Path planning is known as the first stage in kinematics and control of robotic systems. For robotic systems with excess degrees of freedom, redundancy allows us to minimize some kinematics or dynamic performance indices along a pre specified path. In the present work, the optimal trajectory planning of redundant serial and cooperative robotic systems involving flexibility in their links and joints, with the aim of minimization of vibration along a desired path has been studied. Local and global optimization methods are defined as the main approaches in trajectory planning of flexible robots. In local optimization methods, only the instantaneous information of the robot motion is utilized, whereas in the global optimization methods, the information of robot motion along the pre specified path is used. For global trajectory optimization, at first, dynamic () optimization methods are utilized. These methods lead to some differential equations with split boundary conditions which are known as two point boundary value problems (TPBVP). Also, static (parametric) optimization methods which are known as direct methods are defined and used as the second approach in optimal path planning of flexible redundant serial and cooperative manipulators. Also, a new kind of degrees of freedom which are known as controllable local degrees of freedom and have no effect on kinematics of the main chain of the manipulator, have been defined and used to improve the movement characteristics of the flexible manipulators. Keywords Trajectory Planning, Redundancy, Flexibility, Manipulator