Real-time smoothing of G01 commands for five-axis machining by constructing an entire spline with the bounded smoothing error

•A real-time five-axis tool path smoothing algorithm is proposed for CNC machining of short line segments.•The uniform smoothing of adjacent two corners is developed for different lengths of G01 commands.•All the G01 commands are smoothed by an entire B-spline through connecting pieces of B-splines.•The smoothing error of the locally asymmetrical B-spline is theoretically proved to be constrained.•Experiments verify that the machining efficiency can be significantly improved by more than 26%.