Feedrate scheduling for interpolation of parametric tool path using the sine series representation of jerk profile

This article proposes the sine series representation of jerk profile for acceleration/deceleration feedrate scheduling of parametric interpolator used in computer numerical control machining tools. By selecting the geometric sequence as the coefficients of the sine series, the closed-form expressions of the feedrate, acceleration and jerk profiles are obtained. The resulting feedrate profile is more concise compared with the polynomial profile and more efficient compared with the trigonometric profile. It can be well accepted by the conventional acceleration/deceleration feedrate scheduling algorithms. Also, an approach is proposed to determine the optimal geometric sequence that makes the tracking time as small as possible. Simulations and experiments of tracking complex contours expressed as free-form non-uniform rational B-spline curves are conducted. The results demonstrate the effectiveness of the proposed feedrate profile and the resulting feedrate scheduling strategy.