  One-parameter hyperbolic planar motion was first studied by S.
Y$\ddot{\texttt{u}}$ce and N. Kuruo$\tilde{\texttt{g}}$lu. Moreover, they
analyzed the relationships between the absolute, relative and sliding
velocities of one-parameter hyperbolic planar motion as well as the related
pole curves, \cite{Yuc}. One-parameter planar motions in the Euclidean plane
$\mathbb{E}^2$ and the Euler-Savary formula in one-parameter planar motions
were given by M$\ddot{\texttt{u}}$ller, \cite{Mul}. In the present article, one
hyperbolic plane moving relative to two other hyperbolic planes, one moving and
the other fixed, was taken into consideration and the relation between the
absolute, relative and sliding velocities of this movement was obtained. In
addition, a canonical relative system for one-parameter hyperbolic planar
motion was defined. Euler-Savary formula, which gives the relationship between
the curvature of trajectory curves, was obtained with the help of this relative
system.
