Kinematic and dynamic analysis of the lifting mechanism of a sorting truck manipulator equipped with a hydromechanical damper based on Euler and Runge-Kutta methods

An analysis of research into the kinematics and dynamics of work processes of technological machine manipulators is presented. The aim of the study is to reduce the dynamic load and increase the productivity of the forest manipulator by kinematic and dynamic analysis of the boom lifting mechanism equipped with a hydromechanical damper. Calculation schemes for the boom and damper lifting mechanism have been developed. The research is based on a mathematical model describing the kinematics and dynamics of boom lifting, taking into account the action of an additional damper. The model includes equations describing the interaction of the main system parameters, such as the boom lifting angle, pressure in the pressure line and the stroke of the damper plunger. The solution of the system of equations is presented using the approximate Euler method and Maclaurin series expansion, and the obtained functions are analyzed in terms of their dependence on time and other key parameters. The article describes in detail the method of calculating coefficients and the numerical solution using the Runge-Kutta method, including the sensitivity of the model to changes in parameters. The problem is solved in the Maxima computer algebra system. Special attention is paid to the analysis of the influence of small parameters on the behavior of the system, which is demonstrated on the graphs of the dependencies of key variables on time. In conclusion, the main conclusions are formulated, emphasizing the importance of introducing an additional damper to reduce dynamic loading and increase the productivity of loading and unloading operations of the forest manipulator.