Skip to main content

Step 1: M.A.D. Box's Step 2: 12 and 36 Tooth Gears

Step 2 from the MAD Box Build Instructions illustrating how to connect the plastic motor shaft through the center square hole of the 36T gear, and mesh it with the 12T gear.

In Step 2 of the Build Instructions, the 12 Tooth Gear was already on the shaft that connected the M.A.D. Box's handle on that side of the build.

  • Build Expert, find that side of the M.A.D. Box and show it to your teammates. Then demonstrate that when that handle is turned, the shaft turns the 12 Tooth Gear (driving gear - input) which then turns the 36 Tooth Gear (driven gear - output) that is being added in this step of the build.
  • What is the gear ratio of these two gears?
  • Calculator, figure out the equation below and have the Recorder check it.

Formula for Gear ratio with incomplete values. Number of Driven Gear teeth reads 36 and the Number of Driving Gear Teeth is ?. It is reduced to ? over 1, equal to 3:1.

The 3:1 ratio tells us that the driving 12 Tooth Gear needs to turn three times in order to turn the 36 Tooth Gear once.
That leads to a mechanical advantage of torque. What is torque?

Diagram of a 12T Driving Gear meshed with a 36T Driven gear to show a Torque Advantage. The direction each gear is turning is shown with an arrow. The Driving gear turns clockwise and is labeled input, and the Driven gear turns counterclockwise and is labeled output.

Torque is a mechanical advantage that makes the output of the driven gear or machine more powerful. In this case, the M.A.D. Box had three times as much input as output which makes it more powerful.

  • Recorder, be sure to add notes to the engineering notebook about the mechanical advantage of torque within the M.A.D. Box.

Step 2: M.A.D. Box's Step 10: 36 and 12 Tooth Gears

Step 10 of the MAD Box Build Instructions showing the connection of the third gear and handle component to the previous two sections.

In Step 10 of the Build Instructions, the other side of the M.A.D. Box was connected. It had a 36 Tooth Gear on the shaft with the handle.

  • Build Expert, find that side of the M.A.D. Box and show it to the group. Then demonstrate that when that handle is turned, the shaft turns the 36 Tooth Gear (driving gear - input) which then turns the 12 Tooth Gear (driven gear - output).
  • What is the gear ratio of these two gears?
  • Calculator, figure out the equation below and then have the Recorder check it.

Gear ratio formula with incomplete values reads Number of teeth of Driven gear = ? over Number of teeth of driving gear = 36. This reduces to 1 over ? or 1:3.

The 1:3 ratio tells us that the driving 36 Tooth Gear only needs to turn one time to turn the 12 Tooth Gear three times.
That leads to a mechanical advantage of speed.

Diagram shows a 36T Driving gear on the left meshed to a 12T driven gear on the right to indicate Speed Advantage. The direction each gear turns is labeled with an arrow. The driving gear, labeled input, turns counterclockwise, and the driven gear, labeled output, turns clockwise.

Speed is a mechanical advantage that makes the output of the driven gear or machine faster. In this case, the M.A.D. Box has three times as much output as input rotations which makes it faster.

  • Recorder, be sure to add notes to the engineering notebook about the mechanical advantage of speed within the M.A.D. Box.

Step 3: M.A.D. Box's Compound Gear Ratios

  • Build Expert, turn the handle connected to the 36 Tooth Gear slowly and let the group watch how fast the other handle turns.
  • Recorder, after reading the description below, explain what a compound gear ratio is in the engineering notebook.

The gear ratio for the 36 Tooth Gear turning the 12 Tooth Gear was 1:3 with the mechanical advantage of speed. But when you turn the handle connected to the 36 Tooth Gear once, the other handle turns many more than three times.

That is because the M.A.D. Box uses a compound gear ratio. The M.A.D. Box's compound gear ratio is created by having 36 Tooth Gears and 12 Tooth Gears share the same shafts.

A compound gear ratio multiplies the mechanical advantage of speed or torque within a mechanism.

Top down view of the mad box build with the first, second, and third gear structures labeled, with the shafts connecting the structures called out with a red arrow. The first gear is the 12T at the bottom, the 2nd the 36T gear in the middle, and the 3rd is the 12T gear at the top.

The red arrows in the image above show the shafts that have both 36 Tooth and 12 Tooth Gears on them. Those shafts connect the first, second, and third gear ratios to each other. When the shaft turns, both the 12 Tooth and 36 Tooth Gears on the shaft turn.

This multiplies the mechanical advantage created by each gear ratio because they are connected into a compound gear ratio.

The M.A.D. Box has two compound gear ratios because you can give it input on either side - one leading to a torque advantage and the other leading to a speed advantage.

To calculate the compound gear ratio on one side of the M.A.D. Box, we need to find the three gear ratios in the build from that input to the output, and then multiply them by each other.

  • Build Expert, find the side of the M.A.D. Box where the input handle turns the 36 Tooth Gear and show it to the group. Hint: It is the handle at the bottom of the image above. Point out in the build to review where the three gear ratios are found.
  • Remember, all of the driving gears are 36 Tooth Gears and all of the driven gears are 12 Tooth Gears.
  • Calculator and Recorder, complete and check the equations below:

Formulas for calculating compound gear ratios with incomplete values. The First gear ratio is listed as 12 over 36 and the reduced values are ?. The second gear ratio is listed as 12 over ?, reduced to 1 over ?. The third gear ratio is listed as ? over ?, reduced to 1 over 3. The Compound Gear ratio calculating is written as 1 over 3 times 1 over 3 times 1 over 3 = 1 over 27 or 1 to 27.

  • The entire team should try to answer the following questions: What does the 1:27 Compound Gear Ratio mean? When the handle with the 36 Tooth Gear is turned once, how many turns of the other handle should there be?
  • The Recorder should organize the team's best answers and write them in the engineering notebook.

Step 4: The M.A.D. Box's Compound Gear Ratio for Torque

VEX IQ MAD Box

  • Build Expert, find the side of the M.A.D. Box where the input handle turns the 12 Tooth Gear and show it to the group. Hint: It is the opposite side of the M.A.D. Box as you were using above. Point out that when using this input handle, all of the driving gears are 12 Tooth Gears and all of the driven gears are 36 Tooth Gears.
  • Calculator and Recorder, complete and check the equations below:

Formulas for calculating compound gear ratios with incomplete values. The First gear ratio is listed as 36 over 12 and the reduced values are ? over ?. The second gear ratio is listed as 36 over ?, reduced to 3 over ?. The third gear ratio is listed as ? over ?, reduced to 3 over 1. The Compound Gear ratio calculating is written as 3 over 1 times 1? over ? times ? over ? = ? over ? or ? to ?.

  • The entire team should try to answer the following questions: What is the Compound Gear Ratio and what does it mean? How many times do you turn the handle with the 12 Tooth Gear in order to turn the other handle once?
  • The Recorder should organize the team's best answers and write them in the engineering notebook.

Step 5: Thinking about the M.A.D. Box's Design

Why aren't the M.A.D. Box's six gears all in one row?

Six IQ gears are meshed in a horizontal row alternating 36T and 12T, beginning with a 36T and ending with a 12T.

A design where all of the gears are meshed in a line is called a gear train. The image above shows the M.A.D. Box's gears as a gear train.

A gear train like this only has one gear ratio and it is not a compound gear ratio. The ratio is either 1:3 or 3:1 depending on whether the first or last gear is the driving gear. Only the sizes of the first and last gears in this gear train matter to the gear ratio.

The gears between the first and last gears are called idler gears. They do not increase the power or speed. Idler gears only change the direction of the rotation.

Why wasn't the M.A.D. Box designed with only two gears: a small gear and a gear with 27 times more teeth?

Diagram of a 12 tooth gear on the left meshed to a 324 tooth gear on the right, with a close-up image of where the teeth mesh together.

The Compound Gear Ratio of the M.A.D. Box is 1:27 or 27:1. You might wonder why it wasn't designed with only two gears: the 12 Tooth Gear and a 324 Tooth Gear. That would have led to a 1:27 or 27:1 gear ratio.

Completed gear ratio formulas for a 12T and 324 T gear. The top shows the Driven Gear as 324 and the Driving Gear as 12, creating a ratio of 324 over 12, reduced to 27 over 1, or 1 to 27 ratio. The bottom shows a Driven gear of 12T and a Driving gear of 324T, creating a ratio of 12 over 324, reduced to 1 over 27 or 27 to 1 ratio.

 

There are two reasons why the M.A.D. Box wasn't designed with a 324 Tooth Gear.

The first reason is that a VEX Plastic 324 Tooth Gear doesn't exist. The largest gear in the kit is a 60 Tooth Gear. When engineers design builds, they need to take into account what materials are available and a 324 Tooth Gear was not available.

The second reason is that a 324 Tooth Gear, if available, would be very large. A gear that size would make the build difficult to handle. The compound gear ratio makes better sense for designing a handheld device. When engineers design builds, they need to take into account how the device will be used by consumers.

<  Back Return to Labs Next  >