1. ROBOTIC DESIGN CHALLENGE Robotics and Automation Copyright © Texas Education Agency, 2013. All rights reserved.

2. The Starting Point Before you start, there are certain assumptions and prerequisites. You should have a working robot base. Complete Introduction to Robotics Parts 1-5. Complete How to Construct a Robot Parts 1-7. OR You should have a robot kit with parts to work with. Parts kit must include motors, gears, and structural components. Copyright © Texas Education Agency, 2013. All rights reserved.

3. Begin By Planning Start with a robot base (18” X 18”) You will add a variety of assemblies to the robot base in order to be able to complete the objectives. The robot base may need to be modified in order to add these assemblies. Do not modify the base until you have a plan and a design. Copyright © Texas Education Agency, 2013. All rights reserved.

4. The Design Challenge A basketball-playing robot! This involves shooting a ball into a goal from different places on the playing floor. Complete this objective in stages: 1. Shoot a hand-placed ball from a fixed location; 2. Design a robot arm able to pick the ball up off the floor and place it in the shooter; and 3. Build an adjustment into the shooter to be able to make a shot from different locations. Copyright © Texas Education Agency, 2013. All rights reserved.

5. Design Criteria We are NOT going to give you step-by-step instructions on how to build solutions. We will give you some equations, which show how to calculate some design requirements. The primary purpose for these equations is to determine what velocity is necessary to make a basket from one meter. Math and science are often used to prove that a design can meet performance objectives. Copyright © Texas Education Agency, 2013. All rights reserved.

6. Start with Physics The equations we start with are equations of motion with constant linear acceleration. After the ball leaves the shooter, The ball becomes a projectile, and The only force on the ball is gravity. The equations will describe the motion of the ball and (of particular interest to us) where the ball will land. Copyright © Texas Education Agency, 2013. All rights reserved.

7. Practical Considerations You will be given a motor. The motor provided will have a speed in RPM, The motor will produce a particular torque, and Both of those values are for specified conditions. The ball must have an initial velocity in order to make a basket. Use the calculations to determine the gear ratio needed to produce the proper ball velocity using the given motor. Copyright © Texas Education Agency, 2013. All rights reserved.

8. Additional Details The ball shooter Cannot dunk the ball, and The first fixed location should be about one meter from the basket. A ball collector Picks the ball up from anywhere on the floor, and Places the ball into the shooter. An adjustment for the shooter Adjusts the range or distance for a made shot. Copyright © Texas Education Agency, 2013. All rights reserved.

9. More Details An actual basketball is too large and heavy for our robot. We will use a tennis ball instead. Tennis ball specifications: 6.6 – 6.9 cm diameter 57 – 59 grams mass The goal is a standard wastebasket basketball hoop 46 cm (18”) from the floor. The hoop should have an 8” diameter. Copyright © Texas Education Agency, 2013. All rights reserved.

10. Evaluation Students Follow the design process. Work efficiently—there will be limited time to complete this objective! Teachers Use the Robotic Construction Rubric for assessment. Copyright © Texas Education Agency, 2013. All rights reserved.

11. Equations of Motion The generic equations of motion with constant linear acceleration are Where v i = initial velocity v f = final velocity s = distance traveled a = acceleration t = time Copyright © Texas Education Agency, 2013. All rights reserved.

12. Here is a more accurate version of the equations of motion using calculus, showing where the distance is derived from the velocity. Copyright © Texas Education Agency, 2013. All rights reserved.

13. X component (horizontal) Y component (vertical) These equations are usually resolved into their independent “x” and “y” components. The shooter gives the ball an initial velocity, v 0, that is resolved into “x” and “y” components using trigonometry. Copyright © Texas Education Agency, 2013. All rights reserved.

14. Components of Motion There are two components of motion: horizontal and vertical. Only the vertical motion is affected by gravity. The two components of motion are independent of each other. The object will continue to move horizontally at constant velocity until it hits the ground. The distance the object travels is the horizontal velocity times the time in the air. Copyright © Texas Education Agency, 2013. All rights reserved.

15. Two Components of Motion Copyright © Texas Education Agency, 2013. All rights reserved.

16. The Important Formula There is another important formula that is derived from the previous two equations. This formula allows the calculation of distance traveled using only two variables: the angle of the shot and the initial velocity. Can you show how this formula was determined? Copyright © Texas Education Agency, 2013. All rights reserved.

17. Solution to Derivation Copyright © Texas Education Agency, 2013. All rights reserved.

18. Sample Calculation Copyright © Texas Education Agency, 2013. All rights reserved.

19. Solution Copyright © Texas Education Agency, 2013. All rights reserved.

20. Ball Velocity How does a shooter give a tennis ball the required velocity? One way is to use a shooter based on the concept of a pitching machine. A spinning wheel with an angled chute Spinning wheel transfers velocity and momentum to the ball Contact with the ball is with the outer edge of the wheel. Copyright © Texas Education Agency, 2013. All rights reserved.

21. Wheel Velocity r is the radius of the wheel ω is the angular velocity in radians per second Copyright © Texas Education Agency, 2013. All rights reserved.

22. Converting RPM to Velocity Copyright © Texas Education Agency, 2013. All rights reserved.

23. Calculate Tangential Velocity You have a four inch diameter wheel spinning at 100 RPM. Use this information to calculate the tangential velocity of the wheel. Remember, the formula is: r is the radius of the wheel in m ω is the angular velocity in radians per second Copyright © Texas Education Agency, 2013. All rights reserved.

24. Solution Copyright © Texas Education Agency, 2013. All rights reserved.

25. Getting the Required Velocity How do you get the required velocity to make a basket from a motor and a wheel that you are given? Use Gears! Specifically, compound gears Compound gears have two gears/ on the same shaft At least one compound gear is needed because of the high gear ratio needed. About 8 : 1 Copyright © Texas Education Agency, 2013. All rights reserved.

26. Compound Gears It takes at least four gears to see this effect. Here is a picture of a single compound gear. Compound gears allow a higher gear ratio by multiplying the gear ratios of the individual gear pairs. Copyright © Texas Education Agency, 2013. All rights reserved.

27. A Gear Train Here is a picture showing the four gears needed to show the effect of a compound gear. If the driver gear is turning at 100 RPM, the driven gear will turn at 1200 RPM. Gear pairs are the 120 and the 20 tooth gears and the 72 and 36 tooth gears. Driver gear 120 teeth Driven gear (follower) 36 teeth 20 teeth 72 teeth Copyright © Texas Education Agency, 2013. All rights reserved.

28. Here is a compound gear driving another compound gear. Compound gear 1 Compound gear 2 This gear is turning a lot faster… than this gear. Copyright © Texas Education Agency, 2013. All rights reserved.

29. Gear Ratio You will need to calculate the gear ratio you need for your shooter to give you the velocity you calculated earlier. You have to build an assembly that connects your motor to your wheel using the gears you have that give the gear ratio. This will be an assembly that attaches to the robot base. Copyright © Texas Education Agency, 2013. All rights reserved.

30. Use the Design Process This design project requires students to go through the full design process—from research, to sketches, to formal drawings. Students are expected to redesign and rebuild to improve their robot. The first working model is an example of a prototype. Evaluation will be based on the full Robot Construction Rubric. Copyright © Texas Education Agency, 2013. All rights reserved.

31. Another Way to Calculate Time Copyright © Texas Education Agency, 2013. All rights reserved.

32. More Design Challenges For more design challenges, see robotic contest websites or search online “machinations.” The projects you find online may be more step- by-step than the design challenges in this lesson, and it may not require much use of the design process. There are many good examples of various working assemblies, such as arms and grippers. Copyright © Texas Education Agency, 2013. All rights reserved.

33. Even More Design Challenges Build a robot to complete the performance objectives from a robotic contest. You may find robotic contests for land and underwater robots. You do not have to enter the contest, but robotic contests are FUN and EXCITING! Copyright © Texas Education Agency, 2013. All rights reserved.