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mechanics

simple machines
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Automaton mechanics

 

Simple machines

 

The lever family

 

Levers

 

Levers are good for lifting. Archimedes said, ‘Give me a lever long enough and a fulcrum on which to place it, and I shall move the world.’

A lever (from French lever, ‘to raise’) is a rigid object, pivoting on a fulcrum, that can be used to change the distance and power of movement. The load is what we wish to manipulate with the lever, and the effort is the energy input. The load arm and the effort arm are the names given to the distances from the fulcrum to the load and effort, respectively. To achieve eqilibrium, the Law of the Lever is:

Load arm x load force = effort arm x effort force.

In 1, below, for example, the load arm = 3 units; load force = 1 unit; effort arm = 3 units; and effort force = 1 unit. Thus 3 x 1 = 3 x 1. In other words, if a 1 gram feather were balanced by a one kilogram rock, the feather would be 1000 times further from the fulcrum than the rock; if a 1 kilogram rock were balanced by another 1 kilogram rock, the fulcrum would be in the middle.

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There are three orders of levers, defined by whether the fulcrum, load or effort is in the middle. A first order lever, with the fulcrum located in the middle, is what you have when you use a pair of scissors or a pair of pliers to work with something. A second order lever, with the load located in the middle, is what you see when you use a pair of nutcrackers or a wheelbarrow. A third order lever, with the effort located in the middle, is what you see when you use a fishing rod or a pair of tweezers or tongs with a spring at one end.

 

 

First-order lever
Examples: seesaw; scissors (double lever); shoe horn; hammer claw
In a first-order lever the fulcrum is located between the input effort and the output load. By moving the fulcrum closer to, or further away from, the load, you change the distance the lever needs to travel and the amount of effort required to move the load.

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The figure above show how, for an equal effort, the load changes with the position of the fulcrum. An effort of 1 can move a load of 5 (as in 3) but you might notice that you have to move the ‘effort end’ of the lever 5 times as much as the ‘load end’ moves. Yes that's a very small wobbly load in 2.

 

Second-order lever
Examples: nutcracker; oar; wheelbarrow (the fulcrum is the wheel axis); push-up; tennis raquet; bottle opener
In a second-order lever the input effort is located at the end of the bar and the fulcrum is located at the other end of the bar, with the output load at a point between these two forces.

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This kind of lever is like a ‘force magnifier’, that is, it uses a small force to overcome the resistance of a heavy load. Note though that, as with all force magnifiers, the effort must move a greater distance than the load.

 

Third-order lever
Examples: broom; hammer; fishing rod; mandible; stapler; tweezers; nail clippers
In third-order levers, effort is applied between the output load on one end and the fulcrum on the opposite end. The input effort is higher than the output load, which is different from second-order levers and some first-order levers. However, the distance moved by the load is greater than the distance moved by the effor... you could call third-order levers ‘movement amplifiers’.

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* AN IMPORTANT NOTE TO REMEMBER ABOUT LEVERS: the movement of any lever will always follow the arc of a circle, NOT a straight line.

 

 

Wheel and axle

 

Examples: doorknobs; screwdriver; gears
Wheels are found in all sorts of machines. A wheel is actually considered a type of lever that moves in a complete circle. The fulcrum is at the centre of the wheel.The axle is a small wheel at the centre of larger wheel. The axle turns with the larger wheel and can move a load a great distance. You can see an axle when you look at a bicycle. The axle is the smaller wheel at the centre of the larger wheels.

Gears are also wheels. Gear wheels have teeth around the edge that fit into teeth on other gears or wheels. These toothed wheels turn other toothed wheels. Gears are used to make things turn faster or slower and to increase the turning force. There's more information on gears here.

 

 

Pulley

 

Examples: block and tackle; reel, winch
Yet another modified lever, composed of a wheel (called a sheave) with a groove between two flanges around the wheel's circumference. A rope, cable, belt or chain usually runs inside the groove. Pulleys are used to change the direction of an applied force, transmit rotational motion, or realise a mechanical advantage in either a linear or rotational system of motion.

A fixed pulley simply reverses the direction of a force...it doesnt provide any mechanical advantage. A moveable pulley or two or more pulleys connected together do pruduce a mechanical advantage; they permit a heavy load to be lifted with less force. The trade-off is that the end of the rope must move a greater distance than the load.

 

 

The inclined plane family

 

Inclined plane

 

Examples: ramp; screw jack
An inclined, or slanted, plane can help move objects. Using an inclined plane requires a smaller force exerted through a greater distance to do a certain amount of work. A common inclined plane is a ramp

The plane's mechanical advantage lies in its ability to split the force of gravity into two smaller forces; one perpendicular to and one parallel to the plane. It is only the parallel force which needs to be counteracted by pushing an object laying on the plane. If there is no friction on the plane, the pushing or pulling effort required will be 1/10th the weight if the length of the plane is 10 times its height. A similar relationship holds for any plane: the extra distance makes it possible to apply an effort smaller than the weight.

inclined plane

 

 

Wedge

 

Examples: nearly all cutting tools
A wedge is an active inclined plane. Instead of using the smooth side of the inclined plane, you can also use the pointed edges to do other kinds of work. For example, you can use the edge to push things apart. Then, the inclined plane is a wedge. An axeblade is a wedge. Think of the edge of the blade. It's the edge of a smooth slanted surface.

A wedge converts motion in one direction into a splitting motion that acts at right angles to the blade. Nearly all cutting machines use the wedge. A lifting machine may use a wedge to get under a load.

 

 

Screw

 

Now, take an inclined plane and wrap it around a cylinder. Its sharp edge becomes another simple tool: the screw. Put a metal screw beside a ramp and it's kind of hard to see the similarities, but the screw is actually just another kind of inclined plane. How does the screw help you do work? While turning, a screw converts a rotary motion into a forward or backward motion.


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