Simulation of dynamics of oscillations of manipulator using Lagrange equations of second order

Abstract

The article discusses the main stages of compiling a dynamic model of manipulator oscillations, based on the method of mathematical modeling, the basis of which is the circuit design of the manipulator under study. A schematic solution of the manipulator has been compiled as a system in which an arbitrary vertical force Pz and moments Mx, My relative to the X and Y axes act on the working panel, elastic elements — springs, with known stiffness coefficients. On the basis of the equation of dynamics, in the form of Lagrange of the second order, a system of equations of oscillatory processes arising from external loads is compiled, natural frequencies of elastic oscillations of the manipulator are determined, and conclusions are drawn.

Keywords

• manipulator
• working panel
• inclined panel
• turntable
• stiffness coefficient
• lagrange equations
• matrix of inertia and stiffness