This paper deals with the constraint analysis of a novel two-degree-of-freedom (DOF) spatial translational parallel robot for high-speed applications named the IRSBot-2 (acronym for IRCCyN Spatial Robot with 2 DOF). Unlike most two-DOF robots dedicated to planar translational motions this robot has two spatial kinematic chains that provide a very good intrinsic stiffness. First, the robot architecture is presented and its constraint singularity conditions are given. Then, its constraint singularities are analyzed in its parameter space based on a cylindrical algebraic decomposition. Finally, a deep analysis is carried out in order to determine the sets of design parameters of the IRSBot-2 that prevent it from reaching any constraint singularity. To the best of our knowledge, such an analysis is performed for the first time.