Integrated Inverse Dynamics and Optimized Mechanical Design in Underactuated Linear Vibratory Feeders Under Periodic Excitation

Abstract

Purpose This paper proposes an integrated method for optimizing the response of underactuated linear vibratory feeders operating in open-loop control, under generic periodic excitations. The goal is ensuring a uniform motion of the tray, despite the presence of less actuators than degrees of freedom and of several specifications of the desired motion. Method To cope with the underactuated nature of these systems and with their non-minimum phase behavior, dynamic structural modification and the inverse dynamics approach are properly integrated by exploiting a common definition of the system internal dynamics. In the inverse dynamics problem, the inverse dynamics is stabilized through output redefinition and the resulting ordinary differential equations are integrated to compute causal actuation forces, ensuring almost-exact tracking for as many coordinates as the number of actuators. The tracking of the remaining coordinates of interest is improved through a proper design of the mechanical parameters, based on the modification of the internal dynamics. Results The effectiveness of the proposed method is assessed through numerical simulations performed on the challenging case of a 14-degrees of freedom underactuated non-minimum phase linear vibratory feeder adopted in manufacturing plants to convey products. Conclusion The results evidence the benefits obtained by integrating structural modification together with inverse dynamics. Inverse dynamics is effective, since the tracking error on the imposed coordinates is negligible. On the other hand, the benefits introduced by dynamic structural modification are proved as well, by the reduction of the tracking error also for the non-imposed coordinates.