A prescribed-time robust nonlinear controller for multi-link robotic manipulators with flexible joints and uncertain input unmodeled dynamics is considered. The controller achieves regulation of the tracking error to within an arbitrarily specified neighborhood of zero (i.e., 'practical' tracking) within an arbitrary time interval specified by the control designer. The controller is robust to disturbance torques as well as uncertainties in parameters of the robotic manipulator in addition to uncertain actuator dynamics in the form of input unmodeled dynamics. Time-varying control gains in a vector backstepping approach along with a dynamic scaling based approach to handle input unmodeled dynamics are used to enforce convergence of the tracking error to within the specified neighborhood within the specified time interval. Simulation studies for a two-link manipulator with flexible joints and input unmodeled dynamics are presented to demonstrate the efficacy of the proposed controller design.