We consider the uncalibrated vision-based control problem of robotic manipulators in this work. Though lots of approaches have been proposed to solve this problem, they usually require calibration (offline or online) of the camera parameters in the implementation, and the control performance may be largely affected by parameter estimation errors. In this work, we present new fully uncalibrated visual servoing approaches for position control of the 2DOFs planar manipulator with a fixed camera. In the proposed approaches, no camera calibration is required, and numerical optimization algorithms or adaptive laws for parameter estimation are not needed. One benefit of such features is that exponential convergence of the image position errors can be ensured regardless of the camera parameter uncertainties. Generally, existing uncalibrated approaches only can guarantee asymptotical convergence of the position errors. Moreover, different from most existing approaches which assume that the robot motion plane and the image plane are parallel, one of the proposed approaches allows the camera to be installed at a general pose. This also simplifies the controller implementation and improves the system design flexibility. Finally, simulation and experimental results are provided to illustrate the effectiveness of the presented fully uncalibrated visual servoing approaches.