Antecedentes de la música y sus conceptos

A gear is a wheel with teeth in it so it won’t slip as it rubs against another gear. Two or more gears connected together make a gear train. Gears may also push against a toothed bar, called arack, making arack and pinion. The gear is called a pinionin this application (Fig. 3-21).

Two gears in a train convert torque from one shaft to force where the gears meet, and back to torque in the other shaft. This makes the gear train a rotary lever, with its mechanical advantage calculated from the radius of the gears. Any number of gears can be paired together like this, in many clever arrangements. Some of these are explored in Chapter 9.

When you select gears and calculate the mechanical advantage of a gear train, you don’t use the gear radius, you use the tooth count. The number of teeth on a gear is directly related to its radius by way of the circumference. The circumference of a circle, including gears, is:

c¼2r ð3-10Þ

The Greek symbol (pi) is a ‘‘magic number’’ that represents the ratio of a circle’s circumference to its diameter. Pi has a value of about 3.14, though the numbers after the decimal point never come to an end. The diameter of a circle is simply the distance all the way across, or twice the radius.

The mechanical advantage generated by two gears is the ratio of the number of teeth on the output gearAto the teeth on the input gear B:

MA¼A:B MA¼A

B ð3-11Þ

Since the number of teeth is directly related to the gear’s circumference,

MA¼Cout

C_in ð3-12Þ

If you stretch the circumference of the gear out flat, you have a rack. While it is flat, it is easy to see that the number of teeth you can fit onto the circumference depends on the width of the teeth and the distance between the teeth.

The size of the teeth is called thepitchof the gear. The larger the teeth, the stronger they will be but the less you can fit onto the gear. The pitch on two meshed gears must be the same. The shape of a gear’s teeth is specially designed to give the gear a smoothly adjusting contact between the meshed teeth at all times.

Many gears can be squeezed into a small space, often with two gears sharing a single shaft. These gears can change huge amounts of distance, in terms of the rotation of the input gear, into huge amounts of torque on the output gear.

Asprocketis a gear designed to mesh with thelinksof a chain instead of with another gear. The chain travels through space and meshes with a dif- ferent sprocket. Sprockets and chains are one method of sending force a long way away. They are commonly used on bicycles.

Sometimes a pair of pulleys are used like sprockets, with a tightly-fitting rubber belt stretched between them instead of a chain. These are easy to make and are used on power tools and other equipment to transmit force. Pulleys and belts are quieter than chains, though they can slip. Sometimes you want things to be able to slip, so if the machine gets stuck force is lost in the slipping instead of breaking your machine.

Inside your car you can see a pulley and belt arrangement. The pulley and belt both have large, square teeth. These prevent the belt from slipping, so you get many of the best features of chains and toothless belts. These toothed belts are often calledtiming belts, while the toothless ones are v-belts, since they tend to have sloping edges giving them a ‘‘V’’ shape.

CHAPTER 3

Simple Machines

Summary

In this chapter we looked at many ways to make yourself stronger. The simple machines let you turn a long, easy push or pull into a short, yet powerful, force that can lift or move an object.

All of the simple machines are based on this principle of mechanical advantage. The simplest machine is just a hill, or inclined plane. A portable inclined plane is a wedge. A spinning wedge is a screw.

A different approach to mechanical advantage is given by the lever and by pulleys. Wheels, we learned, are like rotating levers and have their own force, torque, assigned to them.

Gears and sprockets are toothed wheels that can be combined in large numbers to give a lot of mechanical advantage in a small space.

Quiz

1. If you wanted to study the forces acting on your robot when it is standing still, what would you study? How about when it is in motion? 2. What force is involved when you cut a sheet of paper with scissors?

When you crush a grape? When you break a string?

3. Remember that robot trying to climb a 10 degree hill? As it is being pushed up the hill, how hard is gravity pulling against the push? 4. What kind of lever is your knee a fulcrum of ? Your ankle?

5. You have a gear with twenty-five teeth, each of which takes 1/8 of an inch (eight teeth per inch). How big is your gear? If you mesh it with a gear that has a 4.97 inch diameter, what is the mechanical advantage?

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