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Journal for Geometry and Graphics, Vol. 5, No. 2, pp. 121-132 (2001)
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The Rigidity Rate of Positions of Stewart-Gough Platforms

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J. Lang, S. Mick, O. Röschel

Institute of Geometry, Graz University of Technology

Kopernikusgasse 24, A-8010 Graz, Austria

emails: lang@geometrie.tu-graz.ac.at

**Abstract:** We consider a 6-legged Stewart-Gough platform. The following investigations of such platforms will always be carried out at an arbitrary given position. If the leg lengths are kept constant, the platform in general will be rigid within the Euclidean displacement group, whereas viewed within the Euclidean similarity group it will yet be movable. There exists an infinitesimal transformation of this motion. Its deviation from the Euclidean displacement group is used to define the "rigidity rate" of the platform at this position. In order to obtain some geometric invariant measurement, Lie group methods are applied. An example eventually demonstrates the efficiency of the presented method.

**Keywords:** Parallel manipulator, Stewart-Gough platform, rigidity rate, equiform motions, infinitesimal motion

**Classification (MSC2000):** 53A17

**Full text of the article will be available in mid of 2003.**

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