An Analysis of the Finite Element Method Applied on Dynamic Motion and Maximum Payload Planning of Flexible Manipulators

This paper is concerned with the dynamic motion analysis and the planning of maximum payload path of flexible manipulators. The finite element method was employed for dynamic modelling of the system and the motion of the model was considered as a combination of the rigid displacement and the elastic deformation of each link. Each manipulator link was treated as a finite number of elements and total displacement was derived by means of the shape functions of flexible elements. The problem of maximum payload trajectory planning was formulated as an optimal control problem. An indirect optimal control solution was employed. This method converts an optimality problem to a twopoint boundary value problem. The effect of the number of elements on the dynamic motion, optimal trajectory and maximum allowable dynamic payload of the system was studied. Finally, a number of simulations were performed to verify the applicability and capability of the method for the nonlinear dynamic modelling and the control of flexible manipulators.