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A coordinate-free approach to tracing the coupler curves of pin-jointed linkages

AuthorsRojas, Nicolás ; Thomas, Federico
Issue Date2011
PublisherAmerican Society of Mechanical Engineers
CitationInternational Design Engineering Technical Conferences and Computers and Information in Engineering Conference 6: 417-426 (2011)
AbstractIn general, high-order coupler curves of plane mechanisms cannot be properly traced by standard predictor-corrector algorithms due to drifting problems and the presence of singularities. Instead of focusing on finding better algorithms for tracing curves, a simple coordinate-free method that first traces these curves in a distance space and then maps them onto the mechanism workspace is proposed. Tracing a coupler curve in the proposed distance space is much simpler because (a) the equation of this curve in this space can be straightforwardly obtained from a sequence of bilaterations; and (b) the curve in this space naturally decomposes into branches in which the signs of the oriented areas of the triangles involved in the aforementioned bilaterations remain constant. A surjective mapping permits to map the thus traced curves onto the workspace of the mechanism. The advantages of this two-step method are exemplified by tracing the coupler curves of a double butterfly linkage, curves that can reach order 48.
DescriptionTrabajo presentado al 35th Mechanisms and Robotics Conference celebrado en Washington del 28 al 31 de agosto de 2011.
Publisher version (URL)http://dx.doi.org/10.1115/DETC2011-48147
Identifiersdoi: 10.1115/DETC2011-48147
isbn: 978-0-7918-5483-9
Appears in Collections:(IRII) Libros y partes de libros
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