Maximum Allowable Dynamic Load of Flexible Manipulators Undergoing Large Deformation

In this paper, a general formula for finding the Maximum Allowable Dynamic Load (MADL) of geometrically nonlinear flexible link manipulators is presented. The dynamic model for links in most mechanisms is often based on the small deflection theory but for applications like lightweight links, high-precision elements or high speed it is necessary to capture the deflection caused by nonlinear terms. First, the equations of motion are derived, taking into account the nonlinear strain-displacement relationship using Finite Element Method (FEM) approaches. The maximum allowable loads that can be achieved by a mobile manipulator during a given trajectory are limited by a number of factors. Therefore, a method for determination of the dynamic load carrying capacity for a given trajectory is explained, subject to the accuracy, actuator and amplitude of residual vibration constraints and by imposing a maximum. stress limitation as a new constraint. In order to verify the effectiveness of the presented algorithm, two simulation studies considering a flexible two-link planar manipulator mounted on a mobile base are presented and the results are discussed. The simulation results indicate that the effect of introducing geometric elastic nonlinearities and inertia nonlinearities on the maximum allowable loads of a manipulator.