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High accuracy 3D laser measurment systems are used in applications like inspection and reverse engineering (RE). With automatic RE in mind, we have designed and built a system that is based on a laser profile scanner mounted on a standard industrial robot with a turntable. This paper is concerned with the relatively complex accuracy issues of such a system. The different parts of the system are analyzed individually and a brief discussion of how they interact is given. Finally a detailed analysis of the scanner head along with experimental results is presented.