is characterized by high rigidity and low mass density has a high resonance frequency as a result of which a high limit frequency can be achieved with the inventive positioning device during the scanning or positioning process the object carrier 116 is connected by guide elements 102 105 to the one piece support element 101 wherein the guide elements can comprise a wide variety of different shapes e g l shaped the position detector or detectors 121 128 which is are preferably piezoresistive position sensors is are integrated into at least one guide element 102 105 they serve as deflection sensors for the corresponding directions of movement a field effect transistor can also be used as a position detector the channel serves here as a piezoresistive detection element when silicon is used as a construction material for the inventive device the necessary control electronics can be integrated into the support element for example in an advantageous embodiment of the inventive device position detectors are arranged on all of the guide elements simultaneous multiple evaluation of the position of the object carrier is thus possible to compensate for environmental influences such as temperature fluctuations the position detectors piezoresistive position sensors are in another preferred embodiment connected to form a bridge circuit wherein additional necessary elements of this bridge can be integrated into the nonmoving parts of the inventive device e g the support element the drive elements 112 115 are integrated into the support element 101 the movement generated by the drive elements is transmitted to the object carrier 116 in each case by way of point contacts or ball shaped contact points 117 120 and by way of the movement transmitting elements 108 111 as a result of the point like or ball like contact.