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Simple machines

Year 1 Design for Industry

John Errington

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Simple Machines

A simple machine is any device that only requires the application of a single force to work. They change the direction and/or size of forces.

The traditional list of simple machines is:

* The inclined plane

* The wheel and axle

* The lever

* The pulley

* The wedge

* The screw

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Mechanical advantage

Ideal Mechanical Advantage (IMA) or distance ratio

IMA = distance moved by effort / distance moved by load

Actual mechanical advantage (AMA) or force ratio

AMA = load / effort

Efficiency = AMA / IMA *100%

Work Input = Useful Work Output + Work to Overcome Friction

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Friction

Friction is the resistive force that occurs when two surfaces slide along each other when forced together. It causes physical deformation and heat build up. The frictional force is a function of the force pressing the surfaces together and the coefficient of friction of the two materials.

Ff = Fp * μr

where: Ff is the frictional forceFp is the force perpendicular to the contact surface andμr is the coefficient of friction

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Static Friction

Static friction (sometimes called stiction) occurs when the two objects are not moving relative to each other (like a desk on the ground).

The coefficient of static friction is typically denoted as μs.

The initial force to get an object moving is often dominated by static friction.

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Examples of static friction

In the context of hard disk drives, stiction refers to the tendency of read/write heads to stick to the platters, preventing the disk from spinning up and possibly causing physical damage to the media. Some hard drives avoid the problem by not resting the heads on the recording surfaces.

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Kinetic Friction

Kinetic friction occurs when the two objects are moving relative to each other and rub together (like a sled on the ground). The coefficient of kinetic friction is typically denoted as k, and is usually less than the coefficient of static friction.

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Examples of kinetic friction:

* Sliding friction is when two objects are rubbing against each other. Putting a book flat on a desk and moving it around is an example of sliding friction.

* Rolling friction occurs when the two objects are moving relative to each other and one "rolls" on the other (like a car's wheels on the ground). The coefficient of rolling friction is typically denoted as μr.

* Fluid friction is the friction between a solid object as it moves through a liquid or a gas. The drag of air on an airplane or of water on a swimmer are two examples of fluid friction.

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For our initial treatment of simple machines we will assume friction is negligible.

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Inclined Plane

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Inclined plane

Inclined plane is a device used to raise heavy loads with relatively small forces. For example, pushing a load up a ramp onto a platform requires less force than lifting the load onto the platform.

• Ramps and steps are forms of inclined planes.

• An eccentric cam is another form of inclined plane – often used to clamp materials.

Operating lever

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LeverLever consists of a rod or bar that rests and turns on a support called a fulcrum. A force or effort is applied at one end of the rod to lift a load placed at the other end. A lever can help lift a weight with less effort. Prying something loose with a crowbar is using a lever. Some machines, such as a catapult, use a lever to hurl objects.

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Three Classes of Levers

First-class levers – the fulcrum is in the middle like a seesaw, crowbar, or balance scale.

Second-class levers- the load is in the middle like a wheel barrow, or a nutcracker.

Third-class levers – the effort is in the middle – like a pair of tweezers.

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First-class Lever

Effort

Fulcrum

Load

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Lever

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Wedge

A wedge is a device that has two or more sloping surfaces that taper either to a sharp edge or to a point. Wedges are used to split, clamp or pierce materials, and to adjust the positions of heavy objects.

Knives, chisels, axes, pins, needles, and nails are wedges.

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Wedge

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Pulley

Pulley is a wheel over which a rope or belt is passed for the purpose of transmitting energy and doing work.

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Pulley

Change Force Direction

Same Force Size

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Block and Tackle

Imagine that you have the arrangement of a 100 pound weight suspended from a rope, as shown. If you are going to suspend the weight in the air then you have to apply an upward force of 100 pounds to the rope. If you want to lift the weight up 10 feet, you have to pull in 10 feet of rope to do it.

100lb

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Block and Tackle

Now imagine that you add a pulley. The only thing that changes is the direction of the force you have to apply to lift the weight. You still have to apply 100 pounds of force to keep the weight suspended, and you still have to reel in 10 feet of rope to lift the weight 10 feet

100lb

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Block and TackleHere you can see that the weight is suspended by two ropes rather than one. Each rope holds only half the weight, or 50 pounds. That means that if you want to hold the weight suspended in the air, you only have to apply 50 pounds of force (the ceiling exerts the other 50 pounds of force on the other end of the rope). If you want to lift the weight 10 feet higher, then you have to reel in twice as much rope - 20 feet of rope must be pulled in. This demonstrates a force-distance tradeoff. The force has been cut in half but the distance the rope must be pulled has doubled.

100lb

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The mechanical advantage of a block and tackle is simply found by counting the number of ropes from the bottom pulley system.

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More pulleys

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Screw

A Screw is an inclined plane wrapped in a spiral around a shaft.

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Screw

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Wheel and AxleWheel and axle is a mechanical device used in lifting loads. It is one of the six simple machines developed in ancient times and ranks as one of the most important inventions in history. Sometimes teeth or cogs may be placed around the edge of the wheel, as in a cogwheel, or on the sprocket wheel of a bicycle.

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Wheel and axle

A large wheel on a small axle reduces the frictional force at the bearing by an amount equal to the ratio of their diameters.

FD = Fd * d / D

D

d

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Gears

An adaptation of a wheel and axle

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Gear teeth

For gears to mesh together the tooth spacing has to be the same on each gear. So we can calculate the mechanical advantage (or the speed reduction) as

R = N1 / N2 where N1, N2 are the number of teeth on each gear.

Example:

A gear of 50 teeth is driven by a gear with 10 teeth. This gives a mechanical advantage of 5 (and a speed reduction of 5)

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‘A’ frame

A simple lifting machine (just a lever with force and effort at the same point) used to change the direction in which a pull force is applied. Used in ancient times for raising heavy stones.

Side view

Front view

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Examples of simple machines• Inclined plane: wheelchair ramp, slide, hill, roller coaster

• Wedge: chisel, screwdriver, door wedge, thumbtack, pins

• Lever: see saw, wheelbarrow, hammer, crowbar, bottle opener, oar, fork, baseball bat

• Pulley: flagpoles, clotheslines, blinds, crane, fan belt

• Wheel and axle: doorknob, roller skates, eggbeaters, pencil sharpener, skateboard

• Screw: nuts and bolts, jar lid, corkscrew, screw jack

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Worked example: lever

Fulcrum - Hinge joint

Handle

60cm

4cm

• A guillotine as shown below is used to cut brass bar which is 1cm thick.

• If a force of 20kg (196N) at the cutting edge is required to cut the bar, how much force will need to be applied at the handle?

• How far will the handle move while making the cut?

• What will be the force F in the support?

F

(note the use of two wedges to cut the bar)

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Worked example: lever

Fulcrum

Hinge joint

Handle

60cm

4cm

If a force of 120kg (1176N) at the cutting edge is required to cut the bar, how much force will need to be applied at the handle?

Fhandle = 1176 * 4 / 60 = 78N

• How far will the handle move while making the cut?

Blades move 1cm handle moves 1 * 60/4 cm = 16cm

• What will be the force F in the support?F = 1176 up plus 78N down = 1098N

F

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Worked example – pulley system

• A block and tackle is used to lift a car engine weighing 90kg (882N). The bottom pulley block has six ropes.

• What is the distance ratio?• If it takes a pull force of 180N to lift the engine,

what is the actual mechanical advantage and the efficiency?

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Worked example – pulley system

• A block and tackle is used to lift a car engine weighing 90kg (882N). The bottom pulley block has six ropes.

• What is the distance ratio? 6 (six ropes)• If it takes a pull force of 180N to lift the engine,

what is the actual mechanical advantage (force ratio = load / effort = 882 / 180 = 4.90

• and the efficiency η? η= force ratio / distance ratio * 100%η = 4.9 *100 / 6 = 81.7%