The IRSBot-2 is a two degree-of-freedom translational parallel manipulator dedicated to fast and accurate pick-and-place operations. This paper deals with the determination of the design parameters of the manipulator for the IRSBot-2 to be free of parallel singularity. First, the robot architecture is introduced. The IRSBot-2 is composed of two identical spatial limbs, each one containing a proximal module and a distal module. Then, its actuation singularities and constraint singularities are analyzed. The latter are analyzed in its distal parameter space with a method based on the notion of Discriminant Varieties and Cylindrical Algebraic Decomposition. Moreover, a deep analysis is carried out in order to determine the set of design parameters of the distal modules that prevents the IRSBot-2 from reaching any constraint singularity. To the best of our knowledge, such an analysis is performed for the first time. Finally, a design methodology is proposed to determine the set of design parameters associated with the proximal modules for the IRSBot-2 to be assembled and free of parallel singularity.