A linear toothed chain gear, having a flexible toothed chain toothed on both sides, a transport element and sprockets, wherein the toothed chain engages in the transport element with its tooth flanks (1.1) on the driven side and in the sprockets with involute gear (3.1) with tooth flanks (1.2) of a serrated gear (1.2.1) on the drive side, characterized in that the toothed chain toothed on both sides is equipped with tooth flanks (1.1) of an involute gear (1.1.1) on the driven side and is combined opposite that with tooth flanks (1.2) of the serrated gear (1.2.1) on the drive side, and the tooth flanks (1.1) of the involute gear (1.1.1) engage on the driven side in receiving openings (2.1), facing the toothed chain and symmetrical in curved areas too, of a transport element, that the transport element, a largely rigid strip, in linear or curved form, is equipped with the receiving openings (2.1) symmetrical on one side and open inwards or outwards, and on the other side with slots (2.2) at a distance from one another and extending on its opposite outer face transversely to its running direction, and wherein the transport element is usable in a rigid and in a moving form, wherein in the rigid form of use the transport element is fixed and the toothed chain toothed on both sides must be moved about the sprockets with the drive, and wherein in the moving form of use the transport element moves and the toothed chain must be moved about the sprockets at that point, that during the movement sequence the driven-side links of the toothed chain with involute gear (1.1.1) are expanded in the linear region of the chain drive, extend congruently to one another in the curved region, and in the transition from the curved region to the linear region said driven-side links of the toothed chain engage smoothly and without clearance in the receiving openings (2.1) of the transport element, and several driven-side expanded links of the toothed chain extend in a straight line and in combination in the linear region and at the same time the drive-side links of the toothed chain with serrated gear (1.2.1) extend congruently in a straight line and expanded relative to one another in the curved region, and that in the transition from the curved region to the linear region the drive-side links of the toothed chain engage smoothly and without clearance in the involute gear (3.1) of one or more sprockets. that the toothed chain toothed on both sides is equipped with tooth flanks (1.1) of an involute gear (1.1.1) on the driven side and is combined opposite that with tooth flanks (1.2) of the serrated gear (1.2.1) on the drive side, and the tooth flanks (1.1) of the involute gear (1.1.1) engage on the driven side in receiving openings (2.1), facing the toothed chain and symmetrical in curved areas too, of a transport element, that the transport element, a largely rigid strip, in linear or curved form, is equipped with the receiving openings (2.1) symmetrical on one side and open inwards or outwards, and on the other side with slots (2.2) at a distance from one another and extending on its opposite outer face transversely to its running direction, and wherein the transport element is usable in a rigid and in a moving form, wherein in the rigid form of use the transport element is fixed and the toothed chain toothed on both sides must be moved about the sprockets with the drive, and wherein in the moving form of use the transport element moves and the toothed chain must be moved about the sprockets at that point, that during the movement sequence the driven-side links of the toothed chain with involute gear (1.1.1) are expanded in the linear region of the chain drive, extend congruently to one another in the curved region, and in the transition from the curved region to the linear region said driven-side links of the toothed chain engage smoothly and without clearance in the receiving openings (2.1) of the transport element, and several driven-side expanded links of the toothed chain extend in a straight line and in combination in the linear region and at the same time the drive-side links of the toothed chain with serrated gear (1.2.1) extend congruently in a straight line and expanded relative to one another in the curved region, and that in the transition from the curved region to the linear region the drive-side links of the toothed chain engage smoothly and without clearance in the involute gear (3.1) of one or more sprockets.