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The kinematic nonlinearity of the Stewart platform–based machine tools produces a geometrical error which is shown to have significant value compared to the machining accuracy during the interpolation of non-uniform rational basis spline curves and surfaces, thus needs to be limited during the interpolation. In this study, a fast and sufficiently accurate algorithm is presented to estimate the maximum kinematic error based on the concept of the median osculating circle. Moreover, a weighted search interpolator and an adaptive non-uniform rational basis spline interpolator have been introduced, which are capable of controlling and limiting the feedrate fluctuations and limiting the maximum kinematic error within an interpolation segment. The experimental verification has shown the effectiveness of the proposed algorithm.

In this paper, the effects and optimization of machining parameters on surface roughness and roundness in turning by wire EDM process are investigated. Surface roughness and roundness, were chosen, as the machining parameters to verify the process. In addition, power, time-off, voltage, servo, wire speed, wire tension and rotational speed were adopted for evaluation by Taguchi method. A L18 (21 × 37) Taguchi standard orthogonal array is chosen for the design of experiments. The level of importance of the machining parameters on the surface roughness and roundness is determined by using analysis of variance (ANOVA). The optimum machining parameters combination was obtained by using the analysis of signal-to-noise (S/N) ratio. The variation of surface roughness and roundness with machining parameters is mathematically modeled by using regression analysis method. Finally, experimentation was carried out to identify the effectiveness of the proposed method. A good improvement was obtained.

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.

Contrary to the conventional serial kinematics machine tools, the parallel kinematics machine tools exhibit nonlinear behavior which is a major source of the machining error. This causes even a linearly programmed path to be traversed along a nonlinear path. The resulting error, known here as the kinematic error, should be critically considered during the toolpath planning. The estimation of the maximum kinematic error using the concept of median osculating circle is introduced in this article. The proposed formulation demonstrates that the maximum kinematic error depends on the curvature of the actual trajectory. In order to estimate the curvature, constant curvature contour maps are introduced. These maps depend on the structural parameters of the machine and are recommended to be provided by the machine's manufacturer. The constant curvature contour maps are illustrated to be an effective graphical tool for kinematic error estimation and thus successfully conducting the optimal planning of the toolpath and the workpiece setup. Consequently, it is recommended in this article that the constant curvature contour maps be employed in the format of a database by computer-aided manufacturing systems during toolpath planning and by interpolators during command generation or by a part programmer to optimally setup the workpiece or conduct the toolpath planning such that the least kinematic error occurs during the machining.