Motion planning under fixed travelling time between start and goal point along a specified path is considered in this study. The structure between the actuator and the end point of the robot arm is assumed flexible and is the main cause of positioning error because of residual vibration. An algorithm is developed to generate motion of the manipulator arm along the specified path that significantly reduces the residual vibration, at the goal point configuration. The problem also considers the full nonlinear dynamics of the manipulator arm. The dynamics are described by finite element method using Lagrange's equation and are expressed by the time scale factor. The performance index is optimized successfully through off-line computation for a two link flexible manipulator, one example of which is described in detail.