This paper deals with the computation of the orientation error and the kinematic model of a 3-DOF translational parallel manipulator called the RAF robot. We derived a simple analytical model allowing the computation of the orientation, generated by the deformation of the PKLs, when an external load is applied to the platform. These models allowed us to map the orientation error on the workspace of the robot. We showed in particular that the minimum orientation error can be obtained when the platform is in a certain region of its workspace. Due to its analytical nature, the developed model can also be used for a sensitivity analysis in order to maximize the manipulator precision.