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, an unpositioned cuboid is placed in a rectangular coordinate system. This cuboid can move freely along the X, Y, and Z axes and can also rotate around these axes. The various possible positions are represented by different combinations of movements and rotations.
These six degrees of freedom—three translational (along X, Y, Z) and three rotational (around X, Y, Z)—describe the uncertainty of the workpiece’s position. To correctly position the workpiece, these degrees of freedom must be restricted. If we fix a point in space and ensure the bottom surface of the cuboid touches it, the movement along the Z-axis is limited. By using six fixed points, as illustrated in Figure 3-30, all six degrees of freedom of the cuboid can be controlled. Three points on the XOY plane form a triangular arrangement to restrict three degrees of freedom; two points on the YOZ plane limit two more; and one point on the XOZ plane limits the last degree of freedom. Restricting three or more degrees of freedom is known as the primary positioning reference.
The principle of restricting the six degrees of freedom using six appropriately placed support points is called the six-point positioning principle. The placement of these points is crucial—if they are not properly arranged, the six degrees of freedom may not be fully restricted. For example, the three points on the XOY plane should not lie on a straight line, and the two points on the YOZ plane should not be aligned vertically. This principle forms the foundation of workpiece positioning in manufacturing. The elements used to restrict the workpiece's movement are called positioning elements. Table 3-10 shows which degrees of freedom each common element can limit.
Second: Determine the Number of Degrees of Freedom to Be Restricted 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. Identifying which degrees of freedom must be restricted is the first step in the positioning process.
For instance, in Figure 3-31, a guide plate is being machined for press plates. Since the depth A2 in the groove direction must be accurate, the movement along the Z-axis is restricted. To ensure the bottom of the groove is parallel to the C surface, the workpiece must also have its X and Y rotational freedoms limited. Additionally, to guarantee the length A1 of the groove, movement along the X-axis is restricted. Because the guide slot is centered and aligned with the elongated hole, movement along the Y-axis and rotation around the Z-axis are also limited. In this case, all six degrees of freedom must be restricted, which is referred to as full positioning.
However, if the guide plate from Figure 3-31 is ground on a surface grinding machine, the thickness B of the plate must be maintained, and the top and bottom surfaces must remain parallel. In such a case, only three degrees of freedom need to be restricted based on the processing requirements. This method of positioning with fewer than six degrees of freedom is known as incomplete positioning.
If a workpiece is positioned without restricting the degrees of freedom that are necessary for the machining process, it is considered under-positioning, which is not allowed in manufacturing. Proper positioning is essential to ensure accuracy and consistency in production.
When multiple positioning elements restrict the same degree of freedom simultaneously, it is called over-positioning or repeat positioning. For example, as shown in Figure 3-32, if a part has two or more support points in the same direction, it leads to over-positioning, which can cause instability or even damage during the machining process. Therefore, careful planning of the positioning system is essential to avoid such issues.
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