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• 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]

π = 3.14

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

• 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.

Using the Swing Turn 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

Insert the Number you Calculated Here

{C = π * D}

Circumference of the Traced Circle {C= *

D}

Distance Traveled by Wheel for a 90° turn

Simplified

The distance the wheel travels is equal to the number of times the wheel turns, times the circumference of the wheel.

= 17.6 cm = 17.6 cm X X

Number you just Calculated for

Distance Traveled by Wheel for a 90°

turn

Distance Traveled by Wheel for a 90° turn

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

17.6 cm 17.6 cm

360 360 XX

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

Circumference of the Traced Circle {C= *

D}

Distance Traveled by Wheel for a 90° turn

Simplified formula for Calculation part oneSimplified formula for Calculation part one

Simplified formula for Calculation part twoSimplified formula for Calculation part two

==

Number you just Calculated for

Distance Traveled by Wheel

for a 90° turn

17.6 cm 17.6 cm

360 360 XX

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