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In remote-control robotic systems, the lack of force feedback and imprecise navigation challenge cooperation between the surgeon and robot. This study proposes a manipulation-based evaluation framework to assess the cooperative performance between different operators and robot using kinesthetic, kinematic, and haptic data from multi-sensor technologies. The proposed evaluation framework achieves a recognition accuracy of 99.99% in assessing the cooperation between operator and robot. Additionally, the study investigates the impact of delay factors, considering no delay, constant delay, and variable delay, on cooperation characteristics. The findings suggest that variable delay contributes to improved cooperation performance between operator and robot in a primary-secondary isomorphic robotic system, compared to a constant delay factor. Furthermore, operators with experience in manual percutaneous coronary interventions exhibit significantly better cooperative manipulate on with the robot system than those without such experience, with respective synergy ratios of 89.66%, 90.28%, and 91.12% based on the three aspects of delay consideration. Moreover, the study explores interaction information, including distal force of tools-tissue and contact force of hand-control-ring, to understand how operators with different technical skills adjust their control strategy to prevent damage to the vascular vessel caused by excessive force while ensuring enough tension to navigate complex paths. 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