Robotics has a wide area of application which includes the development of a device for movement rehabilitation for different types of patients, such as stroke victims. Brain injuries can impair the necessary movements of the lower limb, influencing human gait. The use of robotic structures can generate benefits such as reducing costs with active labor for movement-based rehabilitation treatments, as well as expanding the range of exercises performed helping patients to maintain mobility through continuous therapy. The objective of this paper is to present the development of a novel nonmotorized mechanism for ankle rehabilitation. The structure is a mechanical device, to obtain the system with simple operation for both patients and health professionals. The mathematical modeling of the mechanism is based on the four-bar linkage and the static equilibrium of the system. The mechanism transmits angular movement generated by the patient’s arm to an oscillatory movement on the ankle joint. The design of the mechanisms used a differential evolution algorithm and singularity analysis based on the geometrical matrix of the systems. To validate the system, a prototype was constructed to verify the angular outputs, check the existence of singularities, and execute movements with a wooden test dummy.