The present invention provides a back-up tape drive having a precision molded chassis with a fine positioning system for a tape head. This system includes a follower nut threadingly mounted on a lead screw that is bi-directionally rotated by a stepper motor. A lever arm engages the follower nut in a manner such that torsional moments between the forces of the follower nut and lever arm are minimized. The other end of the lever arm engages a tape head mounting unit. The lever arm pivotally engages the chassis at a predetermined midpoint of the lever arm such that a mechanical advantage is derived. The positioning system is designed so the forces acting on the tape head mounting unit are aligned to minimize the torsional forces acting on the tape head mounting unit. The tape head mounting unit further includes reference features that reduce the need for azimuth and zenith adjustment.