Learning Through Play: Exploring Gears

We're learning about gears right now and the thing is, my kids already knew lots about gears. They knew that gears can transfer force and that two gears touching each other will turn opposite directions, and that a small gear will rotate more times than the large gear it is attached to. They knew how to use their lego bevelled gears to switch the force to an axle perpendicular to the first one, and they knew how to use the lego rack and pinion. So then the question becomes, what next?
The first thing to learn was that we really didn't know all that much about gears. For example, we didn't know the terminology. We weren't calling the lego pieces by their right names. Its easy for me to learn the names and then start use them, so the children can pick up on them too.
The second thing for us was to try to learn some of the other things combinations of gears can do. So we looked at how the gears in a little electric motor we have slows down the number of rotations, and we built a model of it out of lego. Playing with gears we could talk about rotational speed and the number of rotations per minute.


We can see how a point on the outer part of a gear has to travel further than a point on the inner part of gear in order to make the same number of rotations. (Think of playing crack-the-whip, and how fast the outermost person has to move compared to the innermost person.) Two gears of different sizes moving together, the outer parts will be moving at the same linear speed so the rotational speed will differ. The idea that the linear speed of a particular part of the gear (the distance that point is travelling) can be different than the rotational speed (the number of times it goes around) is a bit confusing. The whole gear has the same rotational speed. Different parts have different linear speeds.
M was impressed to notice that when he attached a lego piece at an acute angle to a spinning axle it looked like it made a cone. Change the angle to an obtuse one and you have a wider flatter appearing cone. He made up a big story about how the cone was part of a radio system to send messages into outer space.

I wanted my oldest son to look closely at the math behind the gears, so I made my own worksheet for him to do. I asked him to choose gears of different sizes and count the teeth. He was to then take the largest and smallest gear, and find out how many times the smallest would have to turn in order to get the largest to do a full rotation. This took him a little while to figure out how to do it since it is easy to loose track of where he is counting but even there it provided him with an opportunity to practice problem solving. The next questions challenged him to think about the change in rotation speed in gear trains, and I had written the question so that he had the option of modelling it if he needed but he wasn't required to. By starting with small questions and working into harder ones he could discover for himself that if a large gear driven or driving a small gear has three times the number of teeth than the small gear, then it will rotate at a 1/3 of the speed. If a gear train is made where a large gear drives a small gear which shares an axle with another large gear, which in turn drives a small gear then we can write a multiplication equation based on it. If the second axle is turning at 4 times the rate of the first, and the third axle is turning at 3 times the rate of the second, then the third axle is turning at 12 times the rate of the first.


Then I looked online for some inspiration. I found information about cardan gears and decided to try making a model of it out of cardboard. I needed two sizes of gears, one half the diameter of the other. I drew two circles, one inside the other and then marked out angles. After some trial and error I found that my large circle could have the teeth marked out with 15 degree lines and the smaller circle with 30 degree lines. I made two copies of the smaller circle and mounted them on cardboard. I used tacks and a corkboard to spin the gears. My oldest son helped in all of this. Cardboard isn't the best building substance for gears since they could only turn a couple of times before the teeth got too bent but it gave us a chance to get the idea.

Afterwards we watched some simple videos online about more complicated gear set-ups. We saw an example of how a gear with missing teeth can be used to allow a pause, or how using oval gears can allow a constantly rotating axle to drive another axle in a pattern of varying speeds.

The point for me was to encourage the children to see gears as useful mechanisms and to think about the different ways in which they can be used. We are lucky to have a collection of lego gears to play with, although a visit to the website Wooden Gears makes me want to dig out my scroll saw and learn how to use it more accurately. The website is a great one to visit with absolutely amazing marble mazes and other contraptions. They also have some example of lego marble mazes and an interactive tool for generating gear templates if you don't feel like doing all the math yourself.
Follow-up goals for this include:

• Revisiting a project we did earlier, where we taped pencils to lego structures and tried to make little art machines where different gears and levers would move the pens.
• Make a toilet paper engine.
• Making cardpaper oval gears according to the patterns found at Glue2Chronicle.

Using gears provides a perfect opportunity to practice looking clearly at what a problem is and then putting together a combination of steps to solve it.