Angular feedrate interpolation for three-dimensional implicit curves

The paper presents an approach for angular feedrate interpolations for three-dimensional (3D) tool paths in multi-axis machining. The tool path is identified by a position curve assumed to be 3D implicit curve, and a tool orientation curve is obtained based on the position curve. The angular feedrate interpolations calculate the tool position and orientation at each sampling cycle based on specified angular feedrates and given tool paths. The paper relates analytically geometric properties of the prescribed path to rigid body motions along the path by angular feedrates and angular feed acceleration. The results are then used to develop the angular feedrate interpolation. The angular feedrate is further related to the linear feedrate, the contour error and the orientation error. Illustrations for complex implicit curve interpolation are provided with contour error and orientation error analysis. Further simulations are carried out to illustrate the effectiveness of the interpolation scheme for complex curves.