Exact and approximate pure bending of thin sheets

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We design an exact single-degree-of-freedom mechanism whereby a thin sheet of material may be subjected to pure bending up to high curvatures, in order to determine the moment-curvature response of the sheet. The ends of a sheet sample are moved smoothly through a sequence of positions and orientations such that at any time, the centerline of the sheet may deform homogeneously into a circular arc. Loci of the positions is an known curve called cochleoid which can be traced by an known linkage mechanism. While orientations of the moving end is directed through simple trigonometry.