Robotic haircutting requires controlled tool motion near the head while simultaneously accounting for communication, visual feedback, tool actuation, and interruption handling. Existing studies still lack an operator-in-the-loop reference for analyzing these coupled behaviors before human trials or stronger autonomy. This paper presents TeleHairing, a closed-loop teleoperation architecture for mannequin-based robotic haircutting evaluation under local, relay, and remote deployment conditions. Logged timing shows that the main remote latency increase occurs before the robot-side control endpoint: overall timing reached 190.5~ms in remote mode, while robot-side command queue, control processing, and control-to-robot timing remained similar across modes. Trajectory analysis shows that the larger remote command-following error was dominated by the terminal withdrawal segment rather than accumulated uniformly over the path; excluding this segment reduced remote root-mean-square error (RMSE) from 45.1 mm to 9.6 mm. Detection-loss trials further show that rebase events resumed motion without a large target jump under the tested condition. These results clarify how deployment, execution, and interruption affect the robotic haircutting teleoperation loop, providing a quantitative reference for future autonomy, safety, and user-facing studies.

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