  In engineering practice one often encounters planar problems, where the
corresponding vector space of forces, velocities or (infinitesimal)
displacements is three dimensional. This paper shows how these spaces can be
factorized, such that the arising equivalence classes correspond to points and
lines of action of the forces / velocities / displacements in the (projective)
plane. It is shown how the study of projective transformations and dualities of
planar mechanical systems is closely related to the study of linear maps of
these spaces. A few past results are analysed and sometimes extended to show
the power of this description.
