Maximum allowable load of very flexible manipulators by using absolute nodal coordinate

The main objective of the present paper is to develop a general formula for finding the Dynamic Load Carrying Capacity (DLCC) of very flexible link manipulators undergoing large deflection. An efficient finite element formulation, absolute nodal coordinate formulation (ANCF) is employed to describe nonlinear modeling for flexible link manipulator with large deflection, in which both the transverse normal strain and the shear strain are considered. In comparison to other large deflection formulations, the motion equations contain constant mass matrix, and also, the Coriolis and centrifugal forces are identically equal to zero because the terms arising from geometric elastic nonlinearity are moved to stiffness, reactive and external forces, which are originally nonlinear. This makes the formulation particularly efficient in computational terms and numerically more stable than alternative geometrically nonlinear formulations based on lower-order terms. In this investigation, the equations of motion are derived taking into account the shear deformable using the ANCF based approaches. Then, a method for determination of the dynamic load carrying capacity (DLCC) for geometrically nonlinear elastic robot is described giving attention to accuracy and actuator constraints. In order to initially check the validity of the dynamic equations, the proposed model has been implemented and tested on a single-link very flexible arm. A simulation study is carried out to verify the effectiveness of the presented algorithm for finding DLCC of very flexible link manipulators. The results illustrate the power and efficiency of the method to overcome the high nonlinearity nature of the problem.