Polynomial curve is commonly adopted in trajectory planning of robotic manipulators, thanks to its simple formulation and intuitive expression. Aiming at the trajectory continuity for the robot end-effector and motions of the joints, high-order polynomial curve is expected in the trajectory generation. Moreover, in order to reduce the robot vibration and joint buffetings during its movement, the jerks of the trajectory in either Cartesian or joint space should be minimized. This chapter presents the trajectory planning by means of polynomial curve, where the problem of jerk minimization is formulated as a constrained quadratic optimization problem. The formulated optimization problem can be solved rapidly to plan the trajectory in real time. Examples of trajectory planning are illustrated along with the parallel SCARA robot in both the Cartesian and joint spaces, to show the effectiveness of presented trajectory optimization. The computation time of trajectory generation shows that the presented approach of trajectory planning is applicable for real-time robot execution.