Modelling and control of a flexible manipulator with a parallel drive mechanism†

A flexible manipulator having a parallel drive mechanism is treated. Only the forearm of the manipulator is assumed to be flexible, because it is slender and carries a heavy end-effector. Both the elastic vibration of the arm, which occurs owing to flexibility, and the position of the driving motors should be controlled simultaneously. A partial differential equation and the boundary conditions that govern the clastic vibration of the arm are derived, and the related eigenvalue problem is solved. On the basis of a finite-dimensional modal model of the distributed-parameter systems, an optimal feedback control system is constructed by using the outputs of several sensors.