Maximum allowable dynamic load of flexible manipulators with imposing residual vibration constraint

The main objective of this study was formulating and determining the maximum allowable dynamic load (MADL) for flexible link-flexible joint manipulators along a predefined trajectory with imposing the amplitude of residual vibration as a new constraint in addition to two earlier constraints, actuator torque capacity and end-effector precision constraints. In the rest-to-rest motion, the end-effector of the flexible manipulators vibrates not only during the path but also after reaching to the goal point. These vibrations will continue with a magnitude and frequency which relates on the carried payload. The finite element method is employed for modelling and deriving the dynamic equations of manipulator with flexible joint and link robot. The dynamic equations of flexible link robot have been brought from previous works for developing the required equations for flexible joint robot. Two simulations have been carried out for a flexible manipulator along a predefined path for joints and end-effector considering the different payloads. Base on the obtained results, a practical way of using the residual constraint as a new constraint for calculating the MADL is presented. Finally, the MADL is calculated for a two-link flexible robot with imposing the new defined constraint along a predefined path.