In this paper,two new interpolation algorithms for CNC machining along curved tool 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. In this paper, two new interpolation algorithms for CNC machining along curved tool 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. Chen, 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.