  This paper unifies the concept of kinematic mappings by using geometric
algebras. We present a method for constructing kinematic mappings for certain
Cayley-Klein geometries. These geometries are described in an algebraic setting
by the homogeneous Clifford algebra model. Displacements correspond to Spin
group elements. After that Spin group elements are mapped to a kinematic image
space. Especially for the group of planar Euclidean displacements SE(2) the
result is the kinematic mapping of Blaschke and Gr\"unwald. For the group of
spatial Euclidean displacements SE(3) the result is Study's mapping.
Furthermore, we classify kinematic mappings for Cayley-Klein spaces of
dimension 2 and 3.
