A double eccentric positioning apparatus uses two equal offset eccentric bushings to accurately position a tool in two dimensions. Miniature servo motors and precise gearing control the rotation of each eccentric bushing, which controls the direction of the offset vectors. The offset vectors are used to determine the final position of the drill bushing. The desired rotation angles can be mathematically calculated based on desired position. The inner eccentric bushing is located concentric to the offset of the outer eccentric bushing. This allows any position, within a radius of two times the eccentric offset, to be achieved. The use of worm gearing on the eccentric bushings prevents back-driving of the servo motors, due to the lead angle of the worm gears, and the friction between the worm wheel and worm gear.