Six-point positioning principle and selection of positioning datum
A workpiece that is not yet positioned has an uncertain location. As shown in Figure 3-29, the unpositioned workpiece, which is a cuboid, is placed within a rectangular coordinate system. This cuboid can move freely along the X, Y, and Z axes, as well as rotate around each of these axes. These movements represent different degrees of freedom.
The six degrees of freedom are used to describe the uncertainty of the workpiece’s position. These include three translational movements along the X, Y, and Z axes, and three rotational movements around the same axes. To correctly position the workpiece, it is essential to restrict these degrees of freedom.
Imagine placing the cuboid on a fixed point so that its bottom surface remains in contact with it—this limits its movement along the Z-axis. If six fixed points are used, as illustrated in Figure 3-30, the three faces of the cuboid will be in contact with these points, effectively limiting all six degrees of freedom. Three points in the XOY plane, arranged in a triangle, limit three degrees of freedom; two points in the YOZ plane limit two more; and one point in the XOZ plane limits the final degree. Limiting three or more degrees of freedom is referred to as the main positioning reference.
The principle of restricting the six degrees of freedom using six appropriately placed support points is known as the six-point positioning principle. However, the placement of these points must be carefully considered—otherwise, they may fail to fully constrain the workpiece. For instance, the three points in the XOY plane should not lie on a straight line, and the two points in the YOZ plane should not be aligned vertically. The six-point positioning principle is fundamental in manufacturing, as it ensures accurate and consistent workpiece positioning. The elements used to restrict the workpiece's degrees of freedom are called positioning elements. Table 3-10 shows how common positioning elements can limit various degrees of freedom.
Second, Determine the Number of Degrees of Freedom to Be Limited Based on Processing Requirements
When positioning a workpiece, only the degrees of freedom that affect machining accuracy need to be restricted. Other degrees of freedom may or may not be limited, depending on the specific situation.
Determining which degrees of freedom must be restricted is the primary concern in workpiece positioning. For example, consider Figure 3-31, which shows a guide plate used for machining press plates. Since the groove depth A2 is required, the movement along the Z-axis must be limited. Additionally, because the bottom of the groove must remain parallel to the C surface, the degrees of freedom about the X and Y axes must also be restricted. To ensure the groove length A1, movement along the X-axis is limited. Furthermore, since the guide slot is centered on the press plate and aligns with the oblong hole, movement along the Y-axis and rotation around the Z-axis are also restricted. In this case, all six degrees of freedom are limited, which is known as full positioning.
However, if the guide plate from Figure 3-31 is ground on a surface grinding machine, only the thickness B of the plate needs to be controlled, and the top and bottom surfaces must remain parallel. In such cases, only three degrees of freedom need to be restricted, based on the actual processing requirements. This method of positioning with fewer than six degrees of freedom is called incomplete positioning.
On the other hand, if a workpiece is positioned without restricting the degrees of freedom that should be limited according to the processing requirements, it is called under-positioning. Under-positioning is not acceptable in manufacturing processes.
When a single degree of freedom is restricted by more than one positioning element at the same time, this is known as over-positioning or repeated positioning. For instance, as shown in Figure 3-32, if a part has multiple support points in the same degree of freedom, it results in over-positioning, which can cause instability or interference during the machining process.
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