The fundamental criteria for industrial manipulator applications are vibration free and smooth motion with minimum time. This paper investigates the trajectory tracking and vibration control of rotary flexible joint manipulator with parametric uncertainties. Firstly, the dynamic modeling via Euler Lagrange equation for a single link flexible joint manipulator is discussed. Secondly, for the execution of smooth motion between two points, bounded and continuous jerk trajectory is developed and implemented. In addition, the prospective strategy uses the concatenation of fifth-order polynomials to provide a smooth trajectory between two-way points. In the planned algorithm, user can independently define the position, velocity, acceleration and jerk values at both initial and final positions. The feature of user-defined parameters gives the versatility to the suggested algorithm for generating trajectories for diverse applications of robotic manipulators. Moreover, the planned scheme is easy to implement and computationally efficient. In the last, the performance of the presented scheme is examined by comparison with cubic splines and a linear segment with parabolic blends (LSPB) techniques. Generated trajectories were evaluated successfully by carrying multiple experiments on QUANSER's flexible joint manipulator. [ABSTRACT FROM AUTHOR]