This research delves into the enhancement of control mechanisms for the da Vinci Surgical System, focusing on the implementation of gravity compensation and refining the modeling of the master and patient side manipulators. Leveraging the Robot Operating System (ROS) the study aimed to fortify the precision and stability of the robots movements essential for intricate surgical procedures. Through rigorous parameter identification and the Euler Lagrange approach the team successfully derived the necessary torque equations and established a robust mathematical model. Implementation of the actual robot and simulation in Gazebo highlighted the efficacy of the developed control strategies facilitating accurate positioning and minimizing drift. Additionally, the project extended its contributions by constructing a comprehensive model for the patient side manipulator laying the groundwork for future research endeavors. This work signifies a significant advancement in the pursuit of enhanced precision and user control in robotic assisted surgeries. NOTE - This work has been submitted to the IEEE for publication. Copyright may be transferred without notice, after which this version may no longer be accessible. Copyright on this article is reserved by IEEE