A tape drive system is described which incorporates a zero clearance bearing for use on a lead screw positioning system having a structure which inherently flexes or closes onto the external surfaces of the lead screw to cause a precise positioning of the lead screw axis relative to a bearing and a bearing support for the bearing. The bearing contact surfaces of the central passage of the bearing which engage the external surfaces of the lead screw are generally planar in form and thus form line contacts with the external surface of the lead screw. The disclosed tape drive system is enhanced in that the play and loose fitting parts in conventional bearing systems are eliminated, and the subject bearing will act to confine the axis of the lead screw to a fixed position relative to the carriage structure of a high density tape drive or other device utilizing a precision lead screw positioning system.