An apparatus for processing containers such as glass bottles and the like includes a plurality of dimensional gauges which are swept in a tracking motion with a container moving at a constant speed on a conveyor while the several gauging operations are performed. The gauges are mounted on four-bar linkages which have orbital links swept in adjacent relationship with the conveyor so that the gauges move at substantially the same speed as the articles along a tracking segment of the conveyor where the gauging operations are performed. A plug or choke gauge carried on one of the orbital members is reciprocated in and out of a moving container by a separate drive mechanism at a speed modulated to provide low impact velocities and rapid reciprocation of the gauge in and out of the container during the portion of the orbital movement wherein the gauges accurately track the article. A finish-height gauge is carried coaxially about the plug gauge and is reciprocated at a modulated speed different from that of the plug gauge so that the impact velocities on the container can be separately optimized for each of the gauges. The apparatus also includes a set of gauging rings which are orbited at a modulated speed along the tracking segment of the conveyor to check the body dimensions of the containers. The combination of the three gauges in a single inspection machine permits the important dimensions of a container, such as a glass bottle, to be inspected simultaneously along a single segment of a conveyor on which the containers are transported prior to filling or other operations.