Backlash in balancing systems using approximate spring characteristics

A mechanical model of a balancing system is constructed and its stability analysis is presented. This model considers an interesting practical problem, the backlash. It appears in the system as a nonlinear spring characteristic with noncontinuous derivative. The upper equilibrium of the pendulum can be stabilized without backlash. Backlash causes oscillations around this equi- librium. Phase space diagrams are revealed based on simulations. Bifurca- tion analysis is carried out by the continuation method. The noncontinuous derivative of the spring characteristic causes problems during the calcula- tion, therefore different types of approximate characteristics are used. The conditions of the existence of stable stationary and periodic solutions are determined in case of the approximate systems and conclusions are obtained for the exact piecewise linear system.