robotic design challenge robotics and automation copyright © texas education agency, 2013. all...

ROBOTIC DESIGN CHALLENGE

Robotics and AutomationCopyright © Texas Education Agency, 2013. All rights reserved.

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.

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.

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; and3. Build an adjustment into the shooter to be able to

make a shot from different locations.


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.


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.


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.


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.


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.


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.


Equations of Motion

• The generic equations of motion with constant linear acceleration are

Where • vi = initial velocity • vf = final velocity• s = distance traveled• a = acceleration• t = time


Here is a more accurate version of the equations of motion using calculus, showing where the distance is derived from the velocity.


• X component (horizontal) • Y component (vertical)

These equations are usually resolved into their independent “x” and “y” components.

= + = + 𝑥=𝑣 𝑖𝑥𝑡+

12𝑎𝑥 𝑡

2 𝑦=𝑣 𝑖𝑦 𝑡+12𝑎𝑦 𝑡

2

The shooter gives the ball an initial velocity, v0 , that is resolved into “x” and “y” components using trigonometry. = cos θ = sin θ


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.


Two Components of Motion


• The two components are independent; they have to be calculated independently.

• The initial velocity is a vector, which has a magnitude and a direction.

• The “X” and “Y” components of the initial velocity vector form a right triangle.

• VX = V cos θ• VY = V sin θ• Use an initial velocity of 1

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?

𝑥=2𝑣0

2sin θ cosθ𝑎𝑦


Solution to Derivation


• We want to get the distance the ball travels from the shooter to the basket, which is the “x” direction.

• Start with this formula: • We can calculate the “x” component of the velocity using and we know the

only acceleration is gravity, which acts only in the “y” direction. “X” acceleration is zero.

• But we don’t know time.• Time can be calculated from the time the ball is in the air, and that is the time it takes

to go up and down.• Up and down is the “y” direction, so the initial “y” velocity makes the ball go up and

gravity makes the ball come down.• This calculation uses the formula , solve for time, • If the initial velocity is up and the final velocity is down, then = and they are also

equal so , and substitute this “t” into the top equation.

= + 𝑡=𝑣 𝑓𝑦−𝑣𝑖𝑦−9.8

𝑥=𝑣 𝑖𝑥𝑡+12𝑎𝑥 𝑡

2

= cos θ

Sample Calculation

• We want to determine the initial velocity needed to make a shot from one meter

• Use the previous formula:

• Assume a shooter angle of 60° and solve for

𝑥=2𝑣0

2sin θ cosθ

9.8m /𝑠2


Solution• Re-arrange:

¿√9.8¿ ¿¿¿ ¿ √ 9.8𝑚2

𝑠2

2 sin θ cos θ¿ √ 9.8

𝑚2

𝑠2

2 ( .866 )( .5)

= = 3.36


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.


Wheel Velocity

• The outer edge of the wheel will be moving at a measurable velocity

• We need to calculate the velocity of the wheel at its outer edge• This is called the tangential velocity

• The formula is: • Where: r is the radius of the wheelω is the angular velocity in

radians per second


Converting RPM to Velocity

• Normally, a motor speed is given in RPM• Rotations per minute

• One rotation is 2 π radians• 60 RPM is 1 rotation per second• 60 RPM = 2

• Robot kits usually specify the wheels by their diameter in inches• A 1 inch wheel has a radius of 0.0127 m


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 wheelin mω is the angular velocity in

radians per second

in when:


Solution

•r = 4 in x = 0.0508 m•ω = 100 RPM x = 10.472 • = 0.0508 x 10.472 = 0.532 •This is not nearly the velocity needed to make a basket from one meter


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


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.


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 gear120 teeth

Driven gear(follower)36 teeth

20 teeth

72 teeth


Here is a compound gear driving another compound gear.

Compound gear 1Compound

gear 2

This gear is turning a lot faster…

than this gear.


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.


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.


Another Way to Calculate Time• First, calculate the height using the “Y” velocity:h = •This is the height the object climbs to. Use this height to calculate time

t1 =

•This is the time it takes for the object to climb to the height calculated from velocity vy


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.


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!


robotic design challenge robotics and automation copyright © texas education agency, 2013. all...

Documents

robot parts

better design

design requirements

design processto

design criteriawe

design flexibility

robot kit

working robot base