Numerical Simulation of Nonlinear Oscillation Modes of a Three-Link Manipulator

The paper deals with the construction of nonlinear oscillation modes of a three-link manipulator operating in the gravity field and having identical parameters of weightless links and end loads, using numerical procedures. A nonlinear mathematical model of oscillations of the system is presented, and as a result of its calculation by means of numerical integration, the specific options for setting initial conditions of motion are determined which are leading to the single-frequency oscillations on the first, second or third nonlinear mode. The main qualitative features and quantitative characteristics of all three nonlinear oscillation modes are noted, and their difference from traditional modes of small oscillations is discussed. In addition, graphical dependencies are constructed which illustrate the change in all key quantities on the period of nonlinear oscillations for each of the nonlinear modes. The obtained results are of interest for analytical mechanics and for theory of nonlinear oscillations, and they can also be useful in solving specific applied problems in the field of robotics and biomechanics.