Gears are the toothed wheels used in many machines, including bicycles, where they work together to change the relationship between the driving mechanism and the moving parts. You pedal the cranks to turn the chainring, which is connected by a chain to smaller gears that move the rear wheel. You change gears depending on terrain. If you are riding up a steep hill, you might want to shift into a lower (larger) gear. This makes it easier to turn the cranks, but the rear wheel doesn’t turn as much with each rotation of the cranks. When you get to a level or downhill stretch of road, you probably switch to a higher gear, where each turn of the cranks leads to more turns of the rear wheel.
Your muscles might know all about bike gears, but your mind might need an opportunity to play around with them to really understand how they work. In this activity, you will learn how to make gears from scratch. Then, you can move them around. Let’s learn some math before we get started.
The radius of a circle is the distance from its center to its edge. Diameter is twice the radius—it’s the straight line distance across the center of a circle. Circumference is the distance around a circle. Thousands of years ago, Greek mathematicians discovered the ratio of a circle’s circumference to its diameter and called it π (pi), which is approximately equal to 3.14159. The circumference of a circle can be found using the following equation: πd=C. This equation will come in handy when cutting out your cardboard gear teeth.
How do gears work?
- Cardboard box made of corrugated cardboard. Corrugated cardboard has the ridges inside. Most shoe boxes are not made of corrugated cardboard.
- Grown up to help with cutting cardboard
- Compass (the kind you draw circles with)
- Sharp scissors, box cutter, or razor
- Permanent Marker
- Cut out a piece of cardboard that is at least 8“x8”. This will be your base.
- On another piece of cardboard, use the compass to trace out at least four circles with 1 inch, 1.5 inch, 2 inch, and 3 inch diameters. Remember that a radius is half the diameter, so if you set the compass radius at 1 inch, you will get a circle with a two inch diameter.
- Ask your grown-up assistant to help cut out the circles you traced. The rounder your circles are, the better they will work.
- Figure out the circumference of each of your circles by multiplying the diameter by π. For example, for the 3 inch circle, the circumference would be about 9.42 inches.
- Next, you are going to give each of your gears toothed edges. Making sure to cut along the corrugates, cut a long strip of cardboard ¼” wide.
- Jam your fingernail into the corrugate and carefully remove the brown paper on one side of the corrugated cardboard. You should be left with lots of bumps, without any paper still stuck on. This can be tricky, so be patient!
- Using the circumferences you calculated, cut out a piece of stripped corrugated cardboard for each of your circles.
- Cover your work area with newspapers to keep it clean.
- Spread glue around the edge of your first circle.
- Roll the correctly measured piece of corrugated cardboard around the circle, making sure the bumps are on the outside.
- Secure the stripped corrugated cardboard with a push pin or painter’s tape until dry.
- Repeat for each of your other circles.
- Let your gears dry overnight.
- Use a black permanent marker to make a black mark at one tooth of each of your gears. This way you will able to track when each has made a rotation.
- Attach the 3-inch and 1 ½-inch gears to your board, using pushpins at the center of each and making sure that the gears’ teeth interlock.
- Rotate the 3-inch gear clockwise. Which way does the 1 ½-inch gear turn?
- Using the black marks to keep track, turn the 2-inch circle once. How many times does the 1 ½-inch gear turn?
- Now, turn the 1 ½-inch gear once. How many times does the 3-inch gear turn?
- Arrange the other gears as you wish, and experiment!
When you turn the 3-inch gear clockwise, the 1 ½-inch gear turns counter-clockwise. When you turn the 3-inch gear once, the 1 ½-inch gear goes around twice. When you turn the 1 ½-inch gear once, the 3-inch gear makes half of a rotation.
Gears transmit torques (twisting forces) in predictable ways—this is why they are so useful in machines that require exact movements, like clocks. The 3-inch circle made the 1 ½-inch gear spin around twice because the 3-inch gear has twice the circumference.