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On the primal and dual forms of the Stewart platform pure condition

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10.1109/TRO.2012.2204531
 
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hdl:2117/17431

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Borràs Sol, JúliaMés informació
Thomas, FedericoMés informacióMés informació
Document typeArticle
Defense date2012
Rights accessOpen Access
Attribution-NonCommercial-NoDerivs 3.0 Spain
Except where otherwise noted, content on this work is licensed under a Creative Commons license : Attribution-NonCommercial-NoDerivs 3.0 Spain
Abstract
The algebraic characterization of the singularities of a Stewart platform is usually presented as a 6 × 6 determinant, whose rows correspond to the line coordinates of its legs, equated to zero. This expression can be rewritten in a more amenable way, known as the pure condition, as sums and products of 4×4 determinants whose rows correspond to the point coordinates of the legs attachments. Researchers usually rely on one of these two expressions to find the geometric conditions associated with the singularities of a particular Stewart platform. Although both are equivalent, it is advantageous to use either line or point coordinates depending on the platform topology. In this context, an equivalent expression involving only plane coordinates, a dual expression to that using point coordinates, seems to be missing. This paper is devoted to its derivation and to show how its use is advantageous in many practical cases mainly because of its surprising simplicity: it only involves the addition of 4 × 4 determinants whose rows are plane coordinates defined by sets of three attachments.
CitationBorras, J.; Thomas, F. On the primal and dual forms of the Stewart platform pure condition. "IEEE transactions on robotics", 2012, vol. 28, núm. 6, p. 1205-1215. 
URIhttp://hdl.handle.net/2117/17431
DOI10.1109/TRO.2012.2204531
ISSN1552-3098
Publisher versionhttp://dx.doi.org/10.1109/TRO.2012.2204531
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  • IRI - Institut de Robòtica i Informàtica Industrial, CSIC-UPC - Articles de revista [290]
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