how to design the optimal quantum cloning
machines (QCMs) for qubit system, with the help of Bloch-sphere representation.
In stead of the quality factor there, the Fiur\'{a}\u{s}ek's optimal condition,
where the optimal cloning machine should maximize a convex mixture of the
average fidelity, is used as the optimality criterion in present protocol.
Almost all of the known optimal QCMs in previous works, the cloning for states
with fixed polar angle, the phase-covariant cloning, the universal QCMs, the
cloning for two arbitrary pure states, and the mirror phase-covariant cloning,
should be discussed in a systematic way. The known results, the optimal
fidelities for various input ensembles according to different optimality
criteria, are recovered here. Our present scheme also offers a general way of
constructing the unitary transformation to realize the optimal cloning.
