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For the purpose of positioning the 80 kg, 2 T superconducting coil/cryostat used in the development version of a magnetic stereotaxis system, a four degree-of-freedom goniometer has been designed, built, and tested. Computer-controlled, stepping motor actuators enable movement of the coil via either joystick, keyboard, or translator-module keypad commands. An integral arrangement of counterweights and counterbalances minimizes the overall weight and size of the goniometer while maintaining static and dynamic stability during operation. As much of the structure as possible has been made of nonmagnetic materials (mostly aluminium) to minimize distortion of the superconducting coil's field. The design principles for the goniometer, the essential features of its construction, and its performance characteristics and limitations are discussed, along with a strategy for performing precision magnetic stereotaxis procedures with an arrangement of static superconducting coils.