Application of Math and
Science Principles
Creating a robot that moves a specified
distance straight ahead
and
Creating a robot that turns
a specified number of degrees.
NXT Smart Motors
NXT Smart Motors
• How do the motors keep track of the
distance traveled?
• The interactive Servo Motors have
built-in Rotation Sensors that measure
how much the motor has rotated to the
nearest two degrees.
Moving Straight Program Details
Investigating Wheels and Distance
• Determine the
relationship between
wheel size, motor
rotations and distance
traveled. The goal is
to find out how to
move your robot a
certain distance
predictably in
centimeters.
Hypothesis
• For every 360 degrees of wheel rotation
the robot travels one circumference of the
robot’s tires.
• Distance traveled =
circumference X rotations
Procedure Step 1
π = 3.14
• Measure the diameter of
the wheel.
• Using the diameter
calculate the
circumference.
[C = π * D]
• Calculate the distance
your robot will travel for
three complete rotation
of the wheel.
[Distance = C * Rotations]
Procedure Step 2
• Run the robot and
measure how far it
actually goes with the
move straight program
you created.
• Repeat the run and
measure 3 times. Take
the average of that
measurement and
compare it to the
calculations you made in
Step 1.
• How close is the
calculated to the actual
robot movement?
Turning the robot
• Robots can perform two different types
of turns:
– Point Turns
• Point turns rotate both wheels in opposite
directions causing the robot to spin in place.
– Swing Turns
• Swing turns rotate one wheel and stop the other,
causing the robot to swing.
Point Turn Program Details
Point turns rotate both
wheels in opposite
directions causing the
robot to spin in place.
Swing Turn Program
Swing turns rotate one wheel and stop
the other, causing the robot to swing
Swing Turn Motor Block 1 Details
Swing Turn Motor Block 2 Details
Creating Measured Turns
A 90° turn should be ¼ of the distance
the wheel travels around the circle.
Creating Measured Turns
Hypothesis:
• As the robot makes a swing turn the
moving wheel traces out a portion of a
circle. The amount the robot turns is
proportional to the portion of the circle that
the wheel travels.
• A 90° turn should be ¼ of the distance the
wheel travels around the circle.
Remember you want the robot
to turn 90°
Not the wheel to turn 90°.
Create a Pen Attachment
Using the Swing
Turn Program
• Place the robot on a
large sheet of paper.
Make sure the tracer
attachment will leave
a mark as the robot
moves.
• Run the program.
When the robot has
traced at least one full
circle press the grey
button on the NXT to
stop the program.
Measure the path traced by the
robot’s wheel
• Measure the diameter
of the traced circle.
• Calculate the
circumference of the
traced circle.
[C = π * D]
Calculating for a 90° turn
Fill in all Known Variables
Simplified
{C = π * D}
Insert the Number you Calculated Here
Circumference of the
Traced Circle {C= * D}
Distance Traveled by
Wheel for a 90° turn
The distance the wheel travels is
equal to the number of times the
wheel turns, times the
circumference of the wheel.
Distance Traveled by
Wheel for a 90° turn
Number you just
Calculated for
Distance Traveled by
Wheel for a 90° turn
= 17.6 cm
X
Fill in the variables using the
numbers you calculated previously
for your robot and simplify
Number you just
Calculated for Distance
Traveled by Wheel
for a 90° turn
360 X
17.6 cm
=
Final Calculation determines number of motor
degrees to be input into the rotation senor’s
dialog box to make the robot spin 90° to the right.
Calculations for a 90° turn
Simplified formula for Calculation part one
Circumference of the
Traced Circle {C= * D}
Distance Traveled by
Wheel for a 90° turn
Simplified formula for Calculation part two
Number you just
Calculated for Distance
Traveled by Wheel
for a 90° turn
360 X
17.6 cm
=
Using the number of degrees you used to
make the robot turn 90 degrees with a swing
turn. Calculate how many motor degrees
the program would need to spin to turn the
robot:
• 180 degrees
?
• 270 degrees
?
• 360 degrees
?
• 450 degrees
?
Using the number of degrees you used to
make the robot turn 90 degrees with a swing
turn. Calculate how many motor degrees
the program would need to spin to turn the
robot:
• 180 degrees =
778
• 270 degrees =
1167
• 360 degrees =
1556
• 450 degrees =
1945