In this paper is shown the dynamic modeling and design of a passivity based controller for the RV-3SB robot. Firstly, the dynamic modeling of the of the Mitsubishi Rv-3SB robot is done by the Euler-Lagrange formulation in order to obtain a decoupled dynamic model considering the actuators orientation besides the position of this analyzed robot. It is important to remark that the dynamic model of the RV-3SB robot is done based in the kinematic model obtention in which is developed by the implementation of screw theory. Then the passivity based controller is obtained by separating the end effector variables and the actuator variables by making an appropriate coordinate transformation. The passivity based controller is obtained by selecting an appropriate storage function and by the Lyapunov theory the passivity based control law is obtained in order to drive the error variaable, which is the difference between the measured end effector position variable and the end effector desired position variable. The passivity based controller makes that the error variable reach the origin in finite time taking into consideration the dissipation properties of the proposed controller in order to stabilizes the desired end effector position. A numerical simulation experiement is performed in order to validate the theoretical results obtained in this research study. It is verified by numerical experimentation that the proposed control strategy is efficient and effective in order to drive the error variable to the origin in comparison with other modified techniques found in the literature. Finally, the appropriate discussion and conclusion of this research study are provided.