A multicoordinate sensing measuring device is proposed in which a sensing lever (5) that is resiliently spring-pretensioned in a resting position in a housing (3) can be displaced along a measuring axis (7) and can be pivoted transversely to the measuring axis (7). A connecting piece (25) is guided in a movable manner in the direction of the measuring axis (7) on a guide surface (23) of the housing (3). The sensing lever carries along the connecting piece (25) via a linkage (31, 33) when the sensing arm (5) is displaced in the direction of the measuring axis (7) as well as when the sensing am is deflected in the direction of the measuring axis (7). A measuing device (21) detects the position of the connecting piece (25) relative to the housing (3). The connecting piece (25) and the guide surfaces (23) form bearing suaces for balls of the ball bearing arrangement (27) where the bearing surface of at least one of these componentsnullconnecting piece (25) and housing (3)nullcan be elastically deflected transversely to the bearing surface and clamps the balls (65) flee of play between the bearing surfaces. The connecting piece (25) or/and the housing (3) are made of aluminium or an aluminium alloy and are coated with a comparatively thin hard-anodized layer into which the balls (65) can wear a track groove. Such a sensing meaasring device can be manufactured with relatively large manufacturing tolerances and is nevertheless able to guide the connecting piece (25) in a movable manner essentially free of play in the housing (3).