Computer controlled machine tool

A machine tool is provided for allowing complex shapes to be machined on a workpiece at high speed. The system is computer (13) controlled and receives workpiece profile data which are converted into a succession of tool position signals during machining. Not all the digital signals are calculated at one time, a number of future digital signals are calculated during a succession of time intervals. Further, for symmetrical profiles, data defining only one symmetrical portion is fed to the computer (13) which then produces digital signals for the whole profile. In each time interval, a tool position signal is outputted which is of a constant amplitude corresponding to the required tol position and which is fed to a signal processor (19) where it is converted into a signal which is used to drive a linear motor (23). Proportional and differential feedback (24, 25) are provided from the motor (23) for feedback control.