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Journal for Geometry and Graphics 08 (2004), No. 1, 033--039
Copyright Heldermann Verlag 2004

An Investigation of an Octahedral Platform Using Equiform Motions

N. H. Abdel-All
Dept. of Mathematics, Faculty of Science, Assiut University, 71516 Assiut, Egypt

Fathi M. Hamdoon
Dept. of Mathematics, Faculty of Science, Al-Azhar Univ. Assiut Branch, 71524 Assiut, Egypt

We investigate motions of the 7-parameter group of equiform transformations with the property that three points move on three circles with axes in one plane. We give an algorithm to find the corresponding one-parametric motion. It can be displayed as a curve in the space of motion parameters. As in general there seems to be no global parametrization of this curve, we give a local one up to the second order. An example demonstrates the effciency of the presented method.

Keywords: Parallel manipulator, equiform motion, flexible octahedra.

MSC: 53A17

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