Flexure-based constant-force mechanisms belong to the category of zero-stiffness mechanisms. They present a non-zero elastic restoring force which does not depend on the deformation of the mechanism. However, their design and modeling are frequently complex, and most of known designs involve sophisticated and often cumbersome structures, some requiring preloading elements, which restricts their application fields. Furthermore, in most implementations, only a limited region of the force-displacement characteristics provides a constant elastic restoring force. This paper presents a novel constant-force planar flexure-based translation stage consisting of only two parallel beams used to guide the stage, plus an initially straight inclined buckling beam. This additional beam buckles when a compressive critical force is exerted, generating in turn a force offset and a constant negative stiffness along the stage motion direction. For specific design conditions, this negative stiffness can advantageously compensate the intrinsic positive stiffness of the guiding beams. Analytical modeling is conducted based on Euler-Bernoulli beam theory to provide design criteria to make the force constant irrespective of the stage displacement. To validate the analytical modeling and the constant-force behavior, finite element modeling is carried out, as well as experiments on a mesoscale prototype. The mockup is based on three metal blades assembled with 3D-printed plastic parts with an outer volume of 70 x 100 x 6 mm 3. Measurements show that the actuation force is bounded within 10% from a constant-force reference of 1 N for a displacement range of 10 mm. The pre-buckling (compression) region corresponds to only 0.5 mm of travel from the neutral position. Given the unprecedent performances, the compactness and the simplicity of the mechanism, we can conclude that this mechanism constitutes a key building block which could easily be integrated in sophisticated devices such as, force-limiting end-effectors, gravity and stiffness compensation systems, or probes used to passively apply a predetermined contact force onto objects.