Parametric interpolation using sampled data

Trajectory in high-speed precision machining requires very small feed-rate fluctuation and contour error, which can be achieved with parametric interpolation. Since it is impossible to exactly compute the arc-length of a general parametric curve, the conventional parametric interpolation obtains a parameter through a real-time update. Thus it cannot be used with a preplanned feed-rate profile, which restricts its applications. To overcome such a problem, the proposed algorithm estimate parameters using tabulated parameter and length data. The simulations show the proposed method useful with smaller contour error and acceptable feed-rate fluctuation comparable to the second order real-time parametric interpolation.