The Vision Based Automatic Theodolite (VBAT) is an automatic partial pose measurement system for robot calibration. It uses low resolution rotation stages and resolution enhancement from a vision system to determine the line-of-sight to a spherical illuminated target. Automatic tracking, focusing, and centring provide the calibration system with speed, reliability, and repeatability. A kinematic model of the VBAT is described which includes both the mechanical parts of the system and the optics, using a modified Denavit-Hartenberg approach. All parameters in the VBAT model are identified and embedded into the system controller producing an instrument of 2 arc second accuracy. The system is then used in a conventional manner to calibrate a six degree of freedom PUMA robot, and the results compared to another calibration of the same arm by a coordinate measuring machine with repeatability and accuracy of 0.02 mm. The calibration using the VBAT enhances the accuracy of the PUMA to within 0.2 mm of that produced by the CMM calibration, compared to an accuracy of 14 mm prior to calibration.