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A coordinate-free approach to tracing the coupler curves of pin-jointed linkages
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posted on 2023-06-09, 00:28 authored by Nicolás Rojas, Federico ThomasIn 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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Publication status
- Published
External DOI
Page range
417-426Presentation Type
- paper
Event name
ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering ConferenceEvent location
Washington, DC, USAEvent type
conferenceEvent date
August 28–31, 2011Book title
Volume 6: 35th Mechanisms and Robotics Conference, Parts A and BDepartment affiliated with
- Engineering and Design Publications
Full text available
- No
Peer reviewed?
- Yes
Legacy Posted Date
2016-03-07Usage metrics
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