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For a very restricted range of situations, earlier work has shown that the exact equilibrium positions of discrete dislocations in a planar array may be obtained analytically, in the sense that they are given by the zeros of classic polynomial functions satisfying certain second‐order differential equations; at the same time analytic expressions have been derived for the stresses acting on obstacle dislocations. This paper explores the various models that evolve as a consequence of applying an appropriate coordinate transformation to the most general situation hitherto considered, and the range of application of the analytical approach is thereby extended.