Meccanica

, Volume 48, Issue 5, pp 1177–1190

Types of self-motions of planar Stewart Gough platforms

Authors

    • Institute of Discrete Mathematics and GeometryVienna University of Technology
Article

DOI: 10.1007/s11012-012-9659-6

Cite this article as:
Nawratil, G. Meccanica (2013) 48: 1177. doi:10.1007/s11012-012-9659-6

Abstract

We show that the self-motions of general planar Stewart Gough platforms can be characterized in the complex extension of the Euclidean 3-space by the movement of three platform points in planes orthogonal to the planar base (3-point Darboux motion) and a simultaneous sliding of three planes orthogonal to the planar platform through points of the base (3-plane Mannheim motion). Based on this consideration, we prove that all one-parametric self-motions of a general planar Stewart Gough platform can be classified into two types (type I DM and type II DM, where DM abbreviates Darboux Mannheim). We also succeed in presenting a set of 24 equations yielding a type II DM self-motion that can be computed explicitly and that is of great simplicity seen in the context of self-motions. These 24 conditions are the key for the complete classification of general planar Stewart Gough platforms with type II DM self-motions, which is an important step in solving the famous Borel Bricard problem.

Keywords

Self-motionStewart Gough platformBorel Bricard problemDarboux motionMannheim motion

Copyright information

© Springer Science+Business Media Dordrecht 2012