Modeling the movement of different parts of the body has been studied a lot in recent years. Body movement models such as fingers movements are good guides for designing different robots. Also, motion disability is one of the common diseases that have a great impact on patients' life quality. To treat the rupture of finger tendon, individual rehearsal rehabilitation exercises for each phalanx is required. In order to achieve this aim and take control of each phalanx movement, the mathematical model of the desired trajectory for each joint is necessary. The angle of each joint is measured with the help of a gyro sensor installed on a novel wearable rehabilitation robot proposed in this paper. The mathematical models of the phalanges motions are obtained by curve fitting. The model is applicable not only in the rehabilitation robots but also in the other robotic works. In most of the works in this area, the desired trajectory diagram was drawn and tracking of the trajectory was investigated. Thus, the desired trajectory formula should be fined for the other works. But in this work, the corresponding formula was found and it can help other researchers to easily use of these formulas for their work. To ensure the accuracy and efficiency of the calculated trajectories, the trajectories are implemented in a control system. In order to control this system, a suitable sliding mode controller was designed and the results of system controlling and trajectory tracking using this controller was obtained.