Mechanics 2

Version 1.1

Index:

1. Rack and pinion 1

2. Worm and gear 1
3. Cam and eccentric wheel 2
4. Crank and connecting rod 2
5. Cardan joint 3

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1. Rack and pinion

1.1. Rack and pinion

The rack and pinion mechanism allows for the conversion of circular motion into
alternate rectilinear motion. This also works conversely: it can transform rectilinear
into circular motion, even though the first type of application is more common. It is
made up of two elements: the pinion, a regular gear, and the rack, which may also
be considered a gear, except for the fact that it has been "flattened". In the right
image, you can see its components. We will look at several examples.

1.2. Sliding door

Some types of automatic sliding doors feature a rack and pinion mechanism driven by an electric motor that makes
them move forward or backward.

1.3. Drill press

Most drill presses feature a rack and pinion mechanism to raise or lower the platform where the parts to be drilled are
placed. The pinion is activated by turning a crank. This mechanism is also used to raise or lower the drill bit.

1.4. Rack railway

In some mountainous areas, where the slope is too steep for a conventional train to operate, rack railways are used.
These are characterised because, in addition to the two typical tracks of a regular railway, they feature a third toothed
track or rack located at the centre of the railway. The drive axles of the train have a pinion that interlocks with the rack
and drives the train upwards easily. Without this system, the train would slip and would not be able to climb.

1.5. Car steering

In the basic mechanism of a car's steering gear, upon turning the steering wheel, a pinion rotates and activates a
rack. In turn, the rack changes the direction of the wheels and the car turns.

2. Worm and gear

2.1. Worm and wheel
The worm and gear mechanism allows for rotating motion to be transferred
between two perpendicular axles. It is characterised because it drastically
reduces the turning speed of the axle driven (the one that is not connected to
the motor). In the right image you can see the name of its components. We will
look at several examples.

2.2. Conveyor
Many industrial machines, such as conveyors, use this mechanism as a speed reducer. Machines in factories are
usually powered by electric motors. These motors rotate very fast while the machines require a slower turning speed.
It is thus necessary to install a reduction mechanism between the motor and the machine. One of the reducing
mechanisms used is a worm.

2.3. Opening and closing of a hydraulic valve

The manual opening and closing of a large hydraulic valve, such as the ones used in dams and irrigation systems,
requires a lot of force, much more than the force that a person can exert. To solve this problem, a worm mechanism is
used. Being a great speed reducer, by exerting a small amount of turning force on the gear, we can obtain a large
amount of force in the wheel, enough to open or close the valve.

2.4. Remote control of a surveillance camera

A worm mechanism is used in many devices that need to turn or move with great accuracy and at slow speeds, such
as surveillance cameras. Other examples: telescopes or antennas that must follow the movement of a star or artificial
satellite, solar panels that follow the movement of the sun, moving parts in robots, etc.

2.5. Anchor lifting mechanism in a ship

Attached to a winch that winds a steel cable or chain, a worm mechanism is used in many lifting systems, such as a
ship's anchor, lifts, cranes, etc.

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3. Cam and eccentric wheel

3.1. Cams and eccentric wheels

Cams and eccentric wheels are mechanisms that transform
the rotary motion of an axle into alternate rectilinear motion.
They are comprised of a rotating piece, the cam or eccentric
wheel itself and an element that touches it, the rod or follower.
Cranks are circular in shape, with the particular characteristic
that their rotating axle does not coincide with their centre.
Cams can be shaped in any way, depending on the type of
motion intended for the follower. Below we'll study several
examples.

3.2. Activation of a toy

Cams and eccentric wheels are used in many machines to drive parts with a back-and-forth motion. An example: a
toy that uses an eccentric wheel.

3.3. Switching a circuit on and off

Cams are often used to open and close electrical, pneumatic or hydraulic circuits. For example: a cam activates a
micro-switch that switches on a light bulb, creating an intermittent effect.

3.4. Tachometer
In combination with electrical, pneumatic or hydraulic sensors, cams are used to capture information about the
operation of machines or technical systems of any type. For instance, a cam, a micro-switch and an electronic counter
can be used to detect the number of turns of an axle.

3.5. Opening and closing of valves in a combustion engine

One of the best known applications of cams is opening and closing valves in petrol and diesel engines. For an engine
to work properly, its valves must open and close, following a very precise cycle. This is achieved by activating them
using cams with the necessary shape. All cams in an engine are mounted on one or two axles, these axles are called
camshafts.

4. Crank and connecting rod

4.1. Crank and connecting rod

A crank is a lever that allows us to manually turn a mechanical device.
If we attach a rod that can rotate freely on both ends, a connecting rod,
we obtain a crank and connecting rod mechanism. This mechanism
allows for the transformation of rotary motion in the crank into alternate
rectilinear motion. It also works in reverse: by applying alternate
rectilinear motion on the connecting rod, we can make the crank turn.
Take a look at the image. Below we will look at several examples.

4.2. Internal combustion engine

In internal combustion engines in cars, lorries and motorcycles, crank mechanisms are of great importance. They are
used to transform the back-and-forth motion of pistons in the engine into rotary motion to drive the wheels, with the
intermediation of a gearbox. Cranks in internal combustion engines are called crankshafts. We can think of a
crankshaft as a series of cranks joined together, forming a bent shaft. The number of bends is proportional to the
number of pistons in the engine.

4.3. Steam locomotive

In old steam locomotives, a crank mechanism was used to make the wheels turn using the alternating motion
generated by a steam engine. Unlike internal combustion engines, the crank moved the wheels directly, without going
through a gearbox.

4.4. Sewing machine

Many machines use a crank mechanism to obtain alternating motion. An example of this is a sewing machine. Note
that, in this case, unlike the engines we saw above, the driving component is the crank. An electric motor makes the
crank turn rapidly to obtain alternate rectilinear motion at one end of the connecting rod. The needle is placed on this
end.

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5. Cardan joint

5.1. Cardan joint

Cardan joints, or universal joints are a mechanism for transferring motion.
They are used to transfer rotary motion between two axles.
Both axles must be placed one next to the other but it is
not necessary for them to be completely aligned,
there can be an angle between them.
It consists of a cross made up of two
perpendicular arms. In each of
the arms, a fixed yoke articulates
at the ends of each axle.
The cross can move
at the joints with the yokes.

5.2. Operation
When the first axle turns, the driving axle, transmits the same average rotational speed to the second axle, the driven
axle. Both make the same number of turns per minute, therefore, the transmission ratio is 1.
When the angle between them is of 0 degrees, they turn as though they were a single axle. As the angle increases,
transmission becomes more difficult. The maximum admissible angle is 45 degrees, even though angles are usually
below 20 degrees.

5.3. Example: Transmission in heavy vehicles

On many occasions, when it is necessary to transmit the movement created by an engine across various meters, an
axle is used with two Cardan joints. This is the case of heavy vehicles, such as lorries, where the motion created in
the combustion engine (front part of the lorry) has to be transmitted to the back wheels of the cabin.

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