Dynamic Deflection of Paper Emerging from a Channel

In many machines handling lightweight, flexible sheets, the sheet must transit an open space. Examples include magnetic tape drives, xerographic copiers, and sewing machines. The nonlinear theory of the elastica has often been used to model nonlinear, static deflections. Dynamic modeling is more difficult, and far less studied. Recently, however, L. Mansfield and J. G. Simmonds (1987) have considered the dynamic deflection of a sheet emerging from a horizontal channel at constant velocity and subjected to gravity loading. In this paper, we consider a generalization of that problem to include arbitrary exit angles and an accelerating “feed” rate. Gravity loading is retained. The resulting nonlinear equations of motion are tractable and are solved numerically.