# Gears and train of pulleys

One of the systems of transmission of used movement more is the set formed by gears, each in an axis, that turns according to makes the wheel.
The image of the left we have that system and we can appreciate that
a) The speed of both is different. The small faster tour
b) The union, when becoming by teeth, is very strong
c) We can lubricate them with oils improving his operation
d) The turn of the wheels is opposite one to another one
These systems are very used to as much modify the speeds to the rise as to the loss and example of them is the machines tools, cranes, robots, videos, systems of CD and DVD, programmers of washing machine, electric home appliances or the gear boxes of marches in the cars, among others many applications.

How we can calculate the speed of one of them knowing the speed of the other.

Simpler than it seems. As the connection is by teeth, it means that each tooth that advances the small wheel causes the advance of a tooth of the great wheel.
On the other hand, if the small tour to 10 r.p.m and has 20 teeth, means that the great wheel must advance the same teeth, that is 10 Xs 20 = 200 teeth
If the great wheel has 100 teeth and must fulfill that the speed by the teeth of the wheel is the advance teeth, then V X Teeth = 200, of where we have V = 200/100 = 2rpm
That is that enters the two wheels are fulfilled:

The teeth of the small wheel by the speed of the small wheel > is equal to the teeth of the great wheel by the speed of the great wheel - Ï‰1 X D1 = Ï‰2 X D2

In many occasions we were the wheels stuck some to others on the same axis. They are the gears doubles.
The step (distance between tooth and tooth) and the speed of turn are the same in the two wheels.
If one of them is not shared in common to the axis (free wheel) can turn at another speed.
We will see an example of system of double wheels
In this case we have the conductive wheels (those that push) and the lead ones (those that is dragged).
The direction of rotation is changing according to we looked of left at right.
Developed formulas exist that allow us to find out the speed of the useful axis according to the teeth of each wheel but he is better to use the basic formula and to make the necessary steps.
We will see an example:

The number of teeth of each wheel comes as Za (for the brown one), Zb for great of 2 the axis, etc.
They give the speed us of axis 1 as N1 and we must find out the speed of axis 4.
We do 1 step:
Za X N1 = Zb X N2, of where N2 = $fracZa&space;*&space;N1Zb$
In order to know the value of N3, we let the same: Zc * N2 = Zd * N3 ==>> $N3&space;=&space;fracZc&space;*&space;N2Zd$
Of this form we are finding out each speed in each axis given in r.p.m or RPM
Exercises:
1 the wheel of the left tour at a speed of 100 r.p.m and has 10 teeth. Wheel 2 and 3 is on the same axis and has 20 and 10 teeth respectively. Wheel 4 has 25 teeth. To calculate the speed of wheel 4. Solution:  20 rpm 2 In the image superior we have a train of gears. To calculate the speed of the wheel 7, n7. Solution: 135 rpm

3 Calcular the speed of each one of the axes. Solutions: Eje2 = 1200 rpm, Eje3 = 600 rpm and 100 axis 4 to rpm

4 Piensa and Imagina. A system is formed by 6 gears. Wheel 1 moves to the two, the 2 moves to wheel 3, the 3 to the 4

We know that wheel 1 has 10 teeth and that wheel 6 has 50 teeth, but do not know the number of teeth of the rest of the wheels.

To calculate the speed of turn of wheel 6 if the 1 tour to 30 r.p.m

## Transmission by strap

When the spin axes are very separated is necessary to use strap of union between both wheels. The strap can be a chain or a plastic compound.

We will see one of them that all we know because almost all we have a bike, the chain-Pinion system. This system is formed by a metallic chain whose links fit in the teeth of the gears (pinion and plate). The axes must be positioned fixed to transmit the movement correctly.
The speed relation is the same that always, that is Ï‰1 X D1 = Ï‰2 X D2
In the case of having pulleys and strap (as they exist in the motor of the car), we always have the same formula of (Ï‰1 X D1 = Ï‰2 X D2) but in this case, D means Diameter.

We have to the right an image of a car motor where by means of a rubber strap different components are united, as it is the starter engine, the oil alternator, pump, etc.
The disposition of the same makes necessary east system of transmission.
It would be very well that some of you reasons because the transmission relation is:
Ï‰1 X D1 = Ï‰2 X D2
We stayed it as voluntary exercise.
As in the case of the gears, the double pulleys are formed by two shared in common pulleys to the same axis.
The two wheels are going to turn at the same angular velocity.
They are used much for the trains of wheels (to see attached image). In this case, the wheel of the motor axis tour at a high speed and by the strap makes move axis 2 at smaller speed. Of axis 2 one goes to axis 3 with another pair of pulleys until arriving at the useful axis. The speed in the useful axis will be smaller (reducing system)

Exercise. In the system of the figure, if N1 is 1000 r.p.m and the diameters of the wheels are 20 cm (small) and 60 cm (the great one), to calculate the speed N2, N3 and N4.

## Other mechanisms

The worm drive

Made up of a screw with teeth and one gear. It has   the following properties:

• a) It has a great reduction of speed since the advance of a tooth of the gear supposes that, the worm drive has given a complete return.
• b) The screw is irreversible, that is to say, moves to the wheel, but the wheel to screw no.
• c) The axes that support them are perpendicular
• d) The space that occupies is minimum

### Rack-pinion

Made up of a gear and a fluted strip (rack).

• She is reversible, osseous, one can move to the other.
• It is a system that the type of movement changes, of linear to angular and vice versa
• The data to emphasize of the rack is the number of teeth by centimeter
• A use example is the opening of the tray of the DVD

Resolute exercise:

To calculate the speed of the rack if the wheel has 8 teeth and 120 tour to rpm. The rack has 4 teeth by centimeter.
Solution: They request the speed to us of the rack, that is what advances per time.
We are going to consider that the time is 1 minute and therefore we must know that advances in 1 minute.
In that minute, the wheel turns 120 times and in each turn, it makes move to the rack 8 teeth.
Therefore we have: 1 Vuelva ‰¡ 8 teeth ==>>   120 returns 960 teeth are equivalent to 120 * 8 teeth =
We already have in a minute advances 960 teeth of the rack. As each centimeter are 4 teeth, the 960 teeth are equivalent a $Longitud&space;=&space;frac960&space;dientes4&space;dientes/cm=&space;240&space;cm$
As that advance has done it in a minute, we have it speed is 240 cm/minute

### Follower of levy

We represent two images of this system a levy that is a mechanical element made generally of metal or plastic and subject to an axis with a contour with particular form.
The turn of the axis does that the contour of the levy dissatisfies a called piece   follower (in 2 image comes as pusher).

### connecting rod-crank

The system connecting rod-crank allows to turn a linear revolving motion into one alternative one.
This system or we saw it at the home of the subject the steam locomotive that, although no longer is used in the trains, is very used in other machines as the explosion motor, the windshield wiper or the mountain range to pierce among others.
In order to finish with this part we are going to see an automobile motor where we can appreciate much of the systems seen in this part of the subject

We now happen to see the thermal machines