Journal of Applied Mathematics

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

Davoud Karimi and Mohammad Javad Nategh

Full-text: Open access

Abstract

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.

Article information

Source
J. Appl. Math., Volume 2011 (2011), Article ID 393072, 17 pages.

Dates
First available in Project Euclid: 15 March 2012

Permanent link to this document
https://projecteuclid.org/euclid.jam/1331818618

Digital Object Identifier
doi:10.1155/2011/393072

Mathematical Reviews number (MathSciNet)
MR2820081

Zentralblatt MATH identifier
1358.70003

Citation

Karimi, Davoud; Nategh, Mohammad Javad. A Statistical Approach to the Forward Kinematics Nonlinearity Analysis of Gough-Stewart Mechanism. J. Appl. Math. 2011 (2011), Article ID 393072, 17 pages. doi:10.1155/2011/393072. https://projecteuclid.org/euclid.jam/1331818618


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