Introduction to mechanics

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Two basic types of movement

  • rotation (a.k.a. spinning around a center point)
  • translation (a.k.a. change of position)

Complex movements are often combinations of rotation and translation happening at the same time.

Rotation and translation

And, of course, real life movement can involve movement in three dimensions, not just the two displayed on this screen.


In mechanics, a machine is a device that delivers a movement to a desired location (the output) from a force applied somewhere else (the input). You can build machines to control movement in your projects.

Machines often involve converting one type of movement to another, such as rotary motion to linear motion.

Circular motion is transformed into linear motion by using a mutilated pinion, which alternately drives the top and bottom rack.
Rotating the disk causes the rod to move to-and-fro.

Complex machines are based on simple machines. They involve lots of simple machines merged together. Simple machines include:

  • inclined planes
  • levers
  • wheel and axle
  • pulleys
  • screws

Each of these is generally used to make moving something easier to do.

The inclined plane

Pushing a weight up a slow incline is much easier than lifting it straight up.

Moving something up an inclined plane reduce the effort, compared to lifting straight up

An inclined plan is any inclined surface that is used to reduce effort when applying force to move something.

A moving truck ramp is an inclined plane

Inclined planes are often used in cutting surfaces, like the blade of an axe. In this case, the axe blade has an inclined plane on either side. This allows the axe to more easily move the wood apart, as compared to trying to move the wood apart by pulling on it sideways. The wood travels slowly up and pulls apart as it goes up the two diverging inclined planes.

An axe is a double inline plane a.k.a. a wedge

The lever

A lever consists of three important parts: the load, the effort, and the fulcrum. The lever pivots around the fulcrum. The lever is used to make moving heavy things easier, or to make something move fast. The magnitude of the effort put in, combined with the distance between the effort and the fulcrum and distance between the load and the fulcrum, determines the properties of the lever.

The basic concept is somewhat intuitive to anyone who has played on a see saw.

A lever with a load causes rotation

A lever where the load exerts more force than the effort causes rotation around the fulcrum

The amount of effort necessary to move a given load, depends upon the position of the fulcrum. If the fulcrum is exactly in the middle point, effort that is greater than the weight of the load will move it, but there is no magnification of the effort. The amount the load moves is directly a result of the increase in effort. An example of a centered-fulcrum lever is a weight scale.

Lever with equal load and effort

A lever doesn't rotate if the effort perfectly counter-balances the load. Effort here is represented by a person's weight, but could also be exerted by someone or something pushing or pulling on the lever.

But if the fulcrum is not at exactly the middle-point, there is an adjustment in how much effort is required. For example, if the fulcrum is closer to the load, less effort is required to move the load. Examples of levers with centered, or off-centered fulcrums include scissors, hedge trimmers, and crow bars.

A lever with the fulcrum adjusted

Adjusting the position of the fulcrum allows the lever to move a bigger load with less effort.

The hedge trimmer's fulcrum is closer to the cutting edge, thus reducing the effort required to squeeze the handles.

Examples of more advanced levers include the wheelbarrows, beer bottle openers, and nutcrackers. In these cases the fulcrum is at the very end of the lever, and the effort is applied to the opposite side of the lever than the load.

In a wheelbarrow, the relative positions of the fulcrum, effort, and load, are different. This example allows one to lift a weight 3x as large as the effort put in.
A beer bottle opener magnifies effort the same way a wheelbarrow does. Reward yourself for understanding this concept.

The wheelbarrow and bottle-openers are examples of 'second class levers, where the fulcrum is at the very end of the lever.

Even more advanced levers (third class levers) include a hammer pulling a nail, tweezers, and fishing rods. In these levers, more effort is required to be put in, but the load moves further than the load does. It's like a reversed second class lever.

In a third class lever, more effort is required, but the distance moved is magnified. In this example, the load moves 3x as far as the point on the lever where the effort is actually exerted.
A hammer pulling out a nail is a third class lever. Exerting a lot of force to pull the handle a little results in a larger movement of the nail.

Wheels and axles

The wheel and axle are like a circular lever. The movement of the wheel is converted to a smaller, but more powerful, movement at the axle.

In a wheel, the outer edge travels a further distance than the inner axle during the time it takes for each rotation. So, that means the outer edge moves faster than the axle.

You can turn a large wheel easily, but the outer edge has to travel a long way to go all the way around.

A big ship wheel takes a long time to turn, but exerts a lot of pulling force on the rope.

A smaller wheel requires more force to turn, but has less distance to travel to go all the way around. The axle, which is at the exact center of the wheel, travels the least distance of all, and turns with more force than the outer edge of the wheel. So with a wheel, like with the inclined plane and the lever, you are exchanging distance for force. The easy slow turning at the outer edge of the wheel produces fast, powerful turning of the axle.

The wheels on a car works in the reverse way the force of the motor spins the axle which makes the outer edge of the wheel spin faster following the same principles.

Examples of common items that rely on the wheel and axle include the steering wheel, the water wheels, pulleys, etc.

Moving the bow linearly causes the string to pull the pulley wheel, which has a drill in the middle that spins quickly, since it's at the center of the wheel.

A wheel and axle become even more effective at magnifying force or changing a movement's direction when gears and belts are put into the picture.

Gears can be used to change the direction or speed of movement, but changing the speed of rotation inversely affects the force transmitted. A small gear meshed with a larger gear will turn faster, but with less force, and vice-versa.

Motors involve wheels, axles, and often gears.


Pulleys can be used to either change the direction of motion, or reduce the effort required to produce motion.

A method of transmitting rotation at right-angles by using pulleys.

Compared to other movement devices, pulleys are especially useful because they rely on ropes, which are flexible, rather than solid objects which are hard and inflexible. Due to this flexibility, ropes can be routed through unusual paths, while maintaining their movement properties.

Fixed pulleys don't give you mechanical advantage, but allow you to change the direction of movement. Moveable pulleys give you mechanical advantage, and thus lets you lift things with less force than would be required otherwise.

In the pulley system on the right, the lower pulley is moveable. The weight will move up by 1/2 the distance the rope is pulled. But the force required is reduced by half.

In the pulley on the left (#12), no mechanical advantage is achieved, but the direction of movement is changed. In the pulley system on the right (#13), the lower pulley is movable. So, the weight will move up by 1/2 the distance the rope is pulled down. But the force required is reduced by half.


A screw transforms rotary movement into lateral movement.

Transforming rotary movement into lateral movement.

Rotary motion is imparted to the wheel by the rotation of the screw, or linear motion of the screw by the rotation of the wheel.

Screws are fundamentally a form of inclined plane.


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