The concept and purpose of the matrix equation of the contour
To describe the VAT, elastic PPMs pre -compiled matrix equations of the clushing of the contours of the PPM and the algorithm and the program for analyzing movements are developed. The kinematics of manipulators was studied by the matrix method of Denavit-Harthenberg with six parameters. Coordinates x, y, z nodes of the estimated model of PPM are defined in GSK. PPM links are made of steel rods of a round cross section with a diameter of 0.006.
The shape and dimensions of the cross section, the elastic properties of materials are constant. The size and design of the nodes are neglected. The manipulators are under the influence of the nodal forces of the inertia of the KE, additional forces, nodal external forces, the magnitude of each force, which is 10.0 N, and are attached in nodes 3, 7, 9 for PPM, shown in the figure, and in the PPM in nodes 3, 4.7.
To determine the components of the elastic displacements of the PPM nodes, various modifications of the Gaussa-Wesel methods are used. To solve the dynamics equations, the NewMark method is used. The step of integration by time is selected based on the angular velocity of the leading links and by parameters that determine the required accuracy of the reproduction of the studied processes and the stability of the integration method. Inside each step, the change in both kinematic and elastic movements, speeds and accelerations is taken into account in time.