Research On The NURBS Interpolation And Offset Algorithm Of Edge Banding Curve

Now people’s aesthetic standards reach a new height and the pursuit of personalized become a major tendency. People gradually tend to the furniture which have obvious curve feature, innovative and unique appearance. The traditional furniture in straight lines are not popular. This puts forward to the request to the traditional edge banding machine. So the curved edge banding machine comes into being. The edge banding curve usually demands low-efficiency but hige real time. The interpolation control is the key to the curved edge banding machine. Naturally the research on interpolation algorithm of the curved edge banding machine has become the main point in recent years.Although there is little direct research on the interpolation algorithm of the curved edge banding machine, but many CNC system which introduced NURBS method to enrich the interpolation control function to improve the accuracy and efficiency of the interpolation control are worth learning. This paper made a research on the interpolation algorithm of NURBS curve and proposed an improved NURBS interpolation algorithm for edge curve which based on fourth order one step Obrechkoff differential equations. For furthermore ensuring the high-precision of calculation and the real time control of interpolation, the algorithm was predigested by using rearward difference in place of differential to reduce the computational complexity. Considering the fairness effect of different parametrization, compared the proposed algorithm with the accumulative chord length parametrization and the Adams parametrization, the computer simulation experiments indicated that the interpolation curve which simulated by the proposed algorithm was the best through the different measures contrasted because the maximum chord error of curve interpolation decreased by 66.16% and 66.67% and the average chord error reduced by 35.29% and 21.43%. The new algorithm effectively guaranteed the fairness of curve interpolation. The new algorithm provided a method for interpolation control of the curved edge banding machine.Trajectory planning is usually the next step after the interpolation, but the offset of the curve is the premise of trajectory planning. Therefore, this paper research on the offset algorithm. Utilizing the affine invariance of NURBS, an offset algorithm was presented based on projection. For furthermore reducing the computational complexity,the offset algorithm based on projection was predigested by using projection from three-dimensional space to Two-dimensional plane to avoid calculating the normal vector of space curve and using midpoint in place of vertex to avoid the repetition. Using the projection algorithm to the interpolation curve by the accumulative chord length parametrization, the Adams parametrization and the new interpolation algorithm, the computer simulation experiments indicated that the offset curve was consistent with the source curve. The algorithm established foundation for the trajectory planning of the curved edge banding machine.Finally, in order to proving the two algorithm are feasible and effective, this paper uses the two algorithms to complete a simulation experiments on the curved edge banding machine. The results showed that the two algorithm can better suit for the demand of the curve edge banding machine bescause the overall error can be better control.