Abstract
Aiming at the problem of speed fluctuation caused by the large error between the ideal interpolation step and the actual interpolation step in the traditional non-uniform rational B-spline ( NURBS ) curve interpolation, a NURBS curve interpolation algorithm based on Mline-Gear is proposed. The differential and derivative definitions are derived to transform the Mline and Gear formulas respectively, and the prediction and correction formulas of the interpolation parameters are obtained. Then, it is judged whether the interpolation parameter values obtained by the correction formula meet the speed fluctuation rate requirements, and the interpolation can be continued. Otherwise, the Steffensen descent formula is used to iteratively correct the interpolation parameter values. In order to ensure the calculation accuracy and avoid solving high-order derivatives, the fourth-order Runge-Kutta method is used to solve the initial two interpolation parameters. Finally, the algorithm is simulated. The simulation results show that the algorithm reduces the feed speed fluctuation rate while ensuring a small number of iterations.
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