On transformations and graphic methods of algebraically 3 dimensional force, velocity and displacement systems

Abstract: 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.