Algorithm for determination the type of bilateral motions of a carrier with a mobile load along a horizontal plane

Abstract

The motion of a mechanical system consisting of a carrier and a load is considered. The carrier, located all the time in a horizontal plane, can move translationally along a rectilinear trajectory. The carrier has a rectilinear channel through which the load can move. The load is considered further on as a material point. The load can move in the channel according to a predetermined motion law. The channel axis is located in a vertical plane passing through the trajectory of the carrier. The Coulomb dry friction model is applied for simulation the forces of resistance to the motion of the carrier from the side of the underlying plane. In the conditions of the carrier motion along horizontal plane without detachment, the carrier motion differential equations are a system of three linear second-order differential equations. The influence of the system parameters on the motion of the carrier from the rest state is studied. In the considered mechanical system (carrier + load) only two types of motion are possible: regular motions in which the relative moments of time being the switching times from one of the three differential equations to the other are unchanged, and the irregular motions when such switching times are different in each of the half-periods of the load motion. Definitive expressions allowing determine the type of carrier motion for the studied systems are derived. An algorithm for classifying two-sided carrier motions for a predetermined load motion law in a channel is presented based on the values of the defining expressions. Examples of specific systems are considered and the results of computational experiments are presented.