Vibrations Induced During a Stability Loss of Periodic Trajectories of the Manipulator

We present how to avoid dangerous situations that occur during a robot periodic motion and are caused by different kinds of vibrations. Theoretical analysis of stability regions of nonlinear and linearized system and of the ways of inducing vibrations during a stability loss of periodic trajectories is developed. For practical control of motion a common part of areas of stability received for nonlinear and using linearized Poincare map can be taking into considerations. The areas of stability are identificated by the bifurcation diagrams and Poincare maps. Stability regions of periodic trajectories as a function of varying parameters of the system are investigated . As a practical tool for the control of stability, a spectrum of Lyapunov exponents is proposed. To illustrate our method theoretically and numerically, a model of the RRP-type manipulator has been considered.