Perspective is a particular attitude regarding your point of view on a subject. In most cases, the perspective through which you view a subject skews toward a particular bias based on your historical experiences. A classic example is detailed in Figure 1. It shows two people looking at a number drawn on the floor. One sees the number as the number six. The other sees the number as the number nine. Their bias is that the number is drawn such that it is oriented towards them. However, if either chooses to view the number from the other’s perspective, their answer will change as well.
Another classic example of perspective is detailed in Figure 2. It shows a cylinder that has been tapered on one end. If you view the object in its entirety, you see that it is, in fact, a cylinder with a tapered end. However, if you look at the projection from the tapered end, the object is round. If you look at the projection of the object from the side, the object is rectangular. If you look at the projection from above, the object is triangular. Each of these appears to correctly identify the object, but due to the bias in their perspective, they do not factually describe the object.
When designing or reverse engineering helical gearing, it is important to know which perspective you are working with as helical gears are produced in either the normal or transverse direction (Figure 3).
When helical gears are designed in the normal plane, the effect of the helix angle is to enlarge the pitch diameter as the transverse module determines these values. Table 1 details the calculations of a module 3 helical gear pair. The helical pinion has 12 teeth and the helical gear has 60 teeth. In this example, the pinion is profile shifted due to the low number of teeth in order to minimize undercut.
When designing in the transverse plane, the pitch diameter is not enlarged. This allows a helical gear produced in the transverse plane to have the same center distance as a spur gear with the same module, number of teeth, and profile shift. Table 2 details these calculations.
Regardless of whether the helical gear is produced in the normal plane or the transverse plane, the strength of the gear will be greater than that of a spur gear with the same module, number of teeth, profile shift, and face width. The reason for this additional strength is due to the enlarged face width. For a helical gear, the effective face width is:
Bw = B / cos β
where Bw is the effective face width.
B is the measured face width.
β is the helix angle.
Based on the perspective of the design, a helical gear can either be produced in the normal plane or the transverse plane. This perspective is difficult to determine via reverse engineering as the helix angle, the profile shift, and the module can all be variables. If you can fix two of these three variables in your analysis, then the third can be determined and perspective identified.