We consider Hamiltonian systems of 2 and 1 1 2 degrees of freedom depending on parameters. More precisely, we focus on localization of bifurcation points in families of periodic solutions using a geometrical method. General scheme will be illustrated by several examples: periodically forced mathematical pendulum, Beletsky equation for oscillations of a satellite in the plane of its elliptic orbit etc. Special attention will be paid to a particular non-integrable case of the general n-body problem: the restricted problem of three bodies.