Apparatus for connecting an implement to a three-point hitch of mobile machinery such as a tractor for changing the lateral position of the implement relative to the tractor, the three-point hitch comprising an upper top-link arm and two lower bottom-link arms for attaching to the apparatus, the apparatus comprising: a) a first framework longitudinally disposed in a first plane and comprising at least two parallel, vertically spaced apart laterally extending horizontal rails (48, 49),-at least two vertical opposing studs (53, 56), an upper cross beam and a lower cross beam, each cross beam (47, 52) being horizontal and parallel to the rails (48, 49),; the studs (53, 56) being connected to the rails and the crossbeams (48, 51), the rails (48, 49) and the crossbeams (47, 52) being vertically coplanar; b) three attachments (66, 68) supported by the first framework for attachment to the three-point hitch, a top link attachment and two bottom-link attachments, the upper and lower crossbeams (47, 52) capable of being removably secured to the three-point hitch of the tractor with the attachments; c) a slidable second framework disposed in the first plane of the first framework, and slidably-mounted to the rails (48, 49), to slide laterally back and forth along the rails, the slidable second framework comprising at least two tubular sleeves (57, 58), each of the sleeves is configured to slide on one of the rails (48, 49), the sleeves (57, 58) connected by opposing vertical frame member posts (61, 64), the first framework rails pass through the second framework sleeves, the sleeves (57, 58) being vertically coplanar with the rails (48, 49) and the cross beams (47, 52), d) at least one connector, and generally multiple connectors (136, 130) supported by the slidable second framework for connecting the slidable second framework to the implement; e) at least one driver connected to the first framework and connected to the slidable second framework for driving the slidable second framework laterally back and forth along the rails (48, 51); characterized in that f) at least one lower support member attached to at least one of (i) the slidable second framework for engaging the lower crossbeam or (ii) the lower crossbeam for engaging the slidable second framework, and g) at least one upper support member is attached to at least one of (i) the slidable second framework for engaging the upper crossbeam or (ii) the upper crossbeam for engaging the slidable second framework. a) a first framework longitudinally disposed in a first plane and comprising at least two parallel, vertically spaced apart laterally extending horizontal rails (48, 49),-at least two vertical opposing studs (53, 56), an upper cross beam and a lower cross beam, each cross beam (47, 52) being horizontal and parallel to the rails (48, 49),; the studs (53, 56) being connected to the rails and the crossbeams (48, 51), the rails (48, 49) and the crossbeams (47, 52) being vertically coplanar; b) three attachments (66, 68) supported by the first framework for attachment to the three-point hitch, a top link attachment and two bottom-link attachments, the upper and lower crossbeams (47, 52) capable of being removably secured to the three-point hitch of the tractor with the attachments; c) a slidable second framework disposed in the first plane of the first framework, and slidably-mounted to the rails (48, 49), to slide laterally back and forth along the rails, the slidable second framework comprising at least two tubular sleeves (57, 58), each of the sleeves is configured to slide on one of the rails (48, 49), the sleeves (57, 58) connected by opposing vertical frame member posts (61, 64), the first framework rails pass through the second framework sleeves, the sleeves (57, 58) being vertically coplanar with the rails (48, 49) and the cross beams (47, 52), d) at least one connector, and generally multiple connectors (136, 130) supported by the slidable second framework for connecting the slidable second framework to the implement; e) at least one driver connected to the first framework and connected to the slidable second framework for driving the slidable second framework laterally back and forth along the rails (48, 51); f) at least one lower support member attached to at least one of (i) the slidable second framework for engaging the lower crossbeam or (ii) the lower crossbeam for engaging the slidable second framework, and g) at least one upper support member is attached to at least one of (i) the slidable second framework for engaging the upper crossbeam or (ii) the upper crossbeam for engaging the slidable second framework.