Space curve interpolation for CNC machines

Despite the tremendous development in CNC programming facilities, linear and circular cuts parallel to the coordinate planes continue to be the standard motions of modern CNC machines. However, the increasing industrial demand for parts with intricate shapes cannot be satisfied with only these standard motions. This paper proposes an efficient and accurate method for developing a class of precise interpolation algorithms which can drive the cutter of a CNC machine along three-dimensional (3D) trajectories. Engaging a pair of primitive shapes, the method uses their implicit or parametric definition to interpolate their intersection curve on the basis of Danielson’s step selection rules. The presence of Danielson’s criteria guarantees a position error of at most one step. A general-purpose computer for path generation and real-time control of the machine is employed. The user first chooses a suitable combination of shapes whose intersection gives the desired form of the 3D trajectory and then initiates the algorithm with the desired information of the two shapes.