In this paper a model to cover all possible topologies of robot manipulators composed of prismatic and revolute joints is presented. For simplicity, only planar systems are considered, hence to provide plane positioning, systems handled are of three degrees of freedom. The physical model assumes three moving rigid links in articulation with one revolute and one prismatic joint between each link pair, forming a six degrees of freedom open chain linkage. Among each joint pair, one is real and the other fictitious. The real joint is arbitrarily actuated by an externally applied force or torque while the fictitious one is acted upon by an appropriately controlled force or torque as to keep that joint velocity zero, keeping fixed at its initial position. The physical model is accompanied by a mathematical model obtained by Lagrange formulation. This approach is called ‘The method of Fictititous Degrees of Freedom’.