Journal of Applied Mathematics
Volume 2011 (2011), Article ID 393072, 17 pages
Research Article

A Statistical Approach to the Forward Kinematics Nonlinearity Analysis of Gough-Stewart Mechanism

Tarbiat Modares University, Mechanical Engineering Department, Tehran 14115-143, Iran

Received 26 March 2011; Revised 15 May 2011; Accepted 6 June 2011

Academic Editor: F. Marcellán

Copyright © 2011 Davoud Karimi and Mohammad Javad Nategh. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Both the forward and backward kinematics of the Gough-Stewart mechanism exhibit nonlinear behavior. It is critically important to take account of this nonlinearity in some applications such as path control in parallel kinematics machine tools. The nonlinearity of inverse kinematics is straightforward and has been first studied in this paper. However the nonlinearity of forward kinematics is more challenging to be considered as there is no analytic solution to the forward kinematic solution of the mechanism. A statistical approach including the Bates and Watts measures of nonlinearity has been employed to investigate the nonlinearity of the forward kinematics. The concept of standard sphere has been used to check the significance of the nonlinearity of the mechanism. It is demonstrated that the length of the region, defined as the linear approximation of the lifted line, has a significant impact on the nonlinearity of the mechanism.