A machine tool has a carriage (28), has a workpiece carriage (28) for carrying a workpiece (32) from which material is removed by a tool (54) carried by a tool carriage (48). A two-axis scale (86; 88) is attached to one of the carriages, and cooperates with a reading head (96; 98) attached to the other carriage. The output from the reading head is processed by signalling processing means to provide an indication of the position and/or movement of the carriages relative to each other and for generating positional data about one or both of the carriages to assist in controlling their movement in order to perform a machine operation. By directly measuring the relative positions of the two carriages, problems arising from, for example, distortions of the machine frame on which the carriages are mounted are at least mitigated. A preferred embodiment of the machine incorporates a second reading head attached to one carriage and incorporating the scale on another carriage so that the outputs from the two reading heads can be used to determine whether there has been any relative angular displacement of the paths followed by the carriages. There is also provided a method of determining the linear movement of one of the carriages relative to the other, and the machining process achieved using the machine tool.