A gear differential is a mechanism that is capable of adding and subtracting mechanically. To be more precise, we should say that it adds the total revolutions of two shafts. It also subtracts the total revolutions of one shaft from the total revolutions of another shaftand delivers the answer by a third shaft. The gear differential will continuously and accurately add or subtract any number of revolutions. It will produce a continuous series of answers as the inputs change.

Figure 11-8 is a cutaway drawing of a bevel gear differential showing all of its parts and how they relate to each other. Grouped around the center of the mechanism are four bevel gears meshed together. The two bevel gears on either side are "end gears." The two bevel gears above and below are "spider gears." The long shaft running through the end gears and the three spur gears is the "spider shaft." The short shaft running through the spider gears together with the spider gears themselves make up the "spider."

Each spider gear and end gear is bearing-mounted on its shaft and is free to rotate. The spider shaft connects

with the spider cross shaft at the center block where they intersect. The ends of the spider shaft are secured in flanges or hangers. The spider cross shaft and the spider shaft are also bearing-mounted and are free to rotate on their axis. Therefore, since the two shafts are rigidly connected, the spider (consisting of the spider cross shaft and the spider gears) must tumble, or spin, on the axis of the spider shaft.

The three spur gears, shown in figure 11-8, are used to connect the two end gears and the spider shaft to other mechanisms. They may be of any convenient size. Each of the two input spur gears is attached to an end gear. An input gear and an end gear together are called a "side" of a differential. The third spur gear is the output gear, as designated in figure 11-8. This is the only gear pinned to the spider shaft. All the other differential gears, both bevel and spur, are bearing-mounted.

Figure 11-9 is an exploded view of a gear differential showing each of its individual parts. Figure 11-10 is a schematic sketch showing the relationship of the principle parts. For the present we will assume that the two sides of the gear system are the inputs and the gear on the spider shaft is the output. Later we will show that any of these three gears can be either an input or an output.

Now lets look at figure 11-11. In this hookup the two end gears are positioned by the input shafts, which represent the quantities to be added or subtracted. The spider gears do the actual adding and subtracting. They follow the rotation of the two end

Figure 11-12.The spider makes only half as many revolutions.

gears, turning the spider shaft several revolutions proportional to the sum, or difference, of the revolutions of the end gears.

Suppose the left side of the differential rotates while the other remains stationary, as in block 2 of figure 11-11. The moving end gear will drive the spider in the same direction as the input and, through the spider shaft and output gear, the output shaft. The output shaft will turn several revolutions proportional to the input.

If the right side is not rotated and the left side is held stationary, as in block 3 of figure 11-11, the same thing will happen. If both input sides of the differential turn in the same direction at the same time, the spider will be turned by both at once, as in block 4 of figure 11-11. The output will be proportional to the two inputs. Actually, the spider makes only half as many revolutions as the revolutions of the end gears, because the spider gears are free to roll between the end gears. To understand this better, lets look at figure 11-12. Here a ruler is rolled across the upper side of a cylindrical drinking glass, pushing the glass along a table top. The glass will roll only half as far as the ruler travels. The spider gears in the differential roll against the end gears in exactly the same way. Of course, you can correct the way the gears work by using a 2:1 gear ratio between the gear on the spider shaft and the gear for the output shaft. Very often, for design purposes, this gear ratio will be found to be different.

When two sides of the differential move in opposite directions, the output of the spider shaft is proportional to the difference of the revolutions of the two inputs. That is because the spider gears are free to turn and the two inputs drive them in opposite directions. If the two inputs are equal and opposite, the spider gears will turn, but the spider shaft will not move. If the two inputs turn in opposite directions for an unequal number of revolutions, the spider gears roll on the end gear that makes the lesser number of revolutions. That rotates the spider in the direction of the input making the greater number of revolution. The motion of the spider shaft

Figure 11-13.Differential gear hookups.

will be equal to half the difference between the revolutions of the two inputs. A change in the gear ratio to the output shaft can then give us any proportional answer we wish.

We have been describing a hookup wherein the two sides are inputs and the spider shaft is the output. As long as you recognize that the spider follows the end gears for half the sum, or difference, of their revolutions, you dont need to use this type of hookup. You may use the spider shaft as one input and either of the sides as the other. The other side will then become the output. Therefore, you may use three different hookups for any given differential, depending on which is the most convenient mechanically, as shown in figure 11-13.

In chapter 13 of this book, we will describe the use of the differential gear in the automobile. Although this differential is similar in principle, you will see that it is somewhat different in its mechanical makeup.