Journal Home Page

Cumulative Index

List of all Volumes

Complete Contents
of this Volume

Previous Article

Next Article

Journal for Geometry and Graphics 16 (2012), No. 2, 139--151
Copyright Heldermann Verlag 2012

Necessary Conditions for Type II DM Self-motions of Planar Stewart Gough Platforms

Georg Nawratil
Institute of Discrete Mathematics and Geometry, Vienna University of Technology, Wiedner Hauptstr. 8-10/104, 1040 Vienna, Austria

Due to a previous publication of the author, it is already known that one-parametric self-motions of Stewart Gough platforms with planar base and planar platform can be classified into two so-called Darboux Mannheim (DM) types (I and II). Moreover, the author also presented a method for computing the set of equations yielding a type II DM self-motion explicitly. Based on these equations we prove in this article the necessity of three conditions for obtaining a type II DM self-motion. Finally, we give a geometric interpretation of these conditions, which also identifies a property of line-symmetric Bricard octahedra, which was not known until now.

Keywords: Self-motion, Stewart Gough platform, Borel Bricard problem, Bricard octahedra.

MSC: 53A17; 52B10

[ Fulltext-pdf  (256  KB)] for subscribers only.