Vibration suppression of flexible two link robot using piezoelectric transducer on a predefined path

In this paper, the energy equations of a manipulator, including two flexible links, is extracted based on the Euler-Bernoulli beam assumptions. The robot can carry a specified mass as the load on its end-effector. Applying assumed modes method and considering a finite number of modes, the dynamical motion equations of the arm is achieved using Euler-Lagrange equations. The control and the vibration damping of the arm links is implemented using an active controller. This matter is done by applying a specified voltage on two considered piezoelectric layers, the embedding location of which is external layers of beam. The algorithm of vibration control is designed according to the Lyapunov’s second method. In addition, the path planning of the end-effector is performed by making use of an equivalent two link rigid arm. Regarding the fact that the robot weight is included as well, and also it starts its own motion from the rest, the static deflection is calculated from Castigliano’s method and is used as the initial conditions of beam. The performed simulation shows that the path of the controlled motion of flexible robot follows that of equivalent rigid manipulator end-effector with a good approximation