A full-automatic multi-function workpiece finishing machine provides different types of operations that can be caused to occur in any sequence that meets the requirements for a particular type of workpieces to be surface-finished. The machine includes a series of individual operational or functional units which are controlled by a computer-based sequence controller. The sequences of the different types of operations may be identified by unique code numbers which are entered into the computer from the terminal keyboard or by reading them by any optical or other means.
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