This analysis concerns the important class of conveyors that may be idealized as a nearly horizontal plane oscillating sinusoidally in a straight line with direction inclined to the plane and amplitude great enough to cause particle flights. In Part 1 of this paper it is shown that particle motion perpendicular to the plane becomes a function of a single generalized amplitude, while motion along the plane takes any of four forms. The various equations of motion are derived as well as rules and conditions which predict and establish transitions between the separate motion forms. Part 2 continues this analysis and presents the solutions.

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