Compliant mechanisms enable passive force control through induction of strain energy during deformation. This has been perceived as a desired factor for developing precise handling equipment of limited size where additional sensors and controls are inessential to its operation. In this paper, our objective is to design a monolithic constant-force compliant mechanism to be integrated in a constant-force gripper for extended range of bidirectional motion. A topology synthesis method has been proposed by means of domain definition, discrete parameterization, topology optimization, and nonlinear structural deformation evaluation. This article adapts a compliant topology of a homogeneous beam configuration that exhibits zero stiffness behavior over a pre-established effective region. The optimization by genetic algorithm generates discrete shaping parameters for formation of an optimal geometry. The structural deformation computation via vector form intrinsic finite element that accounts for large displacement motion quantifies an iterative series of load-displacement relations in the optimization. Results have been verified using a conventional finite element method. A conceptual gripper has been proposed with a pair of embedded constant-force compliant mechanisms. This procedure has prepared a general guideline for future development of passive compliant devices that require accurate force regulation over a wide range of motion.