  It is shown that, if the energy in the Schwarzian mechanics (SM) is equal to
the coupling constant in the de Alfaro-Fubini-Furlan (DAFF) model, there exists
a link between these two systems. In particular, the equation of motion,
SL(2,R)-symmetry transformations and the corresponding conserved charges of SM
can be derived from those of the DAFF model by applying a coordinate
transformation of a special type, while the general solution of the DAFF system
maps to the velocity function of SM. A way to reproduce this link via the
method of nonlinear realizations is presented. Schwarzian counterparts of the
DAFF mechanics in Newton-Hooke (NH) spacetime as well as a higher derivative
generalization of the DAFF model are discussed.
