in the following , the invention will be described in detail by referring to exemplary embodiments that are accompanied by figures , in which : fig1 : shows an omega belt drive with vibration damping as one embodiment according to the invention ; fig2 : shows an omega belt drive with bending moment compensation as an embodiment according to the invention ; fig3 : shows an omega belt drive with bending moment compensation and vibration damping as an embodiment according to the invention ; fig4 : shows a further omega belt drive with bending moment compensation and vibration damping as another embodiment according to the invention ; fig5 : shows a further omega belt drive with bending moment compensation and vibration damping as another embodiment according to the invention ; fig6 : shows a further omega belt drive with bending moment compensation and vibration damping as another embodiment according to the invention ; as a first embodiment of the invention , fig1 shows an axis element 1 , a pulley unit 2 comprising a drive pulley 3 and two idler pulleys 4 and 4 ′. a belt 5 is clamped under tension preloading on the axis element 1 via two fixture means 6 and 6 ′. as illustrated by the arrow , the pulley unit 2 is movable forth and back by the drive pulley 3 rotating and thereby pulling its way along the axis element 1 by maintaining grip with the belt 5 . this grip may be realized by a tight fit , for example by the belt being a profiled belt , particularly a toothed belt , on its lower side facing the axis element 1 . the upper surface may be flat or also profiled . a tight fit on this side with the idler pulleys 4 and 4 ′, however , is not necessary , since they merely provide an inner prestress support for the pulley unit 2 against the drive pulley 3 . a guiding of the pulley unit 2 is not shown and may be realized by a further section of the axis element . a damping layer 7 is arranged between the belt 5 and the axis element 1 , wherein the material of the layer may be of a type of rubber or foam . the damping layer 7 may be fixed directly and firmly on the axis element . relative movement between belt 5 and layer 7 has to be provided , since the layer 7 “ swallows ” or reduces vibrations of the belt . between belt 5 and damping layer 7 there may be an air gap , as is shown in fig1 , or both elements may be abutted against each other , for example by the fixture means 6 and 6 ′. fig2 shows an axis element 1 , a pulley unit 2 comprising a drive pulley 3 and two idler pulleys 4 and 4 ′. a belt 5 is clamped under tension preloading on the axis element 1 via two fixture means 6 and 6 ′, wherein the belt is wrapped around the axis element . as illustrated by the arrow , the pulley unit 2 is movable forth and back by the drive pulley 3 rotating and thereby pulling its way along the axis element 1 by maintaining grip with the belt 5 . this grip may be realized by a tight fit , for example by the belt being a profiled belt , particularly a toothed belt , on its lower side facing the axis element 1 . the upper surface may be flat or also profiled . a tight fit on this side with the idler pulleys 4 and 4 ′, however , is not necessary , since they merely provide an inner prestress support for the pulley unit 2 against the drive pulley 3 . a guiding of the pulley unit 2 is not shown and may be realized by a further section of the axis element . in this configuration , on the edges of the axis element 1 the belt is supported by support pulleys 8 and 8 ′. with this support / bearing , the belt is free to expand , contract or slacken , respectively . the wrap - around of the belt about one of the ends of the axis element provides the resulting forces caused by the pretension of the belt to attack in such a way that a bending moment of the axis element is zero or essentially zero . even though pulley unit 2 is configured to drive only on the upper side of the elongated axis element 1 , the belt is carried on to the lower side where it is clamped by fixture means 6 ′. the distance between fixture means 6 ′ and support pulley 8 ′ is arbitrary and may e . g . be maximized , as shown in fig2 and 4 , in order to achieve a higher overall elasticity of the belt . since the belt is frictionless carried on to the lower elongated side of the axis element , it is of no meaning where on the lower side the belt is clamped in order to achieve the zero - sum bending moment of the axis element . fig3 shows an enhanced embodiment of the cmm axis element from fig2 . here , the belt 5 is underlaid by damping layers 7 , 7 ′, and 7 ″ in order to absorb vibrations of the belt . between the belt and the damping layer there may be an air gap , or the belt may abut on the damping layer . anyhow , with the support pulleys 8 and 8 ′ the belt is given chance to compensate the preload stressing distribution , so that forces acting on the support pulleys 8 and 8 ′ are essentially equal in both direction and amount . fig4 shows a configuration of a cmm axis element , on the edges of which the belt is supported by air bearings 9 and 9 ′. with this support / bearing , the belt is free to expand , contract or slacken , respectively . the wrap - around of the belt about one of the ends of the axis element provides the resulting forces caused by the pretension of the belt to attack in such a way that a bending moment of the axis element is zero or essentially zero . fig5 shows a further embodiment of a cmm axis element according to the invention , wherein the belt 5 is clamped in only one clamping point by fixture means 6 . on the edges of the axis element , the belt is supported by air cushion bearings 9 , 9 ′, 9 ″, and 9 ′″. fig6 shows a further embodiment of a cmm axis element according to the invention , wherein the belt 5 is clamped in two separate clamping points by fixture means 6 and 6 ′. guiding of the belt at the edges of the axis element 1 now is realized by support pulleys 8 , 8 ′, 8 ″, and 8 ′″. although the invention is illustrated above , partly with reference to some preferred embodiments , it must be understood that numerous modifications and combinations of different features of the embodiments can be made . all of these modifications lie within the scope of the appended claims .