Simple Machines

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Mechanisms

Since long time ago, the humans searched for a way to solve regular problems that came out and which they have to face. As a consequence the simple machines appeared as a solution with the objectives of lift up big objects, hunt and fish. Since the pre-history the simples machines have been used and, from those, the different types of mechanisms were developed.

The mechanisms are elements used to transmit and transform forces and movements from a driving element to a receptor element. They can be classified in transmission mechanisms and transformation mechanisms.

Mechanisms of linear transmission

These mechanisms transmit the movement and the forces lineally from one point to another one:

1. Lever: A beam or rigid rod pivoted at a fixed hinge, or fulcrum.
   A lever is in its equilibrium when:

   F · d = R · r

   • F is the force done to move the system.
   • R is the resistance that has to be beaten.
   • d is the distance between the hinge and the force.
   • r is the distance between the hinge and the resistance.
2. Fixed pulley: a wheel with a grooved rim attached to a supporting structure around which a cord passes.
   A fixed pulley is in its equilibrium when:

   F = R

   • F is the force done to move the system
   • R is the resistance that has to be beaten
3. Movable pulley: is the combination of a fixed pulley with a secondary pulley that moves lineally.
4. Block and tackle: A combination of paired pulleys, half fixed and half movable.
   A block and tackle is in its equilibrium when

   F=R/n

   • F is the force done to move the system
   • R is the resistance that has to be beaten
   • n is the number of pulleys of the system

Mecjanisms of circular transmission

They transmit the movement, a force or a potency, in a circular way from the input element to the output element.

1. Gear: a toothed wheel that works with others to alter the relation between the speed of a driving mechanism and the speed of the driven parts (the wheels)

                             r = Z1 / Z2; r = N2 / N1
                             
   
                             N1 · z1 = N2 · z2
                           

   where:
   • Z_i is the number of tooth in the wheel i
   • N_i is the speed of the wheel i (rpm)
   • r is the relation of transmission
2. Pulley with belt: It is a combination of two or more separated pulleys in common to a belt. This allows for mechanical power, torque, and speed to be transmitted across axles.
3. Friction drive: System of two or more wheels that are in contact to transfer power to the driving wheels.
4. Endless screw: A screw used to give motion to a helicoidally toothed wheel which axe is perpendicular to the screw.
5. Chain drive: A system of two separated sprocket gears with parallel axes the power of which is conveyed by a roller chain. The teeth of the gear mesh with the holes in the links of the chain.

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Did you know?

The ancient Egyptians used levers, pulleys and inclined planes to build the pyramids and the sphinxes.

In primitive communities, the ancestors used simple machines to hunt. To do so they had to work as a group and, thus, they start to get organized. As they share the effort to hunt, the benefits of the hunt were shared among all the members of the community. To get organized they have had to communicate, which ultimately evolved in the development of the oral language.

Many quotidian tools are simple machines. As examples, we have the seesaw, the scissors, the pliers, tongs, rowing, or the catapult, are all class 1 levers. A weelbarrow and a nutcracker are examples of class 2 levers. And the staple remover or the tweezers are class 3 levers.

In the human body we also have articulations that liken simple machines, as examples we can point out the triceps-elbow-forearm is a class 1 lever, while the system elbow-biceps-forearm or the temporomandibular joint are class 3 levers.

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Questions

1. How can we equilibrate a lever when the force is equal to the resistance?
2. Which is the force needed to re-equilibrate a system if the resistance is doubled?
3. In a class 3 lever, which is the distance between the resistance and the fulcrum if the fulcrum is 30 cm away from the force (which is the double than the distance between the force and the resistance)?

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Exercises

Lever

1. Calculate the force needed to lift a 20 N potato bag with a wheelbarrow considering that the distance between the wheel and the potato bag is 50 cm and from the potato bag to the grip is also 50 cm.
2. At which distance from the fulcrum of a seesaw would we have to sit a 45 N child if there is another 27 N child seated at 1m from the fulcrum?
3. To pull out a thorn with a tweezers we need to do a force of 8 N. The distance between the force and the fulcrum is 2 cm and the distance between the resistance and the fulcrum is 4 cm. Which is the value of the resistance?
4. If two children with the same weight sit at the ends a seesaw, could the distances from the fulcrum be different if we want the system to be in equilibrium?
5. Which is the force needed to re-equilibrate a system if the resistance is doubled?
6. How would you change a force and a resistance of a class 2 lever to re-achieve the equilibrium?

Pulley

1. Which is the force needed to lift a 160 N box using a single pulley?
2. Which is the force needed if we use a chain hoist of 4 pulleys to lift the same box from the previous exercise?
3. Calculate the number of pulley of a chain hoist if the resistance is four times the force.
4. If using a single pulley, the force needed to lift a resistance would be bigger, equal or smaller than the resistance?
5. If using a chain hoist, the force needed to lift a resistance would be bigger, equal or smaller than the resistance?
6. Which is the advantage of using a pulley to lift an object? And that of a chain hoist?
7. How changes the force needed to lift an object with a chain hoist if we increase the number of pulleys?

Gears

1. If we have two gears of 20 and 40 teeth, respectively, which will the output speed be if the smaller one is the driving gear with a speed of 400 rpm?
2. In a three-gear system with 10, 25 and 50 teeth, respectively, with an output speed is of 200 rpm. Calculate the speed of the driving gear.
3. In a two-gear system, how many teeth has to have the driven gear if its speed is 300 rpm and the driving gear has 45 teeth and work at a speed of 200 rpm?
4. Which would have to be the relation between the number of teeth of two gears to decrease the speed of the system three times?
5. If we have three gears of 10, 20 and 40 teeth. Draw how a speed reduction system and a speed multiplier system.
6. Can a speed reduction system have a transmission relation below the unit?
7. Which magnitude of a system do we have to change if we want to increase four times the speed between two axes, and how?Which magnitude of a system do we have to change if we want to increase four times the speed between two axes, and how?
8. Do we have to use an odd number of gears if we want a reversing-speed system?