February 2011 Machining Tip



Machining by the Numbers

We don’t know who first said that the way to make an equine sculpture is to take a block of stone and remove everything that isn’t a horse, but the description applies equally to the processes of Renaissance sculpture and CNC machining. Beyond that similarity, however, the processes are very different. One of the biggest differences is that a sculptor can move freely around his (or her) work and approach the piece at any angle necessary to achieve the end result. But a milling machine, which uses rotating cutters to remove unwanted material (as distinct from a laser, lathe, robot, drill press or other machine tool), is limited to very specific ways of moving in Euclidean space. Firstcut uses 3-axis milling, working sequentially from up to six sides of a workpiece. The part shown below is an example of this (Figure 1). Starting from one side, and then rotating the part 90 degrees or 180 degrees as necessary, we can mill features from six perpendicular sides of a part.

Figure 1

Figure 1


Any point on the surface of a machined part can be described by its position along three axes, X, Y, and Z. The problem is that, in machining, we need to do more than describe a point; we need to mill next to it. And in order to mill next to it, we must extend a rotating mill to the point in question. In typical simple 3-axis milling, the workpiece can move in X and Y (side-to-side and forward-and-back), and the cutting tool can move in Z (up and down). When coordinated, this allows the machine to reach any point on the side of the workpiece that faces the cutting head. Working this way, a 3-axis machine could, for example, mill a profile on the front of a coin. If however, we wanted to use that same equipment to mill a three-dimensional model of a head, we would have to reposition the workpiece several times in order to reach all sides of the piece (see Figure 2). Or, we could use 4- or 5-axis milling equipment.

Figure 2 – To mill a three-dimensional head, we would have to reposition the material several times in order to reach all sides.

Figure 2 – To mill a three-dimensional head, we would have to reposition the material several times in order to reach all sides.


4-axis milling equipment uses the three linear axes described above, but adds a fourth (rotational) axis in the form of a vertical turntable (the rotational axis is generally horizontal) that can rotate the workpiece. This allows the cutting head to access all sides of the piece, though not the top of the head or the bottom of the neck without repositioning. There are still limitations, including the fact that such a machine can only reach the workpiece along lines perpendicular to the axis (see Figure 3).

Figure 3 – 4-axis equipment vertical turntable rotates the workpiece, which allows the four sides of the head to be cut from one positioning, but requires repositioning to reach the top of the head and bottom of the neck.

Figure 3 – 4-axis equipment vertical turntable rotates the workpiece, which allows the four sides of the head to be cut from one positioning, but requires repositioning to reach the top of the head and bottom of the neck.


5-axis equipment adds a second rotational axis creating a configuration similar to a gimbal, allowing the workpiece to be rotated in two rotational axes (see Figure 4).

Figure 4 – 5-axis equipment has an infinite number of ways to access any point of the workpiece.

Figure 4 – 5-axis equipment has an infinite number of ways to access any point of the workpiece.


Returning to our head, 4-axis equipment would allow us to machine the front, back, and sides, but would require repositioning to reach the top of the head and bottom of the neck. 5-axis equipment would let us machine the top of the head without repositioning and could also be used, were we so inclined, to machine some realistically-angled nostrils (see Figure 5).

Figure 5 – 5-axis equipment would allow realistically-angled nostrils to be machined, as well as the top of the head, assuming the workpiece is being held at the neck.

Figure 5 – 5-axis equipment would allow realistically-angled nostrils to be machined, as well as the top of the head, assuming the workpiece is being held at the neck.


Obviously, additional axes add capabilities to milling equipment, but these capabilities come, literally, with a price. First, 4- and 5-axis equipment is more complex than 3-axis systems and, for that reason alone, more costly. Second, unlike 3-axis systems, which allow only one way to reach each point, 4- and 5-axis machines allow an infinite number of ways to access any point, making the setup of toolpaths far more complex. Third, for a machine of given size, additional axes require additional components that take up space within the work area and reduce the maximum size of parts that can be machined. And, finally, additional axes increase the magnitude of machining error due to hardware, software, rounding error, or wear of the equipment. Along the rotational axes of 4- and 5-axis systems, error increases with distance from the axis, so it is particularly problematic in larger pieces. This can be managed by using more precise, more costly equipment, but when equipment costs more, so do the resulting parts.


The alternative to using 4- or 5-axis equipment is to use a 3-axis machine and work from six sides, which can be done with proper fixturing. At Firstcut, we use proprietary fixturing specifically designed to allow quick, easy repositioning of a workpiece in 3-axis milling equipment. This approach provides most of the capabilities of 4- and 5-axis systems, costs less to operate, and is far faster to set up because of our ability to automatically generate 3-axis toolpaths. In the case of the head, there might be some minor features that would not be accessible from any of six sides, and these would be clearly indicated in your FirstQuote® interactive quotation.


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