This paper presents a novel method for nonprehensile manipulation of parts on a circularly oscillating platform when the effective coefficient of dry friction between the part and the platform is being dynamically controlled. Theoretical and experimental analyses have been performed to validate the proposed method and to determine the control parameters that define the characteristics of the part's motion. A mathematical model of the manipulation process with dynamic dry friction control was developed and solved. The modeling showed that by changing the phase shift between the function for dynamic dry friction control and the function defining the circular motion of the platform, the part can be moved in any direction as the angle of displacement can be controlled in a full range from 0 to 2π. The nature of the trajectory and the mean displacement velocity of the part mainly depend on the width of the rectangular function for dynamic dry friction control. To verify the theoretical findings, an experimental setup was developed, and experiments of manipulation were carried out. The experimental results qualitatively confirmed the theoretical findings. The presented analysis enriches the classical theories of nonprehensile manipulation on oscillating platforms, and the presented findings are relevant for mechatronics, robotics, mechanics, electronics, medical, and other industries.
Keywords: dry friction; nonprehensile manipulation; oscillating platform; planar motion; vibration and control.