Mathematical modeling of the longitudinal motion of a robotic construction manipulator with a freely suspended payload

Abstract

The paper develops a mathematical model of the horizontal longitudinal motion of a robotic construction manipulator with a Cartesian kinematic structure. A dynamic model with four degrees of freedom of the manipulator with a freely suspended load has been developed. The real-world system with distributed mass was idealized and presented as concentrated masses. The mathematical models will be used to develop an automatic control system for the longitudinal motion to reduce the vibrations of the metal structure and achieve preassigned kinematic characteristics of the longitudinal motion. For the derivation of the differential equations of motion of the manipulator, the Lagrange equations of the second kind are used. To obtain the kinematic relations homogeneous transformation matrices were used with subsequent differentiation of the obtained expressions. The nonlinear differential equations are used for a numerical study of the dynamic system behaviour under different driving motor laws of motion. The comparison between the obtained results shows that the polynomial trajectory has some advantages over the classical drive with an asynchronous motor in its movement according to the mechanical characteristic, mainly in the significant reduction of the oscillations' amplitudes of the payload.