NURBS Curve Interpolation Method with Flexibility and High Accuracy Based on Curvature Constraint and Displacement Compensation

Feedrate near the maximum curvature points of a NURBS curve can easily exceeds limits.Furthermore,when the interpolation reaches the terminal of a NURBS segment,it may cause a displacement error.Aiming at these problems,this paper presents a NURBS curve interpolation method with flexibility and high accuracy based on curvature constraint and displacement compensation.Firstly,the NURBS curve is divided into several segments according to the maximum curvature points and the length of each segment is estimated.The limits of feedrate are acquired according to NURBS curvature and machine kinematic constraints.Then the jerk-varied flexible acceleration and deceleration is applied to control feedrate.Feedrate is scheduled according to the length of the NURBS segment and NURBS curvature.In the stage of real-time interpolation,the average velocity and displacement compensation is proposed to turn the continuous feedrate curve into discrete feedrate on every interpolation period.Finally,an improved Newton iterative method is applied to generate the position of interpolation point.Experiment is conducted to prove the proposed method can improve the interpolation accuracy and reduce feedrate fluctuation efficiently.