Stability regions of periodic trajectories of the manipulator motion

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 and of the ways of inducing vibrations during a stability loss of periodic trajectories of the manipulator motion, based on the theory of nonlinear systems is developed. Based on the bifurcation diagrams and Poincare maps, an identification of stability areas has been carried out. To illustrate our method theoretically and numerically, a model of the RRP-type manipulator has been considered.