A positioning apparatus for a glass sheet processing system for adjusting position of a heated glass sheet on a conveyor of the glass sheet processing system, wherein the conveyor is configured to convey the glass sheet in a direction of conveyance and the glass sheet processing system further includes a forming station for molding the glass sheet, the positioning apparatus comprising: a carriage configured to be attached to the glass sheet processing system and including first and second carriage bodies (26, 28), the first carriage body being configured to be attached to the glass sheet processing system such that the first carriage body is translatable in the direction of conveyance, and the second carriage body is configured to be supported by the first carriage body such that the second carriage body is movable in a direction generally transverse to the direction of conveyance; a first motor for moving the first carriage body in the direction of conveyance; a second motor for moving the second carriage body with respect to the first carriage body; and a positioning member configured to be connected to the second carriage body and configured to contact the glass sheet to adjust position of the glass sheet with respect to the conveyor; wherein, when the positioning member is connected to the second carriage body, the positioning member is movable between a raised position and a lowered use position in which the positioning member is configured to contact the conveyor, and the positioning apparatus is configured to enable or allow the positioning member to move with respect to the second carriage body and in a direction parallel to a plane of conveyance of the glass sheet when the positioning member is in the lowered use position to compensate for a speed difference between the conveyor and the first carriage body when the first carriage body is being translated in the direction of conveyance and the positioning member is in contact with the conveyor. a carriage configured to be attached to the glass sheet processing system and including first and second carriage bodies (26, 28), the first carriage body being configured to be attached to the glass sheet processing system such that the first carriage body is translatable in the direction of conveyance, and the second carriage body is configured to be supported by the first carriage body such that the second carriage body is movable in a direction generally transverse to the direction of conveyance; a first motor for moving the first carriage body in the direction of conveyance; a second motor for moving the second carriage body with respect to the first carriage body; and a positioning member configured to be connected to the second carriage body and configured to contact the glass sheet to adjust position of the glass sheet with respect to the conveyor; wherein, when the positioning member is connected to the second carriage body, the positioning member is movable between a raised position and a lowered use position in which the positioning member is configured to contact the conveyor, and the positioning apparatus is configured to enable or allow the positioning member to move with respect to the second carriage body and in a direction parallel to a plane of conveyance of the glass sheet when the positioning member is in the lowered use position to compensate for a speed difference between the conveyor and the first carriage body when the first carriage body is being translated in the direction of conveyance and the positioning member is in contact with the conveyor.