Cams and gears transmit positive motion from the driver to the follower by direct contact of the surfaces. As the distance between centers of shafts increases, the driver and follower for such methods of transmission become large, unwieldy, and costly, and rigid links may be used to connect the rotating pieces, as in the case of parallel rods of a locomotive. For a further increase of distance, the transmission is attained by means of belts and pulleys, and, if the distance is very great, by wire ropes and sheaves. As there is always some slipping of the belt (from 1 to 2 per cent), the velocity ratio is not exact; but this is not essential in many classes of machinery. The slip and stretch of the belt reduce the shock when heavy machinery is set in motion - an important feature in many cases.

## Open And Crossed Belts

Fig. 93. Diagram of Simple Open Belt Drive.

The simplest forms of belt drives are the open belt (Fig. 93) and the crossed belt (Fig. 94). In each case the shafts are parallel, and the pulleys fastened to the shaft with set screws or keys. The central planes of the pulleys must obviously be coincident. The belt is then tightly stretched over the pulleys, and, assuming B, the driver, to turn in the direction of the arrow, motion will be transmitted to A, on account of the friction set up between the belt and pulley surfaces. The fibers of the belt, in running on or off the pulley, bend over one another, so that those next the pulley, on the inside of the belt, are compressed, while those on the outside are stretched. Assuming the compression and stretch to be equal, then the central fiber does not change in length. This central fiber is shown in the figure by a "dash-and-dot" line. Considering that there is no slip of the belt on the pulley, the face of each pulley will move exactly with the belt, and the turns of each pulley will depend on its circumference; or,

Fig. 94. Diagram of Simple Crossed Belt Drive.

Turns of A = Speed of belt = S

Circumference of A πXDiameter of A

Turns of B = Speed of belt = S

Circumference of B πXDiameter of B

Ve1ocity ratio = Turns of A = Diameter of B Turns of B Diameter of A

Thus the velocity of the shafts is inversely proportional to the ratio of the diameters of the pulleys. The action of the belt in bending about its central fiber has the effect of increasing the diameter of the pulley by an amount equal to the thickness of the belt, and an exact calculation for velocity ratio must take this fact into consideration.

For example, suppose that the diameters of A and B are 8" and 24" respectively, and that the belt is ¼" thick. Then the velocity ratio:

24 24.25 is 8 = 3 for the usual approximate "calculation; but 8.25 = 2.939 for the exact value.

The direction of shaft rotation depends on the method of applying the belt. In the case of the open belt, the top surfaces of each pulley being connected, each shaft rotates in the same direction; while in the case of the crossed belt, the top surface of A being connected to the bottom surface of B, the shafts rotate in opposite directions. Thus the directions of rotation are the same when the center line of belt lies wholly on one side of the line connecting the centers of pulleys; and different when it intersects the line of centers.