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.
Highlights
The Gough-Stewart platform mechanism GSPM, introduced by Gough and Whitehall 1 and Stewart 2, was originally used as a universal six degree of freedom 6-DOF mechanism in a tire test machine and a flight simulator
To the extent that the authors of the present paper are aware, little attention has been paid to the nonlinearity analysis of GSPM
As a continuation of their studies on the hexapod machine tools, the authors have investigated the nonlinearity of the GSPM mechanism employing the Bates and Watts measures of nonlinearity
Summary
The Gough-Stewart platform mechanism GSPM , introduced by Gough and Whitehall 1 and Stewart 2 , was originally used as a universal six degree of freedom 6-DOF mechanism in a tire test machine and a flight simulator. Based on the presented algebraic method, the forward kinematics problem was reduced to solve a univariate polynomial equation of degree at most 14. Bonev and Ryu presented a method to solve direct kinematics problem of a general GSPM using three linear extra sensors 17 Both the inverse and forward kinematics of GSPM exhibit nonlinear behavior. In the forward kinematics, when pods are actuated linearly the upper platform moves along a nonlinear path This makes the path control and interpolation functions in Stewart-based machine tools become more complex than in conventional machine tools. To the extent that the authors of the present paper are aware, little attention has been paid to the nonlinearity analysis of GSPM This is especially important for the hexapod machine tools where nonlinearity of the mechanism considerably adds to the interpolation algorithms requiring an insightful analysis. As a continuation of their studies on the hexapod machine tools, the authors have investigated the nonlinearity of the GSPM mechanism employing the Bates and Watts measures of nonlinearity
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