  We analyze the common four types of the finite-time singularities using a
generic framework of the phase portrait geometric approach. This technique
requires that the Friedmann system to be written as a one dimensional
autonomous system. We employ a scale factor that has been used widely in
literature to realize the four finite-time singularity types, then we show a
detailed discussion for each case showing possible novel models. Moreover, we
show how different singularity types can play essential roles in different
cosmological scenarios. Among several modified gravity theories, we show that
the f (T) cosmology is in comfort with the phase portrait analysis, since the
field equations include Hubble derivatives only up to first order. Therefore,
we reconstruct the f (T) theory which generates these phase portraits. We also
perform a complementary analysis using the effective equation of state.
Furthermore, we investigate the role of the torsion fluid in realizing the
cosmic singularities.
