Application of distance geometry to tracing coupler curves of pin-jointed linkages

Rojas, Nicolas and Thomas, Federico (2013) Application of distance geometry to tracing coupler curves of pin-jointed linkages. Journal of Mechanisms and Robotics, 5 (2). ISSN 1942-4302

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Abstract

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.

Item Type: Article
Schools and Departments: School of Engineering and Informatics > Engineering and Design
Depositing User: Nicolas Rojas
Date Deposited: 07 Mar 2016 10:35
Last Modified: 07 Mar 2016 10:35
URI: http://sro.sussex.ac.uk/id/eprint/59880
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