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In this paper, a neural network approach is presented for the motion control of constrained flexible manipulators, where both the contact force exerted by the flexible manipulator and the position of the end-effector contacting with a surface are controlled. The dynamic equations for vibration of flexible link and constrained force are derived. The developed control scheme can adaptively estimate the underlying dynamics of the manipulator using recurrent neural networks (RNNs). Based on the error dynamics of a feedback controller, a learning rule for updating the connection weights of the adaptive RNN model is obtained. Local stability properties of the control system are discussed. Simulation results are elaborated on for both position and force trajectory tracking tasks in the presence of varying parameters and unknown dynamics, which show that the designed controller performs remarkably well.