Mathematical modeling of the dynamics of manipulation system for mobile transport and technological machine with reference to the elasticity of elements

Abstract

The approaches to modeling the dynamics of mobile manipulators of transport and technological machines with reference to the elastic compliance of elements are shown. The equations of motion of the manipulator units are recorded using the method of Lagrange multipliers. As the main origin for each element were taken four Rodrigues-Hamilton parameters, coordinates of the element position as absolutely rigid body and elastic movements. The equations take into account the impact of external and internal elastic and quadratic forces. Internal elastic forces are calculated on the basis of the stiffness matrix, which formation is made through calculation of the manipulator by finite element method. To set the join couplings the required number of constraint equations is built. The methods of creating of widespread kinematic schemes of manipulators of cylindrical and prismatic joints using set of constraints involving mutual perpendicular vectors, which belong to articulated elements. Using the developed model the dynamics of articulated manipulator crane ACT-4-A was calculated. It was found that the inclusion of elements elasticity reveals oscillatory behavior of the kinematic and power factors of the process and, thus, increase the adequacy of modeling of manipulation system operation during machine use. Elastic elements causes their oscillations with a frequency, which is commensurable with the first lower natural frequency of metal manipulation system itself, that indicates the desirability of its test for the absence of resonance and, if necessary, the development of positive measures to improve the dynamic reliability of the manipulation system. It has been shown that to calculate manipulators for some machines the chassis dynamics should be taken into account.