Abstract : This paper introduces a novel interpolation algorithm based on polar coordinates in CNC machining systems. The algorithm is simple, easy to implement, and has a small interpolation error. Keywords : polar coordinates, interpolation, pulse, pulse-counting method 1 Introduction In CNC systems, the machining of arbitrary straight lines, arcs, or other complex curve contours is achieved through interpolation. Currently, software interpolation or software-simulated hardware interpolation algorithms are commonly used. These algorithms are based on Cartesian coordinates, while some complex parts (such as cams) often use polar coordinates to represent their contour parameters. For these types of parts, we designed a novel interpolation algorithm based entirely on polar coordinates—called the pulse-counting method. 2. Interpolation Principle Taking a disc cam as an example, the profile curve is represented by polar coordinates of many points. During CNC milling, the linkage of the cam's circumferential rotation and radial linear motion in two feed directions can be controlled, i.e., interpolation calculations are performed in polar coordinates. Let the cam profile curve be represented by a total of coordinate points (called nodes), with polar coordinates (R_i, R_j), where R_i ranges from 1 to 13, including circular arc segments. Take any two adjacent nodes, i and i+1 (see points A and B in Figure 1), and their included angle is: [b][align=center]For more details, please click: A New Interpolation Algorithm Based on Polar Coordinates[/align][/b]