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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 Thomas
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.

History

Publication status

  • Published

Page range

417-426

Presentation Type

  • paper

Event name

ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference

Event location

Washington, DC, USA

Event type

conference

Event date

August 28–31, 2011

Book title

Volume 6: 35th Mechanisms and Robotics Conference, Parts A and B

Department affiliated with

  • Engineering and Design Publications

Full text available

  • No

Peer reviewed?

  • Yes

Legacy Posted Date

2016-03-07

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