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Open-sourced kinematic models of the da Vinci Surgical System have previously been developed using serial chains for forward and inverse kinematics. However, these models do not describe the motion of every link in the closed-loop mechanism of the da Vinci manipulators; knowing the kinematics of all components in motion is essential for the foundation of modeling the system dynamics and implementing representative simulations. This paper proposes a modeling method of the closed-loop kinematics, using the existing da Vinci kinematics and an optical motion capture link length calibration. Resulting link lengths and DH parameters are presented and used as the basis for ROS-based simulation models. The models were simulated in RViz visualization simulation and Gazebo dynamics simulation. Additionally, the closed-loop kinematic chain was verified by comparing the remote center of motion location of simulation with the hardware. Furthermore, the dynamic simulation resulted in satisfactory joint stability and performance. All models and simulations are provided as an open-source package.