A new method to design a cubic Pythagorean-hodograph(PH)spline curve from any given control polygon is proposed.The key idea is to suitably choose a set of auxiliary points associated with the edges of the given contr...A new method to design a cubic Pythagorean-hodograph(PH)spline curve from any given control polygon is proposed.The key idea is to suitably choose a set of auxiliary points associated with the edges of the given control polygon to guarantee the constructed PH spline has G1 continuity or curvature continuity.The method facilitates intuitive and efficient construction of open and closed cubic PH spline curves that typically agrees closely with the same friendly interface and properties as B-splines,for example,the convex hull and variation-diminishing properties.展开更多
In this paper, two new interpolation algorithms lot CNC machining along curve^l tom pathes are proposed： a time-optimal interpolation algorithm under chord error, feedrate, and tangential acceleration bounds, and a g...In this paper, two new interpolation algorithms lot CNC machining along curve^l tom pathes are proposed： a time-optimal interpolation algorithm under chord error, feedrate, and tangential acceleration bounds, and a greedy interpolation algorithm under the chord error and tangential jerk bounds. The key idea is to reduce the chord error bound to a centripetal acceleration bound which leads to a velocity limit curve, called the chord error velocity limit curve. Then, the velocity planning is to find the proper velocity curve governed by the acceleration or jerk bounds ＇~under＂ the chord error velocity limit curve. For two types of simple tool pathes, explicit formulas for the velocity curve are given and the methods are implemented in commercial CNC controllers.展开更多
文摘A new method to design a cubic Pythagorean-hodograph(PH)spline curve from any given control polygon is proposed.The key idea is to suitably choose a set of auxiliary points associated with the edges of the given control polygon to guarantee the constructed PH spline has G1 continuity or curvature continuity.The method facilitates intuitive and efficient construction of open and closed cubic PH spline curves that typically agrees closely with the same friendly interface and properties as B-splines,for example,the convex hull and variation-diminishing properties.
基金supported by a National Key Basic Research Project of China under Grant No.2011CB302400the National Natural Science Foundation of China under Grant No.60821002
文摘In this paper, two new interpolation algorithms lot CNC machining along curve^l tom pathes are proposed： a time-optimal interpolation algorithm under chord error, feedrate, and tangential acceleration bounds, and a greedy interpolation algorithm under the chord error and tangential jerk bounds. The key idea is to reduce the chord error bound to a centripetal acceleration bound which leads to a velocity limit curve, called the chord error velocity limit curve. Then, the velocity planning is to find the proper velocity curve governed by the acceleration or jerk bounds ＇~under＂ the chord error velocity limit curve. For two types of simple tool pathes, explicit formulas for the velocity curve are given and the methods are implemented in commercial CNC controllers.
