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’.