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GRADES 9-12
ROBOT GEARS
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BACKGROUND INFORMATION:
Levers: Force causes objects to move. Newton's 2nd law says that force=mass * acceleration. A torque (or "moment") is like a rotational force. Instead of causing something to translate, it causes something to rotate. A torque is the product of the force times its distance from the pivot point. What happens when a heavy person and a lightweight person get on a teeter-totter together? Where do they need to sit to balance? When the heavy person pushes off the ground, who rotates further? The teeter-totter can be thought of as a simple machine (lever), and the lightweight person is using the mechanical advantage of the teeter-totter to lift the heavy person. How do athletes use their bodies as levers?
Gears: Have you ever ridden a bicycle with gears and found that
in one gear it was easy to peddle very fast,
but you didn't go very far, and in
another gear it was harder to peddle, but you went further?
Gear Ratio is defined to be the number of teeth of
one gear divided by the number of teeth of the second
gear. It gives the ratio of the number of revolutions
executed by each gear in a given amount of time.
Why the Gear Ratio works: Gears roll on each other
without slipping. If a gear were rolling on the table,
in one complete turn or revolution it would travel the length
of its circumference, pd, where
d is the diameter
of the gear. Since our gears all have the same
tooth spacing, the diameter of each gear is related to
the number of teeth by a proportional constant, d = k n,
where n is the number of teeth.
So the smaller gear would have to make 3 revolutions to go
as far as the bigger gear does in one revolution.
The smaller gear would have to turn 3 times as fast.
Remember that torque = force * distance. So the torque on the smaller gear is less than that on the larger gear. If we input a small torque on the small gear, it is transmitted to the larger gear and gets larger at the output gear. However the larger output gear doesn't rotate as much as the smaller gear. Engineers define work to be the product of force and the distance over which it acts:
Work = force * distance = torque * angle of rotation
Power is the rate of doing work:
Power = force * velocity = torque * rotational speed
Ideally, the power we input to the gear box is the same as the power we get out of the gear box.
Gearing up means that the follower in a gear train turns faster than the driver. Gearing down means the follower turns more slowly than the driver. Gearing down causes our output to be more powerful, gearing up causes our output to be less powerful. Relate this to riding a bicycle with multiple gears, or driving a car.
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