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

Rojas, Nicolás and Thomas, Federico (2011) A coordinate-free approach to tracing the coupler curves of pin-jointed linkages. In: ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, August 28–31, 2011, Washington, DC, USA.

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In 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.

Item Type: Conference or Workshop Item (Paper)
Schools and Departments: School of Engineering and Informatics > Engineering and Design
Depositing User: Nicolas Rojas
Date Deposited: 07 Mar 2016 08:03
Last Modified: 07 Mar 2016 08:03
URI: http://sro.sussex.ac.uk/id/eprint/59885
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