An algorithm to derive the pure condition of any double-planar Stewart-Gough platform in a standard form suitable for comparison is presented. By applying the multilinear properties of brackets directly to the superbracket encoding of the pure condition, no straightening is required. It is then shown that any 3-3 platform has a corresponding 6-6 platform having its same superbracket, meaning that they have identical singularity loci. In general, the superbracket of any doubleplanar platform can be written as a linear combination of the superbrackets of 3-3 platforms, leading to a direct singularity assessment by inspecting the resulting decomposition.
CitationBorras, J.; Thomas, F.; Torras, C. Straightening-free algorithm for the singularity analysis of Stewart-Gough platforms with collinear/coplanar attachments. A: Computational Kinematics. "5th International Workshop on Computational Kinematics". Duisburg: Springer Verlag, 2009, p. 359-366.
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