Auto-parametric resonance in cable-actuated systems

Cable-actuated systems provide an effective method for precise motion control over various distances. Motion control using such systems has traditionally focused on eliminating longitudinal resonances and disturbance. Moreover, longitudinal cable resonances are usually assumed to be at much higher frequencies compared to transverse resonances, ensuring minimal coupling between the two. However, in high-speed high-precision applications, the coupling between longitudinal and lateral cable oscillations cannot be ignored in the presence of high-inertia components. In this paper, we describe the mechanism of auto-parametric resonance in cable-pulley systems through which longitudinal vibrations can couple strongly to transverse vibrations. We model exact dynamics of coupled cable-pulley oscillations and solve them numerically to observe the intrinsic non-linear behavior. Preliminary experimental results show the effect of this coupling on pulley rotation.