Constant-force mechanisms are designed to keep a constant or nearly constant input force along a prescribed stroke of the mechanism. The implementation of this kind of mechanisms has been approached in literature using compliant mechanisms or through a certain combination of springs and nonlinear transmissions. In this work, three new constant-force mechanisms based on the use of springs, rollers, and cams are presented and analyzed. The rolling friction forces between the rollers and the cam are included in the force equilibrium equations and considered in the integration of the cam profile. The influence of the friction force on the input force as well as the design parameters involved is studied based on numerical techniques and simulations. In fact, the results evidence that to obtain a precise constant-force mechanism, rolling friction forces must be considered in the cam profile definition. The main design guidelines for the three constant-force mechanisms proposed are described.