Machining apparatus wherein arc length along a tool path is determined in relation to a parameter which is a monotonic function of time

摘要

Machining apparatus wherein the cutting tool is controlled to follow a path defined by successive splines, the geometry of a spline being described as a function of a parameter other than arc length along the spline and which is related to time. At a present position along a spline, the change in such parameter corresponding to a change in arc length is explicitly determined by approximation and used to determine an incremented position on the spline. A desired constant tool speed can thereby be maintained. By using only the first or the first two terms of a Taylor series approximation, a change in the parameter can be explicitly approximated as a linear or quadratic predictor. Alternatively, polynomial or rational approximations may be employed.