This study addresses the problem of adaptive controllingof both a nonredundant and a redundant robotic manipulator with state-dependent constraints. The task of the robot is to follow a prescribed geometric path given in the taskspace, by the end-effector. The aforementioned robot task has been solved on the basis of the Lyapunov stability theory, which is used to derive the control scheme. A new adaptive Jacobian controller is proposed in the paper for the path following of the robot, withboth uncertain kinematics and dynamics. The numerical simulation results carried outfor a planar redundant three-DOF (three degrees of freedom) manipulator whose end-effector follows a prescribed geometric path given in a two-dimensional (2D) task space, illustrate the trajectory performance of the proposed control scheme.