Accurate real-time interpolation of 5-axis tool-paths with local corner smoothing

5-axis machining tool-paths, when programmed in workpiece coordinates, translational and rotational tool motion in terms of Cartesian tool center points (TCPs), and unit tool orientation vectors (ORI). This paper presents a computationally efficient real-time trajectory generation algorithm for 5-axis machine tools to interpolate translational and rotational tool motion synchronously for accurate 5-axis machining. Finite Impulse Response (FIR) filters are used to generate jerk limited motion trajectories in real-time. Linear translational motion of the tool center point (TCP) is interpolated by FIR filtering of Cartesian velocity pulses in G01 blocks. In order to generate constant speed tool axis rotation, spherical linear interpolation is used, and unit tool orientation vectors (ORI) are filtered directly in the spherical coordinates. Precise tool motion synchronization is realized by matching time-constants of FIR filters utilized for translational and rotational interpolation. Non-stop path interpolation is achieved by locally blending consecutive linear G01 commands. Instead of fitting geometric blending curves and solving feed scheduling problem, smoothing functionality of FIR filtering is used, and a direct 1-step path smoothing algorithm is proposed for real-time implementation. The algorithm considers path blending errors in Cartesian (Euclidian) as well as in spherical (orientation) coordinates due to transient response of the FIR filter. As a result, both tool-tip and the tool-orientation errors are controlled accurately. Effectiveness of the developed algorithms are validated in simulations and also experimentally on an open-NC controlled 5-axis machine tool.