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Journal for Geometry and Graphics 12 (2008), No. 2, 141--149
Copyright Heldermann Verlag 2008

On the Degenerated Cases of Architecturally Singular Planar Parallel Manipulators

Georg Nawratil
Institut für Diskrete Mathematik und Geometrie, Technische Universität, Wiedner Hauptstrasse 8-10/104, 1040 Wien, Austria

In Theorem 3 of A. Karger, "Architecturally singular non-planar parallel manipulators" [Mechanism and Machine Theory 43(3) (2008) 335--346] all types of architecturally singular parallel manipulators with four collinear anchor points are listed. As the manipulator is assumed to be architecturally singular in the cited theorem the given conditions for each entry of this list are sufficient for classification. However, we prove that in contrast to the items 1 to 10, the degenerated planar cases (items 11 and 12) do not contain conditions which are sufficient for an architecturally singular manipulator design. We propose sufficient conditions for these two cases in order to decide whether a given manipulator (with 4 points collinear) is architecturally singular or not by checking only the list instead of calculating the determinant of the Jacobian in all poses. Moreover we give a geometric interpretation of the degenerated planar cases.

Keywords: Architecturally singular parallel manipulators, Stewart Gough Platform.

MSC: 53A17

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