Investigation: Measuring Rotational Speed and Compound Gear Ratios
Name__________________________________________________ Date__________________
Introduction
In this Investigation, you will measure the rotational speeds of different axles in a gearbox that
you build along the way. The axles will be rotating at different speeds because of the
combination of gears that are used. You will learn how to measure the rotational speed with a
rotation sensor. You will learn how to compute a compound gear ratio, and you will understand
the relationship between gear ratios and rotational speed.
CAUTION
Gears have teeth, which means they bite.
Keep fingers and hair away from the rotating gears!
Procedure
Experiment 1
1) Build the base of the gearbox following the building instructions for Experiment 1.
2) Write a RoboLab program that resets the rotational sensor connected to sensor port 3, turns on
motor A in the REVERSE direction for 10 seconds, then turns off motor A. If you do not know
how to write this program, the program is given to you on the last page of this Investigation.
3) Download the program to the RCX.
4) Now we will measure the rotational speed of just the motor axle. Run the program and use the
View button to view the rotational sensor reading.
5) REVIEW: How many counts are there per rotation of the rotational sensor? ______________
6) We will use a technique called averaging to get a more accurate sensor reading. To do this,
run the program 3 times and write down the number of rotational sensor counts in the table
below for each run.
Trial
1
2
3
Rotational Sensor Counts
7) To average the results, add up all 3 numbers and divide by 3. Write the answer here.________
8) Using the number of counts per rotational sensor revolution, how many revolutions did the
motor’s axle make in 10 seconds? Show your work.
9) How many rotations per second did the motor’s axle make? Show your work.
10) Motor speeds are often measured in revolutions per minute (rpm). How many rpms is the
Lego motor? Show your work.
Experiment 2
11) Modify the gear box by following the building instructions for Experiment 2. Make sure
there isn’t too much friction between the new gears and the beams.
12) REVIEW: What is the gear ratio between the gear on the new axle and the gear on the
motor’s axle?________
13) How many rotations (or fractions of a rotation) will the new axle make per every rotation of
the motor’s axle? Can you predict how many rotational sensor counts you will read?
14) Run the program again and record the number of rotational sensor counts for 3 trials in the
table below. Compute the average number of counts as before and add that to the table.
Trial
Rotational Sensor Counts
1
2
3
Average
15) WAIT! The rotational sensor counts are negative. Can you explain why?
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16) How many revolutions did the new axle make in 10 seconds? Show your work.
17) How many rotations per second did the new axle make? Show your work.
18) How many rpms is the new axle? Show your work.
Experiment 3
19) Modify the gear box by following the building instructions for Experiment 3. Make sure
there isn’t too much friction between the new gears and the beams.
20) What is the gear ratio between the gear on the new axle and the gear on the 2nd axle?______
21) What is the compound gear ratio of the gearbox? In other words, what is the overall gear
ratio of both pairs of gears? Show your work.
22) How many rotations (or fractions of a rotation) will the new axle make per every rotation of
the motor’s axle? Can you predict how many rotational sensor counts you will read?
23) Run the program again and record the number of rotational sensor counts for 3 trials in the
table below. Compute the average number of counts as before and add that to the table.
Trial
1
2
3
Average
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Rotational Sensor Counts
24) Why are the rotational sensor counts positive again?
25) How many revolutions did the new axle make in 10 seconds? Show your work.
26) How many rotations per second did the new axle make? Show your work.
27) How many rpms is the new axle? Show your work.
Experiment 4
28) Modify the gear box by following the building instructions for Experiment 4. Make sure
there isn’t too much friction between the new gears and the beams.
29) What is the gear ratio between the gear on the new axle and the gear on the 3rd axle?______
30) What is the compound gear ratio of the gearbox? In other words, what is the overall gear
ratio of both pairs of gears? Show your work.
31) How many rotations (or fractions of a rotation) will the new axle make per every rotation of
the motor’s axle? Can you predict how many rotational sensor counts you will read?
32) Run the program again and record the number of rotational sensor counts for 3 trials in the
table below. Compute the average number of counts as before and add that to the table.
Trial
1
2
3
Average
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Rotational Sensor Counts
33) How many revolutions did the new axle make in 10 seconds? Show your work.
34) How many rotations per second did the new axle make? Show your work.
35) How many rpms is the new axle? Show your work.
Data Analysis
Using the results from the 4 experiments, fill in the table below.
Experiment
Overall Gear Ratio
RPMs of Measured Axle
Ratio between
motor axle’s RPMs
and last
axle’s RPMs.
1
2
3
4
Conclusion
Explain in your own words the relationship between gear ratios and rotational speed. Give
reasons why the measured numbers might not match the theoretical numbers.
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BONUS
Factorization exercise
Factorization can be used to figure out what combination of gears you need to achieve a certain
gear ratio. Using only 8 tooth, 24 tooth, and 40 tooth gears, can you describe or sketch the gear
box that you would need to achieve the following gear ratios?
1) 9 to 1:
2) 45 to 1:
3) (HARD) 375 to 1:
4) (HARDER) 25 to 9:
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Building Instructions
Experiment 1
1
1x16 beam
black connector peg
2x
3
1x10 beam
2x
1x8 beam
black connector peg
2x
5
2
2x
2x
4
1x8 beam
1x
black connector peg
2x
2x4 brick
1x
2x6 plate
4x
Double plates
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Place pieces in this configuration.
6
1x8 plate
7
1x4 plate
1x8 plate
1x
1x
1x
1x8
1x4
1x4
8
1x16 beam
2x
2x2 brick
9
motor
1x
1x8
Axle coupler
2x
1x
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1x4 plate
1x
10
axle
11
8 tooth gear
1x
2x6 plate
2x
1x
make sure there is not too much
friction between the gear and beams.
12
rotation sensor
1x
13
rcx
Short motor cable
1x
1x
connect the cables as exactly as shown
Robotics Academy 2002. All Rights Reserved
Robotics Academy 2002. All Rights Reserved
Robotics Academy 2002. All Rights Reserved
Robotics Academy 2002. All Rights Reserved