This paper presents the development of a novel Actuation-Coordinated Mobile Parallel Robot (ACMPR), with a focus on studying the kinematics of the mobile parallel robot with three limbs (3-mPRS) comprising mobile prismatic joint-revolute joint-spherical joint. The objective of this research is to explore the feasibility and potential of utilizing omnidirectional mobile robots to construct a parallel mechanism with a mobile platform. To this end, a prototype of the 3-mPRS is built, and several experiments are conducted to identify the proposed kinematic parameters. The system identification of the 3-mPRS mobile parallel mechanism is conducted by analyzing the actuation inputs from the three mobile base robots. To track the motion of the robot, external devices such as the Vicon Camera are employed, and the data is fed through ROS. The collected data is processed based on the geometric properties, CAD design, and established kinematic equations in MATLAB, and the results are analyzed to evaluate the accuracy and effectiveness of the proposed calibration methods. The experiment results fall within the error range of the proposed calibration methods, indicating the successful identification of the system parameters. The differences between the measured values and the calculated values are further utilized to calibrate the 3-mPRS to better suit the experiment environment.