Geometry of the shoulder of a packaging machine

The shoulder of a packaging machine is a developable surface that guides the packing material without stretching or tearing. The shoulder is traditionally manufactured by bending a flexible plate along a given bending curve, also without stretching or tearing. In this paper, the shoulder geometry is described mathematically by methods from classical differential geometry. For a given bending curve the generating lines of the (developable) shoulder surface are completely specified. It is shown that the bending curve can be chosen such that the resulting shoulder contains a planar triangle. The special case of a conical shoulder is also discussed, and the underlying bending curve is determined explicitly