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.
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ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
August 28–31, 2011
Washington, DC, USA
Conference Sponsors:
- Design Engineering Division and Computers and Information in Engineering Division
ISBN:
978-0-7918-5483-9
PROCEEDINGS PAPER
A Coordinate-Free Approach to Tracing the Coupler Curves of Pin-Jointed Linkages
Nicola´s Rojas,
Nicola´s Rojas
Institut de Robo`tica i Informa`tica Industrial, Barcelona, Spain
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Federico Thomas
Federico Thomas
Institut de Robo`tica i Informa`tica Industrial, Barcelona, Spain
Search for other works by this author on:
Nicola´s Rojas
Institut de Robo`tica i Informa`tica Industrial, Barcelona, Spain
Federico Thomas
Institut de Robo`tica i Informa`tica Industrial, Barcelona, Spain
Paper No:
DETC2011-48147, pp. 417-426; 10 pages
Published Online:
June 12, 2012
Citation
Rojas, N, & Thomas, F. "A Coordinate-Free Approach to Tracing the Coupler Curves of Pin-Jointed Linkages." Proceedings of the ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. Volume 6: 35th Mechanisms and Robotics Conference, Parts A and B. Washington, DC, USA. August 28–31, 2011. pp. 417-426. ASME. https://doi.org/10.1115/DETC2011-48147
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