In 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.
Application of Distance Geometry to Tracing Coupler Curves of Pin-Jointed Linkages1
Contributed by the Mechanisms and Robotics Committee of ASME for publication in the Journal of Mechanisms and Robotics. Manuscript received July 25, 2011; final manuscript received January 23, 2013; published online March 26, 2013. Assoc. Editor: Qiaode Jeffrey Ge.
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Rojas, N., and Thomas, F. (March 26, 2013). "Application of Distance Geometry to Tracing Coupler Curves of Pin-Jointed Linkages." ASME. J. Mechanisms Robotics. May 2013; 5(2): 021001. https://doi.org/10.1115/1.4023515
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