Lesson: Not So Simple

Contributed by: Integrated Teaching and Learning Program, College of Engineering, University of Colorado Boulder

A black and white photograph of a girl getting on an old bicycle. The bicycle has one big front wheel and a small back wheel.
Figure 1. The bicycle, a compound machines.
Copyright © Queen's Printer for Ontario, 2007, Archives of Ontario, http://www.archives.gov.on.ca/english/common/c510681.htm


Students expand upon their understanding of simple machines with an introduction to compound machines. A compound machine — a combination of two or more simple machines — can affect work more than its individual components. Engineers who design compound machines aim to benefit society by making work easier for people, even common household tasks. This lesson encourages students to critically think about machine inventions and their role in our lives.

Engineering Connection

Inventing and designing are at the heart of engineering. Engineers use their math and science knowledge to create new products or improve existing ones in hopes of improving people's lives. There is a certain process engineers go through when they invent or design a new or improved product. This process includes identifying the problem, thinking of possible solutions, modeling the system or process, then iterating and improving the product until the optimal solution within the given constraints is achieved. Much of mechanical design involves the simple and compound machines described in this unit.

Pre-Req Knowledge

Students should be familiar with the six simple machines and their ability to make work easier, as discussed in Lessons 1-3 of this unit.

Learning Objectives

After this lesson, students should be able to:

  • Recognize how compound machines are used in many familiar engineering systems today and name several found in daily life.
  • Explain the difference between compound and simple machines.
  • Explain how to calculate the mechanical advantage of compound machines.

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Compound machines are two or more simple machines interacting with one another to do work. Who can think of a compound machine? What are the simple machines at work? Sometimes compound machines can be very complex, and it is difficult to understand what simple machines comprise it. Other times it is easy to point out the simple machines: a door, for example, has hinges (which serve as a lever) and a door knob (a wheel-and-axle).

Everyone look at the door to this room. Imagine there is a hungry lion in the room, and it's looking at you with interest. You estimate that you certainly have time to run to the door and close it behind you, keeping you safe from the lion. However, you notice there are no hinges on the door. How would you open the door to get out? You would have to somehow pick up the door and move it aside. Yet instead of getting safely out the door and closing it behind you, the lion would already be enjoying his meal. Hmmm.....

Consider a different dilemma: you only have hinges on the door, but no door knob. How would you unlatch the door without a door knob? Opening a door can be a very difficult task without the usual components. A compound machine (such as a door) makes doing work (like opening a door) much easier.

Does everyone remember the concept of mechanical advantage? Who can explain it? (Answer: Mechanical advantage is a mathematical expression for how much easier the machine makes work.) Since a door has both hinges and a doorknob, the mechanical advantage is thought of as the combination of the mechanical advantages of each simple machine. If we remove a simple machine from the whole, such as the hinges of a door, the compound machine loses much of its worth. Since there are two simple machines actually operating in a door, is its mechanical advantage cut in half if one is removed? That is to say, is a door without hinges half as good as a regular door?

Engineers believe that a door without hinges is not even half as useful as a regular door. What did you think when the lion was after you? The door was at least there and could be used, but it just takes a lot more effort (lifesaving, in your case) and time to use it.

Engineers decided that, mathematically speaking, mechanical advantage of a compound machine is not merely the sum of the mechanical advantage of its simple machine components but it is the product of these values. Let's say that the doorknob has mechanical advantage of four and the hinges six. That means the door has mechanical advantage of six multiplied by four, or twenty-four. If we remove the hinges then we are only left with the product of the remaining simple machines, which is four (since there is only the doorknob remaining). The mechanical advantage of the door went from twenty-four to four, which is a lot less than half. Choosing to use the product rather than the sum is an attempt by engineers to model the phenomenon of a machine losing a great amount of its mechanical advantage with the loss of just one component.

Let's look at a familiar compound machine known as the bicycle. Who among you likes riding a bicycle? What's so great about it? (Possible answers: It is a faster and easier alternative to running, bike riding is fun, it is good exercise, etc.) Can you list the simple machines that are found in a bicycle? They have wheels and axles, gears and levers.

Fabian Cancellara, a professional cyclist, competing in the 2007 Tour de Suisse.
Copyright © https://en.wikipedia.org/wiki/Fabian_Cancellara#/media/File:Tds_Fabian_Cancellara.jpg

The first bicycle was engineered in 1817 and has since undergone many changes. The first bicycle known as a "Walking Machine" did not have any breaks or pedals, so you would stop and start with your feet, much like you operate a scooter today. As time progressed, bicycles became much easier, safer and more comfortable to use.

This history of the bicycle is a good illustration of the inventing process. Besides creating new products, inventors and engineers work to improve existing products, making them better in different ways. Sometimes, however, an invention can become more complicated than necessary.

In the early to mid 20th century, there were a lot of machines that were over-complicated. A famous cartoonist by the name of Rube Goldberg saw these machines in society and noticed how they amazed people. It seemed to him that the more complicated the machine, the more impressed people were — even if the machine did just a simple task. He thought this phenomenon was funny and decided to create cartoons that illustrate absurdly complicated machines. Over time, the cartoons became very popular. In our next lesson, we will learn more about Rube Goldberg, who was an engineer before becoming a cartoonist.

Good compound machines — ones which are useful and not overly complicated — are present during our everyday activities. When you go home tonight, be observant of the things you use during your regular daily/nightly routine. Remember that there is an inventor behind each of these items. Little and big machine-like items are a very important part of our society, even if we do not always notice them!

Lesson Background and Concepts for Teachers

Compound Machines

An entire range of devices for your use, from the can-opener in your kitchen to the adjustable umbrella on your patio, fall under the category of compound machines. We use these things continuously, and we ordinarily take them for granted. The design for a compound machine consists of a collection of simple machines, each serving a definite purpose for the whole. This lesson brings to light the dependency a compound machine has on each of its simple machines. Moreover, the lesson points out that the removal of just a single simple machine brings the compound machine close to worthlessness. The concept of mechanical advantage is also discussed as an example of the way engineers quantify designs. Above all, this lesson alerts students to an overlooked, yet ubiquitous, aspect of their lives — compound machines.

A compound machine is two or more simple machines working together to make work easier. Scientifically speaking, a machine cannot do work — this ability is strictly limited to a source of energy, such as a human or a battery. Therefore, a machine does not enable you to do less work; rather it enables you to use less force. You do the same amount of work moving from home to work, regardless of if you walk or ride a bike. In reference to the equation for mechanical advantage (see Lesson 1 of this unit), the wheels on a bicycle reduce the effort forces necessary to move.

Consider the act of opening a door, which is doing work. Without hinges, the door must be lifted up (applying forces against gravity) and moved to the wall. The hinges on a door eliminate the need for many forces (such as the ones against gravity) and allow you to apply just a little push to swing the door open. Note that the hinge as a lever amplifies your force as well: less force is needed on the door away from the hinges. Force, originating from you and generating energy, is directed by a machine onto the best possible course, thereby enabling the exertion of less force to do the same amount of work.

If we look at a door, it is easy to see the simple machines operating. There are the hinges (a lever) which enable the door to open and close easily. There is the doorknob (wheel-and-axle) that dislodges the door. There is also a latch (inclined plane) which slides into position to hold the door shut. (Note that in the Introduction/Motivation section, the latch has been ignored to simplify the discussion of the door's mechanical advantage. This omission does not affect the truth of the discussion; rather the door can be thought of as a simple machine that swings and unlatches.)

The bicycle is a compound machine that is made up of wheels and axles, and levers (the arms extending to the pedals). Of course, the end function of the gear is to enable the pedals to turn the wheels. Consider the logic of the simple machines operating to achieve this end function: pedals turn one gear-wheel which turns with a chain the other gear-wheel which turns the tire-wheel. There is always a certain logic to the simple machine components, which is the way they gather together in the compound machine. Other examples of compound machines include staplers, wheelbarrows and can openers.

Just as simple machines have an associated quantity known as mechanical advantage (see Lesson 1), compound machines have mechanical advantage as well, albeit calculated differently. The values for each simple machine are used to obtain the mechanical advantage for the compound machine. Compound machines tend to lose their effectiveness drastically with the loss of a simple machine component. Given this phenomenon, engineers define the mechanical advantage as the product, rather than the sum, of the mechanical advantage of each simple machine. Therefore, if three simple machines with a mechanical advantage of three, four and five respectively are put together to make a compound machine, that compound machine will have a mechanical advantage of sixty. This mathematics reflects how losing just one component greatly decreases the mechanical advantage. (For example, if we remove the simple machine of mechanical advantage five, then all we have left is a mechanical advantage of twelve.)

The concept of mechanical advantage is useful in that it provides a quantitative way to compare different machines. We can talk generally about how one machine works better than another but using numbers is another audible way to compare and, given trusted calculations, present a more precise discussion. By looking at the mechanical advantage values, it is easy to see that compound machines make work a lot easier than simple machines alone. Also, the effectiveness of a machine may change a lot with a simple addition or removal of a compound machine. As testament to its usefulness, engineers commonly refer to mechanical advantage while designing or talking about their design of a machine.

Rube Goldberg

A Rube Goldberg® Machine is a machine that makes something that would otherwise be a simple task very difficult. Rube Goldberg went to school to be an engineer and, after graduating, he decided to become an artist. He drew cartoons of inventions that did simple things in a very complicated way. His inventions involved many simple machines, some more crazy than others, all organized in a logical row to accomplish a simple task. He is the subject of the next and final lesson of this unit.


Compound Machine: Consists of two or more simple machines and allows for work to be done easier.

Lever: A simple machine consisting of a rigid beam or bar which pivots about a fixed point to move heavy loads with less effort.

Logic: The interrelationship between elements of a whole.

Mechanical Advantage: The number of times a force exerted on a machine is multiplied by the machine.

Model: A pattern of something to be made.

Quantitative: Relating to a number or quantity.

Rube Goldberg: Cartoonist and engineer who poked fun at overly complicated machines.

Simple Machine: The fundamental parts of any machine. Simple machines can exist on their own and are also sometimes hidden in the mechanical devices around you; a device which performs work by increasing or changing the direction of force, making work easier for people to do.

Wheel-and-Axle: A simple machine consisting two circular or cylindrical objects which are fastened together and rotate about a common axis. This machine is primarily used to magnify a torque supplied by the user.

Associated Activities

  • The Magician's Catapult - In this activity, students design and create a grape-throwing compound machine for a grape-catching magician.

Lesson Closure

Who can tell me why a door is considered a compound machine? (Answer: It consists of two simple machines working together: the hinges and the door knob.) When we come across a machine that is not functioning, it becomes apparent how much we depend on it. How would you open a can with no can-opener, or a latched door without a knob? We use these mechanical things everyday. Who has another example of a compound machine you would miss? (Possible answers include: your bike or your adjustable basketball hoop or the pencil sharpener.)

One way to talk about the value of a compound machine is by referring to its mechanical advantage. What is \ mechanical advantage? (Answer: Mechanical advantage is a way engineers quantitatively, or with numbers, talk about the effectiveness of a machine, or how much easier it makes work.)

There is a specific reason why we miss machines when they aren't functioning. Is it because you are friends with the machine you are saddened when it is not completely healthy? Probably not. It saddens you because it no longer works for you. Can you think of a day when you did not use a simple or compound machine? These devices which make work easier for us tend to be a valuable part of our day-to-day life.


Pre-Lesson Assessment

Question/Answer: Ask the students and discuss as a class:

  • What is a compound machine? (Answer: A machine made of two or more simple machines.)

Matching: Create a list of all the simple machines. Write another list with some compound machines. As a class, have the students pick out which simple machine is in each compound machine. For example,

A ist of simple machines and a list of Compounds

(Answers: Bicycle = lever, wheel-and-axle; Drill = screw; Wheelbarrow = lever, wheel-and-axle. Scissors = lever, wheel-and-axle.)

Post-Introduction Assessment

Brainstorming: In small groups, have the students engage in open discussion. Remind students that in brainstorming, no idea or suggestion is "silly." All ideas should be respectfully heard. Encourage wild ideas and discourage criticism of ideas.

  • Ask the students to list some compound machines.
  • After they have listed several compound machines, have students write the simple machines in each compound machine on their list.

Lesson Summary Assessment

Drawing: Have the students draw a picture of an existing or made-up compound machine, one that is made of two or three simple machines. Remind them to include where the force is applied and the machine's end function.

Lesson Extension Activities

If desired, this can be added to the drawing in the Lesson Summary Assessment.

Short Math Activity: Have students calculate the mechanical advantage of each simple machine in their drawing by estimating (or guessing) the forces with and without the machine. Remember that:

Equation of the mechanical advantage of a simple machine
Copyright © Equation by Jake Lewis, University of Colorado at Boulder, ITLL, 2007

Use the SI unit of Newtons (N) for force. (One Newton is about 4.5 pounds.)

Given the students' calculated values for the simple machines, have them calculate the mechanical advantage (which has no units) of the compound machine. Remember this is the product of the mechanical advantages of each simple machine.


Queens Printer for Ontario, Archives of Ontario, July 25, 2007, accessed September 6, 2007. http://ao.minisisinc.com/scripts/mwimain.dll/144/IMAGES?DIRECTSEARCH


Michael Bendewald; Malinda Schaefer Zarske; Janet Yowell


© 2007 by Regents of the University of Colorado.

Supporting Program

Integrated Teaching and Learning Program, College of Engineering, University of Colorado Boulder


The contents of these digital library curricula were developed by the Integrated Teaching and Learning Program under National Science Foundation GK-12 grant no. 0338326. However, these contents do not necessarily represent the policies of the National Science Foundation, and you should not assume endorsement by the federal government.

Last modified: August 16, 2017