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The load is the part of the machine that is being powered. Just as an electrical load resists the ow of electricity, the mechanical load resists the driving force. On horizontal layouts, some slack at the bottom of the loop doesn t cause any trouble. On vertical layouts you should tension the slack with a springloaded idler pulley (Fig. 9-6). For long layouts where the return is on the top there is a danger of the chain touching itself. That is strictly naughty, so an idler can be placed to keep the return chain out of trouble (Fig. 9-7). Long runs don t have to be made with a single chain. The top of Fig. 9-8 shows a layout with four di erent chains. The three sprockets in the middle of the run are double sprockets, one sprocket for each loop attached at that point. At the bottom of Fig. 9-8 we see a single long chain that drives its sprockets in opposite directions. The links of the chain can be adapted for di erent tasks. Tank treads are chains with heavy plates attached to the links (Fig. 9-9). The links can also have vertical or horizontal plates with bolt-holes, for fastening other parts onto the chain. Toothed belts are related to chains. The belt body is made of ber and rubber so it is strong and yet exible. Teeth are molded into the body, and these teeth mesh with special sprockets. Timing belts in your car are built like this, and some motorcycles use a belt drive instead of a chain.



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b 2

Example: Cantilever Beam It is given that a is the thickness of the beam, b is the width of the beam and l is the length of the beam The mass of the beam is given as m = rabl, and the moment is given as M(l) = 0 and M(0) = Fl The problem is solved by approximating the cantilever beam as a mass on a spring The stiffness from the Euler Bernoulli equations is utilized, and the movement should be approximated w =

Fig. 9-9.

Microelectro-mechanical Systems (MEMS)

Fig 816: A cantilever beam [8]





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Get rid of the teeth on your timing belt and sprockets and you have a belt and pulley arrangement. These belts tend to be wedge-shaped, tting into a V-shaped groove in the pulley. The V generates more friction and keeps the belt aligned in the pulley. A variation on the pulley and belt uses steel cable or, for really small machines, string, and wraps it around a shaft or drum. Unlike the pulley and belt, you need to wrap the cable around its support several times so that it doesn t slip. These cable-driven systems don t have to provide continuous rotation. Sometimes you just want to drive something back and forth a little bit, such as when you bend an arm. The cable and drum arrangement works for this. You can also fasten the cables down and avoid the problem of the cable slipping. One of the attachment points can be threaded so you can tighten it as needed (Fig. 9-10). Note the bottom diagram in Fig. 9-10. The cable and idler pulley arrangement changes the axis of motion. Cables are useful for pulling. To get a pull followed by a return, the load can have a spring to move it back to its o position. If you route your cable through a tube, the pull doesn t even have to be in a straight line. The cable/tube system can be snaked around corners, giving a exible coupling

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From the Euler Bernoulli equation, the following can be derived:

x =0

Fig. 9-10.

Fig 817: Effective mass of a cantilever beam [8]

Fig. 9-11.

Evaluating at x = l,

1 2

between the power and the load (Fig. 9-11). The brake cables in a bicycle or motorcycle work like this. Note that the ends of the tube need to be rmly fastened down. If the tube is fastened, the motion of the cable is transferred to the load. If the tube is left loose, the motion of the cable distorts the tube and the load is left unmoved. If the range of the motion is short and the cable is sti , you can also push the load. Model airplanes and other radio-controlled models use this type of pushrod system.

1 2

Microelectro-mechanical Systems (MEMS)

Gears were introduced in 3 as a way to convert torque and speed. Like chains and sprockets, gears can be used to carry power (torque) from one place to another as well as to reverse the direction or axis of rotation.

2 1 E 2 a2 a f = = 3 vsound 2 4 2 3 l 2 l It can be concluded that MacDonald s resonant frequency scaling law is

Fig. 9-12.

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