Theoretical and experimental investigation of dynamic load carrying capacity of flexible link manipulator in point-to-point motion

This paper presents the investigation of general formulation and numerical solution of the dynamic load carrying capacity (DLCC) of flexible link manipulator. The proposed method is based on open loop optimal control problem. A two point boundary value problem (TPBVP) is provided, extracted from the Pontryagin's minimum principle. The indirect approach is employed to derive optimality conditions. The system’s dynamics equation of motion is obtained from Gibbs-Appell (G-A) formulation and assumed mode method (AMM). Elastic properties of the links are modeled according to the assumption of Timoshenko beam theory (TBT) and its associated mode shapes. As TBT is more accurate compared with the Euler-Bernoulli beam theory, it is exploited for mathematical modeling of flexible links. The main contribution of the paper is to calculate the maximum allowable load of a flexible link robot while an optimal trajectory is provided. Finally, the result of the simulation and experimental platform are compared for a two-link flexible arm to verify the introduced technique. The efficiency of the proposed method is illustrated by performing some simulation studies on the IUST flexible link manipulator. Simulation and experimental results confirm the validity of the claimed capability for controlling point-to-point motion of the proposed method and its application toward DLCC calculation.