0.3 Simple machine elements  (Page 3/3)

The force applied to the outer surface of each wheel must also beequal otherwise one of them would be accelerating more rapidly than the other, and again the teeth of the otherwheel would break. However, the forces the forces applied tothe axles are not equal. Returning to the concept of levers, we know that the distance from the fulcrum at which theforce is applied effects the force applied at another point, and a wheel and axle works like a lever. Equal forces are being applied toeach wheel, but on the larger wheel that force is being applied at a greater distance from the axle. Thus, for the larger wheel,the force on the axle is greater than the force on the axle of the smaller wheel.

Cams and cranks

Both cams and cranks are useful when a repetitive motion is desired. Cams make rotary motion a little more interesting by essentially moving theaxle off-center. Cams are often used in conjunction with a rod. One end of the rod is held flush against the cam by aspring. As the cam rotates the rod remains stationary until the "bump" of the cam pushes the rod away from the cam'saxle. Cams can be used to create either a linear repetitive motion such as the oneillustrated in , or a repetitive rotational motion such as using a cam and a rubber band .

Cranks convert rotary motion into a piston-like linear motion. The best examples of cranks inaction are the drive mechanism for a steam locomotive and the automobile engine crankshaft. In a crank, the wheel rotatesabout a centered axle, while an arm is attached to the wheel with an off-centered peg. This arm is attached to a rod fixedin a linear path. A crank will cause the rod to move back and forth. If instead the rod is pushed back and forth, it will causethe crank to turn. On the other hand, cams can move their rods, but rods cannot move the cams.

Pulleys

Pulleys can be used to simply change the direction of an applied force or to provide aforce/distance tradeoff in addition to a directional change, as shown in . Pulleys are very flexible because they use ropes or chain to transfer force rather than a rigidobject such as a rod. Ropes can be routed through virtually any path. They are able to abruptly changedirections in three-dimensions without consequence, except, of course, additional friction. Ropes canbe wrapped around a motor's shaft and either wound up or let out as the motor turns.

illustrates how a compound pulley 'trades' force for distance through anaction/reaction force pair. In a double pulley, as the rope passes over the pulley the force is transmitted entirely butthe direction has changed. The effort is now pulling up on the left side of the bottom pulley. Now, for a moment forget thatthe end of the rope is tied to the bottom of the top pulley. The mechanics are the same if the rope is fixed to theceiling. The important thing is that the end of the rope is immobile. The effort is once again transmitted entirely as therope passes over the bottom pulley and there is a direction change. The end of the rope is attached to the ceiling so therope is pulling down on the ceiling with the force of the effort (and half of the force of the load). We assume that theceiling holds up, so this must mean that there is a force balancing out this downward force. The ceiling pulls up on therope as a reaction force. This upward force is equal to the effort and now there is an upward force on the right side ofthe bottom pulley. From the perspective of a free-body diagram the compound pulley system could be replaced by tying tworopes to the load and pulling up on each with a force equal to the effort.

The disadvantages of pulleys, in contrast to machines that use rigid objects to transfer force, areslipping and stretching. A rope will permanently stretch under tension, which may affect the future performance of adevice. If a line becomes slack, then the operation of a machine may change entirely. Also, ropes will slip and stickalong pulley wheels just like belts. One solution to the problems associated with rope is to use chain. Chain ispliable like rope, and is able to transfer force through many direction changes, but the chain links are inflexible intension, so that the chain will not stretch. Chains may also be made to fit on gears so that slipping is avoided.