Lesson Plan
Course Title: Robotics and Automation
Session Title: Introduction to Robotics Part 3: Propulsion System
Performance Objective:
At the end of this lesson, students will demonstrate knowledge of robotic propulsion systems by
being able to apply mathematical formulas to determine the optimal operating point for a DC
motor and gear train in a robotic application by passing the Introduction to Robotics Part 3:
Propulsion System Quiz.
Specific Objectives:
 Describe the purpose and use of gears in a robotic application.
 Apply mathematical formulas to calculate how a gear train affects either speed or torque.
 Identify the components of a DC motor.
 Describe the relationship between current, speed, and torque in a DC motor.
 Explain the theory of operation of a DC motor.
 Apply mathematical formulas to calculate speed, current, torque, and efficiency for a DC
motor in a robotic application.
 Recognize the relationship between values in a mathematical formula and their graphical
representation for variables like speed, current, and torque.
Preparation
TEKS Correlations:
This lesson, as published, correlates to the following TEKS. Any changes/alterations to the
activities may result in the elimination of any or all of the TEKS listed.
Robotics and Automation:
•
130.370(c)(5)(C)(D)
…demonstrate knowledge of process control factors;
…demonstrate knowledge of motors, gears, and gear trains used in the robotic or
automated systems.
•
130.370(c)(6)(A)(B)
…demonstrate knowledge of rotational dynamics, weight, friction, and traction
factors required for the operation of robotic and automated systems;
…demonstrate knowledge of torque and power factors used in the operation of robotic
systems;
•
130.370(c)(7)(B)
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1
…understand and discuss the relationship of torque, gear ratio, and weight of payload in
a robotic or automated system operation;
•
130.370(c)(8)(B)(C)(D)
…think critically, identify the system constraints, and make fact-based decisions;
…use rational thinking to develop or improve a product;
…apply decision-making strategies when developing solutions;
•
130.370(c)(10)(C)(F)
…improve a product design to meet a specified need;
…evaluate design solutions using conceptual, physical, and mathematical models at
various times during the design process to check for proper functionality and to note
areas where improvements are needed;
Interdisciplinary Correlations:
Algebra I:

111.32(b)(1)(A)(B)(C)(D)(E)
…describe independent and dependent quantities in functional relationships;
…gather and record data and use data sets to determine functional relationships
between quantities;
…describe functional relationships for given problem situations and write equations or
inequalities to answer questions arising from the situations;
…represent relationships among quantities using concrete models, tables, graphs,
diagrams, verbal descriptions, equations, and inequalities;
…interpret and make decisions, predictions, and critical judgments from functional
relationships.

111.32(b)(3)(A)(B)
…use symbols to represent unknowns and variables;
…look for patterns and represent generalizations algebraically.
Precalculus:
111.35(c)(3)(D)(E)
…use properties of functions to analyze and solve problems and make predictions;
…solve problems from physical situations using trigonometry, including the use of Law
of Sines, Law of Cosines, and area formulas and incorporate radian measure where
needed.

111.35(c)(4)(B)
…use arithmetic, geometric, and other sequences and series to solve real-life problems;

111.35(c)(6)(A)(B)
…use the concept of vectors to model situations defined by magnitude and direction;
…analyze and solve vector problems generated by real-life situations.
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2
Physics:

112.39(b)(1)(2)(3)(5) - Introduction.
…Physics.
…Nature of science.
…Scientific inquiry.
…Scientific systems.

112.39(c)(2)(J)(L)
…organize and evaluate data and make inferences from data, including the use of
tables, charts, and graphs;
…express and manipulate relationships among physical variables quantitatively,
including the use of graphs, charts, and equations.

112.39(c)(4)(A)(B)(C)(D)(E)
…generate and interpret graphs and charts describing different types of motion,
including the use of real-time technology such as motion detectors or photogates;
…describe and analyze motion in one dimension using equations with the concepts of
distance, displacement, speed, average velocity, instantaneous velocity, and
acceleration;
…analyze and describe accelerated motion in two dimensions using equations, including
projectile and circular examples;
…calculate the effect of forces on objects, including the law of inertia, the relationship
between force and acceleration, and the nature of force pairs between objects;
…develop and interpret free-body force diagrams;

112.39(c)(5)(D)(G)
…identify examples of electric and magnetic forces in everyday life;
…investigate and describe the relationship between electric and magnetic fields in
applications such as generators, motors, and transformers;
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3
Occupational Correlations: (reference: O*NET – www.onetonline.org)
Electrical Engineering Technologists 17-3029.02
Similar Job Titles: Engineering Technicians
Tasks:
 Design or modify engineering schematics for electrical transmission and distribution
systems or for electrical installation in residential, commercial, or industrial buildings,
using computer-aided design (CAD) software.
 Review electrical engineering plans to ensure adherence to design specifications and
compliance with applicable electrical codes and standards.
 Compile and maintain records documenting engineering schematics, installed
equipment, installation or operational problems, resources used, repairs, or corrective
action performed.
 Review installation or quality assurance documentation.
 Review, develop, and prepare maintenance standards.
Soft Skills:
Realistic; Investigative; Conventional
Teacher Preparation:
Review this lesson. Preview the Introduction to Robotics Part 3: Propulsion System presentation
and the notes. There are many good sources of information on gears and how they are used on
internet websites. Teachers are encouraged to research some in preparation for this lesson
(Slide 4). Teachers may want to locate animation of gears on the internet to show students
(Slide 5). Teachers may want to make up some conversion practice examples to supplement
the ones on Slide 16. You may want to search the internet for good quality cutaway diagrams of
brushed DC motors (Slide 17).
References:
1. Website from the MIT Mechanical Engineering department:
http://lancet.mit.edu/motors/motors3.html
Instructional Aids:
1. Introduction to Robotics Part 3: Propulsion System presentation and notes
2. Introduction to Robotics Part 3: Propulsion System Quiz answer key
3. Pictures of various DC motors and robots from website links
Materials Needed:
1. Paper, pen/pencil
2. Introduction to Robotics Part 3: Propulsion System Quiz
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4
Equipment Needed:
1. Computer with internet access
2. DC motor used for demonstration
Learner Preparation:
It is recommended that students have taken Introduction to Robotics Part 1: Overview and
Introduction to Robotics Part 2: Structural System prior to this lesson. The lessons are found at
www.cte.unt.edu (STEM, Robotics and Automation course).
Introduction
Introduction (LSI Quadrant I):
SAY: Before you can design and build a robot on your own, there are many things you have to
know in order for the robot to perform effectively and efficiently.
ASK: Does anyone know what the requirements are for building a robot?
SAY: You need to follow the design process. It has to perform the performance objectives
given. You need to know why things like DC motors and specific gear ratios are used.
SHOW: A DC motor.
SAY: This is the most common type of motor for a student robot. We have to understand how
this works and how we can design things like a gear train to make it work most efficiently.
SAY: One of the ways we learn how a DC motor works is by looking at the mathematics behind
its operation. This is an example of how something real – making this DC motor work – requires
an understanding of math.
Outline
Outline (LSI Quadrant II):
Instructors can use the presentation, slides, handouts, and note pages in conjunction with the
following outline.
MI
Outline
Notes to Instructor
I.
Propulsion System Basics
A. Students have learned the fundamentals
of building structurally sound robots in
Introduction to Robotics Parts 1: Overview;
and Part 2: Structural System.
B. The main components of the propulsion
system are motors, wheels, and gears.
In this lesson, students
are expected to learn
about DC motor and
gears, but the primary
purpose of this module
is to demonstrate the
importance of math to
robotics and
technology. Begin
Introduction to
Robotics Part 3:
Propulsion System
presentation.
(Slide 1-3)
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II.
Gears
A. Provide a cursory overview of gears and
their application.
B. Search internet for additional information
on gears for more detail. There are a
number of great tutorials, videos, and
animations.
C. The key concept is that gears are used to
either increase speed of rotation of the
wheels or apply additional torque to the
load. Gears trade one for the other.
D. There is an optimal gear ratio that will
maximize both robot speed and motor
efficiency. This gear ratio needs to be
calculated for a specific application.
There is a large
amount of additional
and background
information found in
the slide notes. Make
sure you review these
prior to discussion.
(Slides 4-8)
Slide 7 is a good place
to show a gear video
tutorial from the
internet.
III.
Motors
A. A motor always gets its mechanical
energy from the interaction of 2 magnetic
fields.
B. These example motor specs are for a real
DC motor and are used for the worked
examples in this lesson.
C. The load on a motor in a robot is the robot
weight. The force required to make a robot
move is delivered by the motors through
the wheels.
D. The wheels act like a lever arm with a
distance equal to the radius of the wheel.
Bigger wheels place a larger torque load
on the motor.
There are a variety of
different types of
motors; each of which
works differently and
would have different
characteristic curves.
We chose the
permanent magnet DC
motor because it is the
most common type
found in student-built
robots.
(Slides 9-14)
IV.
Angular Velocity
A. The concept of angular velocity may be
new to some students.
B. There are two categories of units,
American and International (System
International, or SI). International units are
also sometimes called metric units.
C. Students need to be able to make
calculations in both sets of units and so
need to be able to convert back and forth.
D. The units of angular velocity are similar to
work (force times distance) but a motor
Practice some
conversions before
moving on. There will
be questions like this
on the quiz.
(Slides 14-16)
Teachers may want to
make up some
conversion practice
examples to
supplement the ones
on Slide 16. .
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6
only does work when it rotates through an
angle.
V. DC Motor Parts
A. Pictures are provided to clarify the
descriptions.
B. There are some hidden parts, like the
springs used to hold the brushes against
the commutator.
C. Like a wheel, the direction of rotation of
the top of the rotor is opposite of the
direction of the bottom of the rotor. The
direction of movement through the external
magnetic field affects the direction of the
resultant force.
D. In order for the forces in a motor to allow
continuous rotation, the polarities have to
be consistent. For example, the polarity of
the rotor field near the stators N pole
always has to be positive, the polarity of
the voltage in the rotor field near the
stators S pole has to always be negative.
E. If the commutator did not reverse the
polarity, the same polarity (say, positive)
would follow the rotor field from the N pole
to the S pole, the resultant force would
also reverse, and the motor would not be
able to rotate for a full turn.
Students may have
trouble understanding
why the commutator
has to switch the
polarity of the voltage
to the rotor field
(Slides 17-23)
You may want to
search the internet for
good quality cutaway
diagrams of brushed
DC motors (Slide 17).
VI. Generator Action in a Motor
A. A motor is supposed to produce
mechanical energy out.
B. However, as the motor spins the motion of
conductors in a magnetic field generates a
voltage.
C. Generator action in a motor produces
CEMF.
D. This CEMF opposed the supply voltage.
E. The effect is for low current at high speed
(which you get with low or no load on the
motor) and higher current at lower speeds.
F. As the external load applied slows the
motor down, the motor draws more
current.
This will be another
tricky thing for
students to
understand.
(Slides 24-28)
VII. Motor Characteristic Curves
A. These are visual representations of the
(Slides 29-33)
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relationships between torque (load on the
motor), current, and speed.
B. These relationships are also expressed
mathematically.
C. Note the mathematical symbols for the
various quantities.
VIII. Motor Characteristic Formulas
A. There is actually only one formula on slide
34 showing the relationship between
speed and torque. The other formulas
shown are algebraic manipulations solving
for different variables.
B. The relationship between speed and
current involves CEMF. In fact, CEMF is
directly proportional to speed, which
makes current inversely proportional to
speed and CEMF as shown by the formula
on slide 37.
C. The two formulas mentioned here will be
the main formulas used in our
calculations.
D. These are great mathematical formulas to
use because they require a step by step
process to solve and they are not simple
and direct like Ohms Law.
E. The formulas shown on slides 39 and 40
are mostly for information only, although
students will need to use the velocity and
power formulas later.
We primarily use the
formula on the bottom
of slide 34 solving for
motor speed.
(Slides 34-40)
IX. Example Problems
A. These equations are necessary to
calculate exactly where robot motors will
be operating with an actual robot.
B. Students may not be as interested in
efficiency but they should be interested in
being able to determine how to make
their robot go as fast as possible.
C. The examples given are from a real motor
used often in student robotics. These
motor specs were given originally on slide
11.
D. The questions asked involve multiple
steps to solve, and there is a particular
sequence needed for the steps.
These are real world
problems a student
would have to solve
when working with real
robots. If you can,
have students actually
experiment with
different gear ratios to
demonstrate the reality
of the formulas to
applications
(Slides 41-54)
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E. The motor constant Ke is often
determined experimentally because it can
differ slightly from motor to motor even of
the same type.
F. Example motors 2 and 3 are also real
motors used in the BEST robotic contest,
but the answers need to be calculated by
the students so the solutions are not
provided here.
G. Actual motor load torque used in real
robots should be less than half stall
torque to minimize current and to allow
robots to pick up objects without
overloading the motors.
Verbal
Linguistic
Logical
Mathematical
Visual
Spatial
Musical
Rhythmic
Bodily
Kinesthetic
Intrapersonal
Interpersonal
Naturalist
Existentialist
Application
Guided Practice (LSI Quadrant III):
Under the teacher’s guidance, have students calculate speed, current, efficiency, and optimal
gear ratio using example motor 2.
Independent Practice (LSI Quadrant III):
Have students calculate speed, current, efficiency, and optimal gear ratio using example
motor 3.
Summary
Review (LSI Quadrants I and IV):
Question: How would you demonstrate that these calculations actually apply to real motors in
real robots?
Answer: We could build some practice robots and test them.
Evaluation
Informal Assessment (LSI Quadrant III):
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9
Observation, guided and independent practice work and solutions, question and answer, time
on task, ability to work on their own.
Formal Assessment (LSI Quadrant III, IV):
Introduction to Robotics Part 3: Propulsion System Quiz and sample problems.
Extension
Extension/Enrichment (LSI Quadrant IV):
1. Have students create the motor characteristic curves shown on slides 53 and 54 by
themselves from the motor specs given for example motors 2 and 3.
2. Have students look up specs for other hobby/robot motors and work calculations and
create curves.
3. Have students build gear trains that optimize motor efficiency and robot speed.
4. Have students perform time and distance experiments that show the relationship
between gear ratio and maximum robot speed.
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Name______________________________Date___________________Class_____
QUIZ
Introduction to Robotics: Part 3
1.
The propulsion system is also called the:
a.
b.
c.
d.
2.
Which gear always goes in the numerator of a gear ratio calculation?
a.
b.
c.
d.
3.
The ratio of the diameters
The ratio of the number of gear teeth
The ratio of the circumferences
All of the above
Which device converts electrical energy into mechanical energy?
a.
b.
c.
d.
5.
the driving gear
the driven gear
either, it doesn’t matter
neither, this is not the way you calculate gear ratio
The gear ratio of 2 gears with the same pitch is the same as:
a.
b.
c.
d.
4.
Structural system
Motion system
Control system
Sensor system
Generator
Battery
Light bulb
Motor
How do we control the speed of a DC motor?
a.
b.
c.
d.
By changing the wires
By converting from DC to AC
By changing the amount of DC voltage
You cannot control the speed of a DC motor
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6.
What is the relationship between DC motor speed and DC motor current?
a.
b.
c.
d.
7.
What symbol do we use for angular velocity?
a.
b.
c.
d.
8.
Axle
Stator
Commutator
Brushes
Which of the following switches voltage polarity during rotation?
a.
b.
c.
d.
11.
RPM
MPH
MPG
Radians per second
Which of the following gets electricity into the rotor?
a.
b.
c.
d.
10.
Ω
ω
ϕ
τ
What term is common for angular velocity in America?
a.
b.
c.
d.
9.
They are inversely related
They are directly related
It depends on the gear ratio
There is no relationship between DC motor speed and DC motor current
Axle
Stator
Commutator
Brushes
Which of the following connects the motor to the external load?
a.
b.
c.
d.
Axle
Stator
Commutator
Brushes
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12
12.
What symbol is used for torque?
a.
b.
c.
d.
13.
Ω
ω
ϕ
τ
CEMF is directly proportional to:
a.
b.
c.
d.
Current
Torque
Angular velocity
Terminal resistance
Given the following characteristics for a motor: (all values are at 7.2 V)
Free Speed: 43 RPM
Stall Torque: 24 in·lbs
Stall Current: 3.34 amps
Free Current: 0.32 amps
14.
What is the terminal resistance for this motor?
15.
What is the constant of proportionality (ke) for the motor in question 14?
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16.
If the load applied to the motor in question 14 is 10 in-lb, what is the speed of
this motor?
17.
What current would this motor draw at the speed calculated in question 16?
18.
What is the optimal speed of the motor in question 16?
19.
What makes this speed the optimal speed?
20.
What would you have to do to get this motor to its optimal speed?
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14
21.
Describe 3 things gears are used for.
22.
Describe 2 things that happen to a DC motor when physical load (like the weight
of a robot) increases.
23.
Describe why you get generator action in a motor.
24.
Draw a plot of speed vs. torque for a DC motor.
25.
Draw a plot of current vs. torque for a DC motor.
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15
QUIZ Answer Key
Introduction to Robotics: Part 3
1.
The propulsion system is also called the:
a.
b.
c.
d.
2.
Which gear always goes in the numerator of a gear ratio calculation?
a.
b.
c.
d.
3.
The ratio of the diameters
The ratio of the number of gear teeth
The ratio of the circumferences
All of the above
Which device converts electrical energy into mechanical energy?
a.
b.
c.
d.
5.
the driving gear
the driven gear
either, it doesn’t matter
neither, this is not the way you calculate gear ratio
The gear ratio of 2 gears with the same pitch is the same as:
a.
b.
c.
d.
4.
Structural system
Motion system
Control system
Sensor system
Generator
Battery
Light bulb
Motor
How do we control the speed of a DC motor?
a.
b.
c.
d.
By changing the wires
By converting from DC to AC
By changing the amount of DC voltage
You cannot control the speed of a DC motor
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16
6.
What is the relationship between DC motor speed and DC motor current?
a.
b.
c.
d.
7.
What symbol do we use for angular velocity?
a.
b.
c.
d.
8.
Axle
Stator
Commutator
Brushes
Which of the following switches voltage polarity during rotation?
a.
b.
c.
d.
11.
RPM
MPH
MPG
Radians per second
Which of the following gets electricity into the rotor?
a.
b.
c.
d.
10.
Ω
ω
ϕ
τ
What term is common for angular velocity in America?
a.
b.
c.
d.
9.
They are inversely related
They are directly related
It depends on the gear ratio
There is no relationship between DC motor speed and DC motor current
Axle
Stator
Commutator
Brushes
Which of the following connects the motor to the external load?
a.
b.
c.
d.
Axle
Stator
Commutator
Brushes
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12.
What symbol is used for torque?
a.
b.
c.
d.
13.
Ω
ω
ϕ
τ
CEMF is directly proportional to:
a.
b.
c.
d.
Current
Torque
Angular velocity
Terminal resistance
Given the following characteristics for a motor: (all values are at 7.2 V)
Free Speed: 43 RPM
Stall Torque: 24 in·lbs
Stall Current: 3.34 amps
Free Current: 0.32 amps
14.
What is the terminal resistance for this motor?
15.
What is the constant of proportionality (ke) for this motor?
16.
If the load applied to the motor is 10 in-lb, what is the speed of this motor?
= 25.08 RPM
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17.
What current would this motor draw at this speed?
=
18.
What is the optimal speed of this motor?
Half of 43 RPM, or 21.5 RPM
19.
What makes this speed the optimal speed?
The torque applied to the motor will be exactly one half stall torque
20.
What would you have to do to get this motor to its optimal speed?
Add a gear train with a gear ratio of
or 1.2, meaning a gear with 10 teeth
driving a gear with 12 teeth
21.
Describe 3 things gears are used for.
To change a speed of rotation, to change a torque, to change the direction of motion of
the torque
22.
Describe 2 things that happen to a DC motor when physical load (like the weight
of a robot) increases.
Motor speed decreases, motor current increases
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23.
Describe why you get generator action in a motor.
Because you have a conductor moving through a magnetic field, which are the
conditions necessary for electrical generation.
24.
Draw a plot of speed vs. torque for a
DC motor.
Speed
Torque
25.
Draw a plot of current vs. torque for a
DC motor.
Current
Torque
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20