FREE UNDAMPED SPATIAL VIBRATIONS OF A ROBOT FOR PROCESS AUTOMATION IN METALLURGY

This paper presents the results of mechano-mathematical modeling of free undamped spatial vibrations of a robot for process automation in metallurgy.A dynamic model of the robot is made. It is studied as a mechanical system with twelve degrees of freedom, contained by seven rigid bodies.Kinetic and potential energy are derived symbolically by using the kinematics study results. The matrices characterizing the mass-inertial and elastic properties of the mechanical system are obtained. The differential equations that describe the free undamped vibrations are derived. They take into account the geometrical, mass, inertial and elastic characteristics of the mechanical system.A compiled calculation algorithm is entered into a standard mathematical software product. Results are obtained in symbolic and graphical form. The natural frequencies and natural mode of a robot with concrete parameters are determined.Results of the study of free undamped vibrations represent a basis for studying of the free damped and forced vibrations of a robot for process automation in metallurgy.