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Parallel kinematic mechanisms (PKMs) offer advantages of high stiffness to mass ratios, greater potential for accuracy and repeatability, and lower cost when compared to traditional assembly machines. Because of this, there is a strong interest in using PKMs for aerospace assembly and joining operations. This paper looks at the calibration of a prototype Gantry TAU robot by extending the higher-order implicit loop calibration techniques developed for serial link mechanisms to parallel link mechanisms. The kinematic model is based on the geometric model proposed by Dressler et al., augmented with a cubic spline error model of the motion errors for each of the three translation actuators resulting in 185 parameters. Measurements are taken with a 6-DOF laser tracker, and the kinematic parameters are solved as the maximum likelihood parameter estimate.