An indexer fit to a CNC machine allows the part to rotate horizontally. The object is the part fixed to the indexer while the spindle holds the tool. At this point of time we require understanding that the movement is unlike a lathe and hence not repeat not to be confused that we are talking about lathe like movement. The reason is apart from controlling the x, y and z axis even the rotation of the indexer is controlled. This 4-way coordination allows this machine to be called a 4-axis CNC Router. Among the best examples of such Routers is the OMNI 12S model. This is a heavy duty machine with 12 spindles (the 12S is the key to the naming of the machine).
Also another item that requires explanation is that all 4-axis are not functioning at the same time. The rotational movement corresponds to either the x or y axis while the z-axis with the actual cutting tool is removing material as per the tool path. To understand this concept, place the back of your right hand near a screen. Point the thumb in the direction of the X-axis, Extend index finger upright in the direction of the Y-axis. Extend the middle fingerperpendicular to the index finger. This direction indicates the direction of the z-axis. This is in essence the 3D coordinate system and this rule is called the right-hand rule. To determine the direction of rotation curl your fingers; the curled fingers will indicate the positive rotation direction of the object
To explain the concept of 3D machining take the design of a cylinder and lay it flat as in 2 D. Then wrap the flat sheet (with the design) around a cylinder. Thus with the indexer motion in x, y and z axis as well as the coordination with the rotating motion, the 3D design (due to the wrapping) machining takes place with all the twists, curls, spirals.
In the video (https://www.youtube.com/watch?v=JNkJY-7dF-w&feature=youtu.be) there are two examples of 3D machining on the OMNI 12S machine. The first part of the video shows sofa legs. Because there are 12 spindles each of the sofa legs are identical in shape and carving profiles. The latter part of the video profiles the heads of Buddha being carved. The concept as explained above becomes clear with the video