In this paper is considered a planar system of straight cantilever bars with one common end. Resultant force and moment situated in the same plane (the force) and perpendicular to the plane (the moment) act at this common end, so the bars suffer planar deformations consisting in two translations and one rotation, the common end being now in a new position. The equations of equilibrium are written for the case of small deformations for each bar and from the obtained system one can determine the components of the deformation for an arbitrary bar or, equivalently, the components of the force that acts on a particular bar. More systems of coordinates are considered: a general system of coordinates and particular systems of coordinates linked to each bar. The passing matrices from one to another system is also described. The main question is if the original system may be solved for any planar configuration of the bars. The conditions in which the problem can be solved is also determined. A numerical example concludes the paper.