Dynamic Load Carrying Capacity of Flexible Manipulators Using Finite Element Method and Pontryagin’s Minimum Principle

Document Type : Original Manuscript


1 Professor, Robotic Research Laboratory, College of Mechanical Engineering, Iran University of Science and Technology, Tehran, Iran

2 Phd candidate, Robotic Research Laboratory, College of Mechanical Engineering, Amirkabir University, Tehran, Iran

3 MSc, Department of Mechanical Engineering, Damavand Branch, Islamic Azad University, Damavand, Iran


In this paper, finding Dynamic Load Carrying Capacity (DLCC) of flexible link manipulators in point to-point motion was formulated as an optimal control problem. The finite element method was employed for modelling and deriving the dynamic equations of the system. The study employed indirect solution of optimal control for system motion planning. Due to offline nature of the method, many difficulties such system nonlinearities and all types of constraints can be catered for and implemented easily. The application of Pontryagin’s minimum principle to this problem was resulted in a standard two-point boundary value problem (TPBVP), solved numerically. Then, the formulation was developed to find the maximum payload and corresponding optimal path. The main advantage of the proposed method is that the various optimal trajectories can be obtained with different characteristics and different maximum payloads. Therefore, the designer can select a suitable path among the numerous optimal paths. In order to verify the effectiveness of the method, a simulation study considering a two-link flexible manipulator was presented in details.