ACTIVITIES
Know Your Gears
Gear Speed and Torque
Gear Speed and Torque Continued
Gear Ratio
Calculating Power
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Disassemble just about any kind of mechanical toy, wristwatch, or fishing reel and you'll encounter gearing. Gears can be used to increase or decrease force. They can also be used to increase or decrease speed. First, let's analyze gears and force. The term torque is applied to gearing when talking about force. We can explain torque as a mathematical expression (t = rF) or torque (t) equals crank radius (r) times tangential force (F), the force at right angles to the radius. It is that force which causes a vehicle to accelerate, or increase its ëspeedí, the other property of interest. Speed is the rate at which something transverses a distance or length (Rorabaugh,1995). We sometimes also refer to the rotation rate of a wheel or gear as its speed, in revolutions per minute or revolutions/second. (The term ërateí always implies action per unit of time, or speed.) Below are several activities that will explain the basics of gearing. Some of the activities assume that the students understand algebra and some trigonometry.
ACTIVITY #1 KNOW YOUR GEARS
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In this activity, we will learn about the different LEGO gears that are used in the Botball and LEGO Mindstorm robot kits. At the conclusion of this activity, The object is to be able to distinguish between different gear sizes, shapes, and types.
Figure
1. Standard LEGO gears
MATERIALS NEED: 1 gear worksheet (provided), pencil, paper
PROCEDURE
The gears you see in the figure above are two of the 4 different gears you have in your Botball kit. Each have a different number of teeth. Using the examples provided above, count the number of teeth on each gear and list them in the spaces below.
Largest gear_____ Next largest_____ Next______ Smallest______
ACTIVITY #2 GEAR SPEED AND TORQUE
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This activity will allow us to experiment with different gears and distinguish between gearing that generates speed or produces torque. Reducing the number of revolutions is called gear reduction (high torque). Increasing the number of revolutions is called gearing up (high speed). The object is to differentiate between the two conditions.
MATERIALS NEEDED: 8t, 16t, 24t, 40t LEGO gears (t = tooth), four LEGO axles, one 15 hole LEGO support beam (gearblock)
PROCEDURE (Part 1)
1. Put an axle through the middle of any gear and put it on one 15 hole LEGO support beam (gearblock). Do the same for a different gear and put it on the gearblock so that their teeth mesh.
2. When you turn one gear clockwise, which way does the other gear go?
3. What happens if you add more gears?
4. Put an axle through the largest gear and put it on the gearblock. Do the same for the smallest gear and, again, put them on the gearblock so that their teeth mesh.
5. With one hand, turn the axle for the large gear and watch the small gear spin. Is it going faster or slower than the large one?
6. While you're still turning the large gear, try to stop the small gear by pinching its axle. Is it easy or hard to stop (high torque or low torque)?
7. Now twirl the axle of the small gear and watch the big gear go around. Is it going faster or slower than the small one?
8. While you're still turning the small gear, try to stop the big gear by pinching its axle. Is it easier or harder to stop (high torque or low torque)?
ACTIVITY #3 GEAR SPEED AND TORQUE CONTINUED
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MATERIALS NEEDED: 8t, 16t, 24t, 40t LEGO gears, four LEGO axles, one 15 hole LEGO support beam, red marker
PROCEDURE (Part 2)
1. Keep the gears in the same position as in the previous activity. Color one tooth on the big gear red with a marker. Match up the reddish tooth from the big gear with the small gear. Before you actually do this experiment see if you can predict what the answer will be.
2. Make the big gear go around once very slowly and count how many times the small gear goes around before the big gear completes its rotation.
3. Do this experiment using different combinations of gears. Write down your observations.
4. Take the big gear, the second biggest gear, and the smallest gear and line them up with their teeth meshed (in that order) on the gearblock. If the big gear goes around once, how many times will the small gear go around? Can you explain why?
5. Either design your own experiment or build the coolest gearbox you can.
Here are some examples of how to use the crown, bevel, and worm
gears to change
the direction of motion by 90 degrees.
Put two beams together at 90 degrees and hold them together with an
overlapping plate.
Figure 2. Bevel gearing model
Figure 3. Crown gearing model
ACTIVITY #4 GEAR RATIO
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Gear ratio can be defined as the [number of turns of the driver] : [number of turns of the follower]. In this activity, students will determine the gearing ratios for different combinations of the 8t, 16t, 24t, and 40t gears. This can be done using simple mathematics. For example, a 20t gear driver and 40t gear follower produces a gear ration of 2:1. In other words, the 20 tooth gear must make 2 complete rotations to turn the 40 tooth gear 1 time. Users will learn gear ratio basics using division and multiplication.
MATERIALS NEEDED: 8, 16, 24, 40 tooth LEGO gears, three LEGO axles, one 15 hole LEGO beam, 6 gray fasteners, one red maker or pencil
PROCEDURE
1. When I turn the 8t driver__________time(s), the 24t follower turns
________time(s)
This produces a gear ratio of ______:______
2. When I turn the 8t driver__________time(s), the 40t follower
turns_________time(s)
This produces a gear ratio of______:______
3. When I turn the 16t driver__________time(s), the 8t follower
turns_________time(s)
This produces a gear ratio of______:______
4. When I turn the 40t driver__________time(s), the 8t follower
turns_________time(s)
This produces a gear ration of______:______
5. Which gear ratio produces the greatest speed? Explain.
6. Which gear ratio produces the greatest torque? Can you explain this
mathematically?
ACTIVITY #5 CALCULATING POWER
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At the beginning of the gear activity section, we discussed the mathematical formula for torque (t = rF). In this activity, we will introduce additional variables for distance of a circle and revolutions per second. A tangential force at a crank radius of r will move through a distance of 2pr each time the shaft makes one complete revolution. This movement creates a certain amount of work (or energy) described as:
W = (F )( 2p )(r) or 2πrF
Substituting the torque in the equation for work equation, we come up with:
W = (2p )(t) or 2π t
Power is the rate of doing work or work per a unit of time. Thus if we know how fast the crank is turning, or how many revolutions it makes per a unit of time, then the power equation is just:
P = (2p t )(S) or
2π t S
Where S is equal to the crank
speed in revolutions per second (Rorabaugh 1995) If we put a wheel of radius ër ë on a motor, and measure the
force (F) on a string wrapped around the wheel instead of the crank force, the
same equations apply for torque, work, and power. The only other knowledge you need are definitions of units
for work and power.
… A joule is a unit of work or energy and 1 joule = 0.7376 foot*lb.
… A watt is a unit of power, and 1 watt = 1 joule/second
… For mechanical power we often use units of horsepower, and 1 horsepower = 746 watts or 746 joules/second
MATERIALS NEEDED: pencil and paper, calculator
PROCEDURE
1. Calculate the power (in horse power) supplied by a motor running at 3400 rpm while delivering a torque of 800 foot*lb.
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