The aim of this work is the development of a novel exoskeleton device used in wrist joint rehabilitation for patients who have suffered a stroke and are in the recovery period. These patients can use their affected limbs, they are not in a situation of having high-grade muscle atrophy. However, their ability to manipulate objects, precision and muscle strength are affected. The use of an exoskeleton device is very suitable in such situations because it is convenient for the patient to use, and its evolution can be easily monitored by the doctor. The proposed exoskeleton device uses as legs two slider crank linkages which are connected to the mobile platform with universal joints. The mobile platform fixed with the hand allows two degrees of freedom (DOF) for possible movements of the wrist, namely pitch (flexion/extension) and yaw (abduction/adduction). The paper shows the structure analysis, the kinematic analysis, and the 3D model of the proposed constructive solution. A numerical example is also made using values close to those of the human hand.