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Application of distance geometry to tracing coupler curves of Pin-Jointed linkages

AuthorsRojas, Nicolás ; Thomas, Federico
Distance geometry
Configuration spaces
Coupler curves
Double butterfly linkage
Issue Date2013
PublisherAmerican Society of Mechanical Engineers
CitationJournal of Mechanisms and Robotics 5(2): 021001 (2013)
AbstractIn general, high-order coupler curves of single-degree-of-freedom plane linkages 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 method that first traces the configuration space of planar linkages in a distance space and then maps it onto the mechanism workspace, to obtained the desired coupler curves, is proposed. Tracing the configuration space of a linkage in the proposed distance space is simple because the equation that implicitly defines this space can be straightforwardly obtained from a sequence of bilaterations, and the configuration space embedded in this distance space naturally decomposes into components corresponding to different combinations of signs for the oriented areas of the triangles involved in the bilaterations. The advantages of this two-step method are exemplified by tracing the coupler curves of a double butterfly linkage. © 2013 by ASME.
Identifiersdoi: 10.1115/1.4023515
issn: 1942-4302
e-issn: 1942-4310
Appears in Collections:(IRII) Artículos
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