Singularity-invariant leg rearrangements in Stewart-Gough platforms

Postprint (author’s final draft

Regular Polyhedral Linkages

In this paper new overconstrained linkages are described, which are synthesized by inserting planar link groups into the faces of Regular Polyhedra and are interconnected by corresponding multiple gussets. These spatial linkages belong to the category of the so-called paradoxical linkages as they disobey the topological structure formula of GrblerKutzbach. In a general position they are mobile with one degree of freedom and shaky with a number of degrees of freedom in special multifurcation positions. As these linkages considerably change in their overall size while deforming, they lend themselves to being used as deployable structures

Straightening-Free Algorithm for the Singularity Analysis of Stewart-Gough Platforms with Collinear/Coplanar Attachments

Abstract 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.