ROBOTIC DESIGN CHALLENGE
Robotics and Automation
Copyright © 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; 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.
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.
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.
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.
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.
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.
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.
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
Copyright © Texas Education Agency, 2013. All rights reserved.
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.
These equations are usually resolved into their
independent “x” and “y” components.
• X component (horizontal)
• Y component (vertical)
𝑣𝑓𝑥 = 𝑣𝑖𝑥 + 𝑎𝑥 𝑡
𝑣𝑓𝑦 = 𝑣𝑖𝑦 + 𝑎𝑦 𝑡
1
𝑥 = 𝑣𝑖𝑥 𝑡 + 𝑎𝑥 𝑡 2
2
1
𝑦 = 𝑣𝑖𝑦 𝑡 + 𝑎𝑦 𝑡 2
2
The shooter gives the ball an initial velocity, v0 , that is
resolved into “x” and “y” components using trigonometry.
𝑣𝑥 = 𝑣0 cos θ
𝑣𝑦 = 𝑣0 sin θ
Copyright © Texas Education Agency, 2013. All rights reserved.
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.
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 𝑚 𝑠
Copyright © Texas Education Agency, 2013. All rights reserved.
The Important Formula
• There is another important formula that is
derived from the previous two equations.
2𝑣0 2 sin θ cos θ
𝑥=
𝑎𝑦
• 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.
Copyright © Texas Education Agency, 2013. All rights reserved.
Solution to Derivation
• We want to get the distance the ball travels from the shooter to the basket, which is
•
•
•
•
•
•
•
the “x” direction.
1
Start with this formula: 𝑥 = 𝑣𝑖𝑥 𝑡 + 2 𝑎𝑥 𝑡 2
We can calculate the “x” component of the velocity using 𝑣𝑥 = 𝑣0 cos θ 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.
𝑣𝑓𝑦 − 𝑣𝑖𝑦
𝑣
=
𝑣
+
𝑎
𝑡
𝑡
=
𝑓𝑦
𝑖𝑦
𝑦
This calculation uses the formula
, solve for time,
− 9.8
If the initial velocity is up and the final velocity is down, then 𝑣𝑓𝑦 = − 𝑣𝑖𝑦 and they
are also equal so 𝑡 =
2𝑣𝑖𝑦
9.8
=
2𝑣0
9.8
sin θ , and substitute this “t” into the top equation.
Sample Calculation
• We want to determine the initial velocity
needed to make a shot from one meter
• Use the previous formula:
2𝑣0 2 sin θ cos θ
𝑥=
9.8 m/𝑠 2
• Assume a shooter angle of 60° and solve for 𝑣0
Copyright © Texas Education Agency, 2013. All rights reserved.
Solution
9.8 (𝑚 𝑠2 ) 𝑥 (𝑚)
2 sin θ cos θ
• Re-arrange: 𝑣0 (𝑚 𝑠) =
9.8
=
(𝑚
1 (𝑚)
𝑠2)
2 sin 60° cos 60°
=
11.316
=
𝑚2
𝑠2
2
9.8 𝑚
𝑠2
2 sin θ cos θ
=
= 3.36 𝑚
Copyright © Texas Education Agency, 2013. All rights reserved.
2
9.8 𝑚
𝑠2
2 .866 (.5)
𝑠
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.
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: 𝑣𝑟 = 𝑟 ω
• Where: r is the radius of the wheel
ω is the angular velocity in
radians per second
Copyright © Texas Education Agency, 2013. All rights reserved.
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 π 𝑟𝑎𝑑𝑖𝑎𝑛𝑠 𝑠𝑒𝑐𝑜𝑛𝑑
• Robot kits usually specify the wheels by their
diameter in inches
• A 1 inch wheel has a radius of 0.0127 m
Copyright © Texas Education Agency, 2013. All rights reserved.
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:
𝑣𝑟 in 𝑚
𝑠
when:
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.
Solution
• 𝑣𝑟 = 𝑟 ω
• r = 4 in x
0.0127 𝑚
𝑖𝑛
• ω = 100 RPM
= 0.0508 m
2π 𝑟𝑎𝑑 𝑠
x
=
60 𝑅𝑃𝑀
10.472 𝑟
𝑠
• 𝑣𝑟 = 0.0508 x 10.472 = 0.532 𝑚 𝑠
• This is not nearly the velocity needed to
make a basket from one meter
Copyright © Texas Education Agency, 2013. All rights reserved.
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.
Compound Gears
• Compound gears allow a higher gear
ratio by multiplying the gear ratios of the
individual gear pairs.
• It takes at least four
gears to see this effect.
• Here is a picture of a
single compound gear.
Copyright © Texas Education Agency, 2013. All rights reserved.
A Gear Train
Driven gear
(follower)
36 teeth
• Here is a picture showing the
20 teeth
72 teeth
Driver gear
120 teeth
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.
Copyright © Texas Education Agency, 2013. All rights reserved.
Here is a compound gear
driving another
compound gear.
This gear is turning
a lot faster…
than this
gear.
Compound
gear 2
Copyright © Texas Education Agency, 2013. All rights reserved.
Compound
gear 1
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.
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.
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
• This is the time it takes for the object to
climb to the height calculated from velocity
vy
Copyright © Texas Education Agency, 2013. All rights reserved.
More Design Challenges
• For more design challenges, see robotic contest
websites or search online “machinations.”
• The projects you find online may be more stepby-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.
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.