In this article a new method for planning smooth and time-optimal trajectories for robot manipulators is proposed. Trajectory planning is considered as dynamic optimization problem in which the end-effector path as well as the limitations of the joint velocities, the actuator torques and the actuator torque rates are the constraints. These constraints transferred to the space of the path variable using the parametrized system dynamics border an admissible solution space in which time optimality and smoothness are defined. DAE models are derived to construct time-optimal trajectories inside the admissible solution space taking the maximum velocity curve and its properties into account.