  We use a new set of Collins functions to update a previous prediction on the
azimuthal asymmetries of pion productions in semi-inclusive deep inelastic
scattering (SIDIS) process on a transversely polarized nucleon target. We find
that the calculated results can give a good explanation to the HERMES
experiment with the new parametrization, and this can enrich our knowledge of
the fragmentation process. Furthermore, with two different approaches of
distribution and fragmentation functions, we present a prediction on the
azimuthal asymmetries of pion and kaon productions at the kinematics region of
the experiments E06010 and E06011 planned at Jefferson Lab (JLab). It is shown
that the results are insensitive to the models for the pion case. However, the
results for kaon production are sensitive to different approaches of
distribution and fragmentation functions. This is helpful to clarify some
points in the study of the azimuthal spin asymmetries and fragmentation
functions in hadronization processes.
