Determination of displacements in cross-sections of four-bar mechanism links from distributed dynamic loads and their animation using MAPLE

The links of high-speed mechanisms and manipulators are deformed under the action of inertia forces and external loads. These deformations have significantly influence on the accuracy of execution of the required law of motion by the operating point of the mechanism and the positioning of the manipulator grip. Accordingly, longitudinal and transverse displacements, angles of rotation of cross-sections of links under the action of distributed dynamic and external loads are investigated in this paper. The developed technique allows defining deformations of links of mechanisms and manipulators and can be applied at their designing. To determine the transverse displacements, the angles of rotation of the cross-sections of the links – the basic differential equation of the elastic line of the beam, to determine the longitudinal displacements of the points of the links – Hooke’s law and the boundary conditions of the computed scheme of the investigated linkages for elastic computation are used. The bending moment in the basic differential equation of the elastic line of the beam and the longitudinal force in Hooke’s law were determined by the theory developed by the authors of the analytical definition of internal forces in the links of planar linkages with statically determinate structures, taking into account the distributed dynamic loads from the masses of links, dead weight and from the acting external loads. According to the developed technique, programs are created in the MAPLE system and animations of the movement of mechanisms are received, with the construction on the links the diagrams of transverse, longitudinal displacements and angles of rotation of the link cross-sections. The developed analytical technique for determining deformations in the cross-sections of links is used to calculate the strength and stiffness of elements of movable linkages