Development of a novel adaptive nonuniform rational basis spline interpolator with limited kinematic error for hexapod machine tools

Abstract

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.