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We propose a novel problem formulation for the solution of the nonlinear least squares appearing in the static calibration of the parameters of an industrial robot with rotational joints. A further contribution of the presented work is the use of an extended forward kinematic model incorporating both geometric and nongeometric parameters. These novelties facilitate the use of industrial robots as measurement systems. Both the automobile and the general industry are interested in the use of highly accurate robots that can be deployed as measurement instruments, e.g. for noticing incorrectly welded points early in the production process. Instead of absolute measurement data, we make use of relative measurement data by means of a camera attached to the robot flange. In tests based on data generated from simulation of a real experimental setup, we obtain after calibration absolute accuracies better than plusmn 100 mum. This work lays the foundations for a cost-minimal and effective realization of a robot as a measurement instrument.