The two-mass model of the vocal folds is a popular representation of
their dynamical structure used in phonation studies. This paper
presents an analysis of a recent piecewise-smooth version of the
model. This version has two equilibrium positions, and in one of
them (the initial prephonatory position) the system is
nondifferentiable. Standard methods of stability analysis do not
apply for that position, because they require smoothness of the
system. A geometrical approach is applied instead, which is an
extension of a method previously developed for planar systems. The
analysis shows the existence of a transcritical bifurcation between
the equilibrium positions, and a Hopf bifurcation related to each of
them. The oscillation region of the model is next determined as the
area delimited by the Hopf bifurcations. The results are illustrated
by a bifurcation diagram and trajectory plots.