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The calibration accuracy of the intrinsic and extrinsic parameters of the vision system greatly affects the performance of visual servoing. We address the problem of controlling a planar manipulator using a fixed single camera without calibrating its intrinsic parameters and the transformation matrix between the robot base frame and the camera frame, and without measuring manipulator's depth. Based on an important observation that the unknown parameters can be separated from the unknown composite image Jacobian matrix, we propose an adaptive algorithm to estimate the unknown and mixed parameters on-line. It is proved with a full consideration of dynamics of the system by Lyapunov approach that the feature points of planar manipulator approach asymptotically to the desired ones on image plane and the estimated parameters are bounded under the control of the proposed visual servo controller. The performance has been confirmed by simulations and experiments.