This paper deals with the sensitivity analysis and the prediction of the orientation error limits of a three-DoF translational parallel manipulator (3-TPM). An analytical model relating the robot accuracy to the design parameters uncertainties, the joints clearances, the nominal pose, and the external load is developed. Based on this model, an analytical sensitivity analysis is performed to show the influence of each parameter on the orientation error. An algorithm based on the interval analysis is used to predict the bounds of the translator orientation error. Using the RAF robot as an example, it is shown that the pin length of the revolute joint, the width of the parallelogram structure and the radial clearance in the revolute joints are the most influential parameters on the orientation error of the manipulator. Moreover, one of the main results of this analysis is that an increase of the tolerances on certain parameters does not necessarily lead to an increase of the orientation error of the robot, for this specific example.