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This paper introduces a flexible puncture method that can improve the efficiency and safety of robot-assisted central venous catheterization (CVC) surgery systems. Current CVC surgery-assisted manipulators and systems are mainly focused methods for puncture needle insertion into blood vessels. There is no single systematic stratagem for safe high-precision control of the posture of the needle in a blood vessel after needle insertion. However, this type of control stratagem is both necessary and urgently required in surgery to avoid piercing the central vein and to provide a suitable posture for guide wire insertion. Therefore, we propose the remote centre of motion control method to control the needle's posture precisely and safely. Verification experiments were performed in both a simulator and a puncture manipulator. The results indicate that the needle tip trajectory in the simulation is completely accurate and it also agrees well with the theoretical value. The positional and angular errors of the needle tip are smaller than 0.8 mm and 1.8°, respectively, in the real puncture manipulator experiment; these errors are sufficiently small for surgeries. The proposed design is practical and can be used in real puncture manipulators and systems. [ABSTRACT FROM AUTHOR]