Maximum Allowable Dynamic Load of Flexible Manipulators Undergoing Large Deformation

Abstract

In this paper, a general formula for nding the Maximum Allowable Dynamic Load (MADL) of geometrically nonlinear exible link manipulators is presented. The dynamic model for links in most mechanisms is often based on the small de ection theory but for applications like lightweight links, high-precision elements or high speed it is necessary to capture the de ection caused by nonlinear terms. First, the equations of motion are derived, taking into account the nonlinear straindisplacement 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 e ectiveness of the presented algorithm, two simulation studies considering a exible two-link planar manipulator mounted on a mobile base are presented and the results are discussed. The simulation results indicate that the e ect of introducing geometric elastic nonlinearities and inertia nonlinearities on the maximum allowable loads of a manipulator.