ABSTRACT Compliant constant-force mechanisms (CCFMs) are compliant mechanisms that provide nearly constant forces over prescribed deflection ranges. This study proposes a topology optimization method for designing hinge-free compliant constant-output-force mechanisms. Bifurcation cause the objective function to oscillate, leading to convergence failure. Therefore, a constraint for preventing bifurcation in constant-output-force mechanisms is proposed. Moreover, a minimum scale constraint method that extends the design domain is utilized in the proposed optimization algorithm. The relationship between the minimum length scale and the force variation in the optimized CCFM is obtained and discussed, and an optimized CCFM is fabricated and tested. The optimized CCFM exhibits a force variation of 0.7% over a constant-force stroke of 26% of the CCFM length and is thus competitive among recently proposed CCFMs.