Quiz: Measured Turns
Introduction to Mobile Robotics > Measured Turns Investigation
Dr. Turner’s hypothesis from Measured Turns Investigation:
Other useful formulas:
Circumference = π x Diameter
1 rotation = 360 degrees
π ≈ 3.14
1. Horacio’s robot traces out a circle with a diameter of 15cm. His robot travels 20.3cm
per one rotation of the wheel. Answer the following questions, and show your work
for each.
a. What is the circumference of the traced circle?
Circumference = π x Diameter ≈ 3.14 x 15cm = 47cm.
Diameter is given as 15cm in the problem. Students should simply apply the basic
relationship between diameter and circumference to calculate circumference.
b. How many wheel rotations would the robot have to make to travel the full
circumference of the circle exactly one time?
Number of Rotations = Circle Circumference / Wheel Circumference
Number of Rotations = 47 cm / 20.3 cm = 2.3 rotations.
The robot travels 20.3 cm per rotation, so to find the number of rotations, you divide the total
distance (calculated in part (a)) by 20.3.
Viewed as a unit conversion problem:
47 cm ⎛ 1 rotation ⎞ 2.3 rotations
⎜
⎟=
20.3
cm
⎝
⎠
c. How many degrees should Horacio set his motor to run in order to make his
robot turn a full 360 degrees?
830 motor degrees. One full turn of the robot means the wheel must run the full distance of
the traced circumference. The number of rotations to go around the circumference was
calculated in part (b), so students simply need to convert it into degrees.
The hypothesis equation for a 360º (full) robot turn is:
360 degrees X distance
=
360 degrees
47 cm
distance = 47 cm
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In part (b), the student already found the necessary number of rotations to go 47cm, and
simply needs to convert them to degrees.
2.3 rotations ⎛ 360 degrees ⎞ 830 rotations
⎜
⎟=
⎝ 1 rotation ⎠
(830 is used rather than 828 because the equation has only 2 significant figures of precision)
d. How many degrees should Horacio set his motor to run in order to make his
robot turn 90 degrees?
The robot’s wheel will need to go ¼ the distance it did before, or 210 degrees (2 significant
figures again).
90 degrees
X distance
=
360 degrees
47 cm
distance = 12cm
12 cm ⎛ 1 rotation ⎞ .59 rotations
⎜
⎟=
20.3
cm
⎝
⎠
.59 rotations ⎛ 360 degrees ⎞ 210 degrees
⎜
⎟=
1
rotation
⎝
⎠
Or, divide the total Number of Degrees by 4, to get the Number of Degrees to go one quarter
of the circle.
Number of Degrees to go 90º = (Number of Degrees to go 360º)/4 = 830º /4 = 210º
Or, by using ratios:
90 Robot Degrees
X Motor Degrees
=
360 Robot Degrees 830 Motor Degrees
And then solve for X Motor Degrees, which will be the amount needed to go 90 Robot
Degrees.
© Copyright 2006 Carnegie Mellon Robotics Academy
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