Abstract
A generalization of the theory of Bertrand curves is presented for ruled and developable surfaces based on line geometry. Using lines instead of points as the geometric building blocks of space, two ruled surfaces which are offset in the sense of Bertrand are defined. It is shown that, in general, every ruled surface can have a double infinity of Bertrand offsets; but for a developable ruled surface to have a developable Bertrand offset, a linear equation should be satisfied between the curvature and torsion of its edge of regression. In addition, it is shown that the developable offsets of a developable surface are parallel offsets. The results, in addition to being of theoretical interest, have applications in geometric modelling and the manufacturing of products.
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