Reduction and Dynamical Analysis of Stochastic Elastic Joint Systems with Time Delays

This study investigates the dynamic behavior of an elastic joint manipulator system with stochastic noise and time delay. First, considering the time delay caused by the difference in inertial moments between the lightweight link and the heavy rotator, as well as the noise in the system, a model of the manipulator system with delay and stochastic is constructed. Second, the time-delay differential equation is reduced to a finite-dimensional ordinary differential equation using the center manifold, and then the system’s generalized Ito equation is obtained using the stochastic averaging method. The stationary probability density dominated by the Fokker–Planck–Kolmogorov (FPK) equation is studied, followed by an investigation of the system’s stochastic bifurcation behavior. Finally, through numerical simulation, the extent to which time delay, stiffness and damping affect the amplitude of the manipulators are studied.