Vibration control of a two-link flexible manipulator

In this study, a two-link manipulator with flexible members is considered. The end point vibration signals are simulated by developing a MatLAB code based on the finite element theory and Newmark solution. Experimental results are also presented and compared with simulation results. The mass and stiffness matrices are time dependent because the angular positions of the links change during the motion. Trapezoidal velocity profiles for the actuating motors are used. The time dependent inertia forces are calculated by using the rigid body dynamics. The inertia forces are due to the motors, end point payload mass and distributed masses of the links. The acceleration, constant velocity and deceleration time intervals of the trapezoidal velocity profile are selected by considering the lowest natural frequency of the manipulator structure at the stopping position. Various starting and stopping positions are considered. The root mean square (RMS) acceleration values of the vibration signals after stopping are calculated. It is observed that the residual vibration is sensitive to the deceleration time. The RMS values are lowest if the inverse of the deceleration time equals to the first natural frequency. It is highest if the inverse of the deceleration time equals to the half of the first natural frequency. It is observed that simulation and experimental results are in good agreement.