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Calculator Robot in Math

Calculator Robot in Math. A robot driven by a TI-83 demonstrates angles, distances, velocity, measurement & estimation, (while providing a gentle introduction to programming). Dr. Cwiakala 2/20/06. Objective Background: What Is a Robot? Programming a TI-83 Robot Commands Applications

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Calculator Robot in Math

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  1. Calculator Robot in Math A robot driven by a TI-83 demonstrates angles, distances, velocity, measurement & estimation, (while providing a gentle introduction to programming). Dr. Cwiakala 2/20/06

  2. Objective Background: What Is a Robot? Programming a TI-83 Robot Commands Applications Distance Angles Distance & Angles: Golf Game References & more Outline of Presentation

  3. Objective • Demonstrate how math is used to make a robot move. The distance equation is used to determine velocity and desired time required to make the robot go a specified distance. • This concept is also used for angular displacements to make the robot turn a prescribed amount.

  4. Background: What Is a Robot? • An intelligent and obedient machine. • Any machine that does work on its own, automatically, after it is programmed by humans. • All robots are made up of 3 elements: • Hardware: Body • Control: Brain • Software: Behavior

  5. Background: Equipment • Body: Chassis • Control: TI-83 Plus • Behavior: Program in TI-83

  6. Programming the TI-83 • Commands that need to be repeated can be stored in a program. • Results can be stored in variables (STO command). • PROMPT command can request a value and store it in a variable.

  7. Programming - Cont. • Press the PRGM key: • EXEC runs a program • EDIT edits a program • NEW creates a program • While Editing a program the PRGM key provides: • CTL – control statements • I/O – Input/Output • EXEC – Run

  8. Robot Commands • COMMAND FORMAT • SEND({1LR,time}) • L left motor 0-rev, 1-stop, 2 Forward • R right motor • Time in centiseconds • GET(R) • Executes SEND • Returns time in R • Only Two commands are used to activate the robot: • SEND: prepares for action • GET: Activates the action and returns how long the action took

  9. Example Robot Program • Left & Right Motor Forward for 3 seconds • Left Stop, Right Forward for 1.75 seconds • Left & Right Motor Forward for 3 seconds

  10. Applications We have seen that we can cause each motor (wheel) to go forward, backward or stop for a specified amount of time. • Q: How do we get the robot to go where we want? • A: By employing the Distance, velocity and time equation.

  11. Distance, Velocity and Time • We Know that D=V*T • This can be rewritten for Velocity V=D/T • Run Program • For T=1000 (10 sec) • D is measured 10” • V=10/1000 or 0.01 in/centiseconds Robot Moves Forward EXAMPLE EXPERIMENTAL DATA

  12. Determine Time • With the velocity known, given a distance, we can calculate a required time. T=D/V • Example: How much time is required to go 24 inches? T=24/0.01 or 2400

  13. Angular Distance, Velocity and Time • Same approach can be used to determine how fast the robot can turn. • q = w * T • q is angular displacement in degrees • w is angular velocity in degrees/centisec. • T is time in centiseconds. • Rewrite w = q/ T

  14. Determine Angular Velocity • We Know that q = w * T • Rewrite w = q/ T • Run Program • For T=1000 (10 sec) • q is counted 8.5 revolutions • w = 5.5*360/1000 or 1.98 deg/centiseconds Robot Turns CCW EXAMPLE EXPERIMENTAL DATA

  15. Time for a Specified Turn How long will it take to make a 90 degree turn? • T = q/w • T = 90 / 1.98 or • T = 45 centiseconds Program Prompts for an ANGLE and calculates needed TIME.

  16. The Golf Program: Direction & Distance The following program: • Prompts for an angle. • If the angle is nonzero, it executes the turn. • If zero, it prompts for a distance. • If the distance is nonzero, it executes the translation and repeats the program. • If a zero distance is entered, the program ends.

  17. The Golf Program: Direction & Distance - Cont. This program uses CONDITIONAL STATEMENTS and a LOOP.

  18. Example Run • 90 degree turn • Move 10 inches • -90 degree turn • End • Create a course using objects as place markers. • Students learn to estimate angles and distances. • The student with the least maneuvers wins! • You can include handicaps.

  19. Suggested Activities • Determine velocity – each will be different. • Pick distances from a hat and see who can come closest to their selected distance (absolute or by %). • Same exercise with rotations. • Students can program a specified path. • The ‘Golf Game’ activity.

  20. Algebra II Standards Covered • I-B1- Gather & record data. • I-B2- Represent relationships among quantities using concrete models. • II-C2- Use symbols to represent unknowns and variables.

  21. Algebra II Standards - Cont. • I-F1- Recognize that real-world phenomena can be modeled by specific functions.

  22. References & More Info • Learn About Robots: (http://www.learnaboutrobots.com/) All kinds of information about robots! • NASA Education Project: (http://robotics.nasa.gov/matrix.htm) Robotics activities from NASA. About Robots: (http://www.occdsb.on.ca/~proj4632/learnmore.htm) Introduction to robots.

  23. References - Cont. • Norland Research http://www.smallrobot.com/scimath.htmlYou will need: • TI Graphing Calculator kit - $99.95 • TI 12 inch link cable - $4.95 • TI slide cover - $4.95 • Activities are also present on this site! • Guru Online: TI-83 programming tutorials http://bgo.netfirms.com/

  24. THANK YOU • This presentation can be obtained athttp://keenan.rcsd1.org and click under “Teacher Resources”

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