MECHANICAL ADVANTAGE Overview
In this lesson you will learn:
• How to calculate gear ratios
• The influence of gear ratio
on torque and axle speed
Vex 1.0 © 2005 Carnegie Mellon Robotics Academy Inc.
Background Calculating Gear Ratio
•
•
When only two gears are involved, the gear ratio is simply the ratio of the
number of teeth on the driven gear to the number of teeth on the driving
gear.
When there are multiple gears on a single axle, the overall gear ratio can be
calculated by multiplying the individual gear ratios as if they were fractions.
Vex 1.0 © 2005 Carnegie Mellon Robotics Academy Inc.
Background Compound Gear Ratios
•
•
•
•
The simple gear ratios in the picture to
the right are 3:1 (36 teeth on driven
gear; 12 teeth on driving gear) and 5:1
(60 teeth on driven gear; 12 teeth on
driving gear)
In order to find the compound gear
ratio, you need to multiply the gear
ratios which make up the compound
gear ratio by each other.
So the compound gear ratio is 3/1 x
5/1, which equals 15/1, or 15:1
You can calculate compound gear
ratios made up of more than two simple
gear ratios by the same method. If
there were 3 simple gear ratios, and the
gear ratios were 3/1, 5/1 and 5/1, the
compound gear ratio would be 3/1 x 5/1
x 5/1 which equals 75/1, or 75:1
5:1
3:1
Vex 1.0 © 2005 Carnegie Mellon Robotics Academy Inc.
Background Torque
•
•
•
Torque can be used to describe the rotational strength of a motor.
The torque generated by an axle is linearly related to the gear ratio.
Therefore, increasing the gear ratio can improve a hoist’s ability to lift heavy
objects.
See torque helper page and gear ratios and torque helper page for more
information.
Vex 1.0 © 2005 Carnegie Mellon Robotics Academy Inc.
Lesson Mechanical Advantage
Vex 1.0 © 2005 Carnegie Mellon Robotics Academy Inc.
Lesson Materials Needed
•Constructed Gear Box and Lifting Crate—Please note: we used a crate
and rolls of pennies because we thought they're easily available. Feel free
to substitute whatever lifting apparatus and/or weights you prefer. An
especially good solution is a strong spring scale (20 - 60 lb. maximum). By
anchoring the spring scale, then tying it to the string, you do not need to
use a crate or weights.
•Rolls of pennies
•Stopwatch
•String
•Radio Transmitter
Vex 1.0 © 2005 Carnegie Mellon Robotics Academy Inc.
Lesson Step 1
Follow the instructions to build the
lifting crate and the first stage of the
gearbox
Vex 1.0 © 2005 Carnegie Mellon Robotics Academy Inc.
Lesson Step 2
You may have to re-download the RobotC
firmware if you have ever
downloaded any programs or other
firmware to the microcontroller. (If
nothing has been downloaded to the
microcontroller after downloading
the ROBOTC firmware, you may
skip
this step.)
• Connect the programming module to
both the PC and the microcontroller
• Make sure the microcontroller is
turned on
• Open ROBOTC.
• Select Robot/Download Firmware
• Select VEX VM 0724.hex/Open (or
later version of ROBOTC firmware).
Vex 1.0 © 2005 Carnegie Mellon Robotics Academy Inc.
Lesson Step 3
Calculate RPM
•
Record the time it takes for
the wheel to make ten full
revolutions
•
Calculate the rotational
speed in rev/s
•
Convert the value to rev/min
(rpm)
Vex 1.0 © 2005 Carnegie Mellon Robotics Academy Inc.
Lesson Step 4
•
Place 1 roll of pennies in the
lifting crate and tie it to the
spool on the motor’s axle.
Vex 1.0 © 2005 Carnegie Mellon Robotics Academy Inc.
Lesson Step 5
•
Test the system to see if the
gear box is capable of lifting the
load.
Vex 1.0 © 2005 Carnegie Mellon Robotics Academy Inc.
Lesson Step 6
•
Continue to add rolls of pennies
to the crate until the gearbox can
no longer raise the load. Record
the maximum weight that the
gearbox could lift.
Vex 1.0 © 2005 Carnegie Mellon Robotics Academy Inc.
Lesson Step 7
•
•
Modify the gearbox so the
wheel is on the second
axle.
Determine the gear ratio
between driven and driving
axles.
Vex 1.0 © 2005 Carnegie Mellon Robotics Academy Inc.
Lesson Step 8
•
•
Calculate the rpm and compare it
to axle 1.
Use the gear ratio and the data
from the first axle to calculate the
maximum weight that the axle
could lift if the spool were placed
on it.
Vex 1.0 © 2005 Carnegie Mellon Robotics Academy Inc.
Lesson Step 9
•
•
Tie the lifting crate to the spool and
measure the maximum weight that
the gearbox can lift using this axle.
How does this measured value
compare to your theoretical value?
Vex 1.0 © 2005 Carnegie Mellon Robotics Academy Inc.
Lesson Step 10
•
Modify the gearbox so the spooling
wheel is on the third axle.
Vex 1.0 © 2005 Carnegie Mellon Robotics Academy Inc.
Lesson Step 11
•Predict, and then calculate, the rpm
for this axle.
•Predict the maximum weight that this
axle can lift.
Vex 1.0 © 2005 Carnegie Mellon Robotics Academy Inc.
Lesson Step 12
•
If an appropriate set of weights is
available, test the theoretical value
you just calculated.
Vex 1.0 © 2005 Carnegie Mellon Robotics Academy Inc.
Lesson Step 13
Repeat the steps for the final axle
• Predict and measure rpm
• Predict maximum weight
• If possible, measure maximum
weight
Vex 1.0 © 2005 Carnegie Mellon Robotics Academy Inc.
Lesson Analysis
Graph your results:
• RPM vs. Gear Ratio
• Lifting Capability vs. Gear Ratio
• Find the best-fit line
• Find the slope of the best-fit line
• Extension activity--discuss: What would happen to the gear ratio if the
spooling wheel had a smaller diameter? Could you predict the amount a
different-sized wheel would lift using gear ratios, the Lever Law, or
both?
Vex 1.0 © 2005 Carnegie Mellon Robotics Academy Inc.
Download

mechanical_advantage