Download Robotics and Automation

1
INTRODUCTION TO
ROBOTICS
Part 3: Propulsion System
Robotics and Automation
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2
Robot Systems
• Structural System
• Physical system that provides support and stability
• Propulsion System (motion)
• Drive system includes motors, wheels, and gears
• Control System
• Microcontroller, operating program, electrical
power, and joystick
• Tool and Actuator system
• Arms, grippers, manipulators
• Sensor and Feedback system
• Perception, transducers
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3
Propulsion System Components
• Also called the motion system
• The most important propulsion system
components are gears and motors.
• All examples shown are for permanent
magnet type DC motors.
• We will discuss servos in another section
because they are used primarily in arms,
actuators, and grippers.
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4
Gears
Gears are used for several things:
• To increase the speed of rotation
• To increase the torque, or the rotating force
•
applied to a load
To change the direction of a torque
Gears trade one for the other:
• If you use gears to increase speed, torque will
•
decrease.
If you use gears to increase torque, speed will
decrease.
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More Gear Info
• Gears use teeth to transmit torque.
• Teeth must be the same size, even on
different size gears.
• The number of teeth varies for different size
gears:
• A smaller gear has fewer teeth
• A larger gear has more teeth
• A big gear driving a small gear
increases speed.
• A small gear driving a big gear increases
torque.
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6
Gear Calculations
• The ratio of the number of gear teeth
equals the ratio of the torque.
{ Assume gear one (g1) driving gear two (g2) }
𝑔1
𝑔2
=
𝑇1
𝑇2
• The ratio of gear teeth equals the inverse
ratio of the speed.
𝑔1
𝑔2
=
𝑆2
𝑆1
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7
Optimal Gear Ratio
• There is an optimal gear ratio.
• The optimal gear ratio puts load torque on
the motor at exactly half stall torque.
• Load torque on the motor is due to:
• The weight of the robot
• The number of drive wheels (motors used)
• The diameter of the drive wheels
• This gear ratio will maximize robot speed
and motor efficiency.
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8
More Gear Info
• For further information, there are some
great gear video tutorials available on-line.
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9
Motors
• A motor converts electrical energy into
mechanical energy.
• The mechanical energy comes from the
interaction between two magnetic fields.
• Magnetic fields produce physical forces:
• Like poles repel (N – N, S – S)
• Unlike poles attract
• These forces make a motor spin.
• One magnetic field is usually a permanent
magnet, the other is an electromagnet.
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10
Types of Motors
• Most motors are 2 wire, but
some hobby motors are 3 wire
because they are modified
servos.
• 2 wire motor may require a
motor driver board to provide
higher current.
• 3 wire motors use a servo
type RC signal output and
are generally low current.
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Photo Credit: VEX Robotics, Inc.
11
Example Motor Specs
• Free Speed: 100 rpm
• Stall Torque: 8.6 in-lbs
• Stall Current: 2.6A
• Free Current: 0.18A
• All motor specifications are at 7.2 volts.
• Often designed to connect to a
Photo Credit: VEX Robotics, Inc.
specific structural system:
• Drive shaft connection
• Mounting connections
Note screw connections sizes such as 6-32 or 8-32
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12
DC Motor Speed
• A DC motor is a variable speed device.
• Speed is controlled by the amount of DC
voltage applied:
• Varying the amount of DC voltage is covered
under control systems
• The physical load applied to the motor also
affects its speed:
• A higher load slows it down
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13
Motor Specs
• One interesting note is that as the load on
a DC motor increases, it will draw more
current from the power supply and make
the motor rotate more slowly.
• DC motor speed is inversely related to
motor current (but proportional to voltage).
• The torque a motor provides is always
equal to its load.
• We will discuss this in more detail later.
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14
Motor Specs
• Motors turn and spin, so we have to start thinking about
•
•
•
•
rotating motion.
Many motor formulas and equations involve rotational
units and concepts.
Angular velocity is the primary term used in rotational
motion.
Greek symbols are used for the quantities.
Ww
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15
Angular Velocity
• Angular velocity has a symbol, ω (omega)
• The speed that something is rotating
• In America we use RPM, or rotations per
minute
• Science uses units of radians per second
• There are 60 seconds per minute and 2π
radians per rotation, so:
60 RPM = 2π 𝑟𝑎𝑑
𝑠𝑒𝑐
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Conversion Practice
1. Convert 150 RPM to 𝑟𝑎𝑑 𝑠𝑒𝑐
2. Convert 12π 𝑟𝑎𝑑 𝑠𝑒𝑐 to RPM
3. Convert 85 𝑟𝑎𝑑 𝑠𝑒𝑐 to RPM
4. A motor rotates 120 times in 200 min.
Convert this speed to 𝑟𝑎𝑑 𝑠𝑒𝑐.
5. A motor rotates 1 radian in 2.5 sec.
Convert this speed to RPM.
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17
DC Motors
A motor has several parts:
• The rotor (the spinning part)
• Connected to an axle which is also the rotor shaft
• The stator (stationary part)
• The frame
• Supports the permanent magnets
• The commutator
• Switches the DC voltage polarity for continuous
rotation (polarity has to switch every half rotation)
• The brushes
• Gets electricity into the rotor
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18
Permanent Magnet DC Motor
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Rotor
Stator
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Bearings
Commutator
Armature
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Armature
Electromagnetic
Field Coil Windings
Field Coil
Poles
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Permanent
Magnet
Field Poles
Brushes
The positive and negative DC voltage on these wires connects
to the brushes giving
power to the armature field.
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http://commons.wikimedia.org/wiki/File:Electric_motor.gif
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Brief Motor Description
• An increase in motor load requires the motor
to draw more current from the power supply.
• An increase in load slows the motor down,
and the decrease in speed decreases
something called CEMF, allowing the current
to increase, creating higher motor torque
which balances the increase in load.
• Current is directly related to motor torque
because torque is produced through the
interaction of 2 magnetic fields.
• Magnetic field strength increases with current.
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25
Generator Action
• In order to understand how a motor works,
you must understand how a generator works.
• A generator converts mechanical energy into
electrical energy.
• The mechanical energy comes from an
external source called a prime mover.
• The electrical energy is created from a
conductor moving relative to a magnetic field:
• Relative motion.
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26
Motor Action in a Generator
• Current in a conductor creates a magnetic field.
• The magnetic field created by the induced
current always opposes the original field.
• The interaction of the 2 fields creates a force
that opposes the applied mechanical force.
• This is the load on a generator.
• More current drawn creates a larger
mechanical force which opposes the applied
mechanical force from the prime mover.
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27
Generator Action in a Motor
• A motor also has induction due to
conductors moving in a magnetic field.
• The induced voltage always opposes the
applied voltage from the power supply.
• The induced voltage in a motor is called
CEMF.
• A larger external load slows the motor
down, it produces less CEMF and draws
more current from the power supply.
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28
Motors and Generators
• Motors convert electrical energy into
mechanical energy.
• Generators convert mechanical energy into
electrical energy.
• All motors are generators and all generators
are motors.
• The load on a generator is the physical force
created by the interaction of 2 magnetic fields.
• The electrical load on a motor is the current
which is controlled by the induced voltage due
to conductors moving in a magnetic field.
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Motor Characteristic Curves
All motor specifications are at 7.2 volts
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30
Motor Current and Torque
This line shows that current and
torque are directly proportional
2.0
150
100
1.2
.8
50
.4
0
2.5
5.0
7.5
Torque (N-cm)
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10
Current (amps)
Speed (RPM)
1.6
31
Motor Speed and Torque
This line shows that current and speed
are inversely proportional, meaning that
as torque goes up, speed goes down
2.0
150
100
1.2
.8
50
.4
0
2.5
5.0
7.5
Torque (N-cm)
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10
Current (amps)
Speed (RPM)
1.6
32
Motor Characteristic Curves
No-Load Speed ωn
No-Load
Current
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Motor Characteristic Curves
Stall Current
Stall Torque τs
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Motor Characteristic Formulas
ω
ω
𝑚
τmotor = τs - τs ω = τs (1 - ω𝑚 )
n
n
τ
ωmotor = ωn ( 1 - τm )
s
τmotor (τm) and ωmotor (ωm) are actual
motor operating torque and speed
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35
• The stall torque, τs, represents the point on
•
the graph at which the torque is a maximum,
which is when the shaft is not rotating.
No rotation means no CEMF which allows
maximum current.
• The no load speed, ωn, is the maximum
output speed of the motor (when no load
torque is applied to the output shaft meaning
the motor is freely spinning).
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36
Torque, Current, and Speed
• Torque is proportional to current.
• Current is proportional to supplied voltage.
• The relationship between speed and
current is more complex.
• Speed is inversely proportional to current.
• Torque generated equals the load applied.
• As load increases, the motor slows down,
current increases, torque generated rises
to meet the higher load.
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37
Motor Formulas
• From Ohms Law:
𝑉𝑆 𝑉𝑒
I=
𝑅
Where:
VS = Supply voltage (from power supply or control circuit)
I = Motor Current (Amps)
R = Terminal Resistance (Ohms)
Ve = Back EMF (Volts) (also called counter emf, or CEMF)
The back EMF generated by the motor is directly
proportional to the angular velocity of the motor.
Ve = k e · ω
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38
Formula Application
• We will only use these simple equations in
our calculations.
• There are actually many other factors that
influence motor operation.
• Fortunately, most of those factors are
constant for a given motor and can be
accounted for in a single constant of
proportionality.
• See the next slide for an example of some of
the factors we will NOT be taking into account
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39
•Φ=
𝑁
μAI
𝑙
• Φ = magnetic flux density
• μ = magnetic permeability of the core
• A = cross sectional are of the magnetic pole
• I = current
• N = number of turns of wire around the core
• l = path length of the flux field
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40
Additional Formulas
• Speed equals cemf over shunt field flux
• N = 𝑉𝑒 Φ
• Motor Torque equals armature current
times shunt field flux
• τ = Ia · Φ
• Tangential velocity, v = r·ω
• Power in rotational motion: P = τ ·ω
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41
Typical Questions
• Assume you have a particular motor with
specs for that motor.
• What is the constant of proportionality, ke,
for that motor?
• Given a load, what is the motor speed?
What current does the motor draw?
• How does motor speed vary with applied
voltage?
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42
Example 1
• Use the specs for the motor given on slide 8
• Free Speed: 100 rpm
• Stall Torque: 8.6 in-lbs
• Stall Current: 2.6A
• Free Current: 0.18A
• All motor specifications are at 7.2 volts
• Calculate ke , speed, and current for this
motor given motor load equals 3 in-lbs
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43
Example 1
• Calculate R from stall current (ω = 0, Ve = 0)
𝑉𝑆 𝑉𝑒
I=
𝑅
Solve for R,
𝑉𝑠 7.2 𝑉
= 2.77 Ω
R= =
𝐼𝑆 2.6 𝐴
• Calculate Ve from free running current
Ve = VS – IR = 7.2 V – (.18 A · 2.77 Ω) = 7.2 - .5 = 6.7 V
• Calculate ke from Ve (use free running speed)
Ve = ke · ω,
𝑉𝑒
ke =
ω
=
6.7 𝑉
100 𝑅𝑃𝑀
= 0.067
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𝑽
𝑹𝑷𝑴
44
Example 1 continued
• Calculate motor speed from load
3 𝑖𝑛−𝑙𝑏𝑠
τ
ωmotor = ωn ( 1 - τ ) = 100 RPM ( 1 - 8.6 𝑖𝑛−𝑙𝑏𝑠 )
s
= 65.1 RPM
• To calculate current, you need Ve
Ve = ke · ω = 0.067 · 65.1 = 4.36 V
𝑉𝑆 𝑉𝑒
I=
𝑅
=
7.2 𝑉 − 4.36 𝑉
2.77 Ω
= 1.02 A
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45
Efficiency
• Motor efficiency is power out divided by
power in.
• Power out is mechanical energy, P = τ · ω
• Power in is electrical energy, P = V · I
% Eff =
𝑃𝑜
𝑃𝑖
τ·ω
x 100 = V · I =
2.312 𝑗𝑜𝑢𝑙𝑒𝑠/𝑠𝑒𝑐
=
7.344 𝑗𝑜𝑢𝑙𝑒𝑠/𝑠𝑒𝑐
.339 𝑁−𝑚 · 6.82 𝑟𝑎𝑑/𝑠𝑒𝑐
7.2 𝑉 ·1.02 𝐴
𝑋 100 = 31.5%
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46
Robot Linear Speed
• Assume the motor is coupled directly to a
wheel.
• The formula is slightly different when using
American units vs. metric units.
• American Units: Ѵ = ω · C
Units for ω in RPM, C is circumference of the wheel = 2πr
• Metric Units: Ѵ = ω · r
Units for ω in radians per second, r is radius of the wheel
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47
Calculating Linear Speed
• Wheel diameter equals 2.75 inches.
Ѵ = ω· C = ω · π d
= 65.1 RPM · π · 2.75 in
= 562.4
𝑖𝑛
𝑚𝑖𝑛
= 46.87
𝑓𝑡
𝑚𝑖𝑛
• This is NOT the optimal speed of the robot.
• Optimal speed would require gears that
place the load on the motor equal to half of
the stall torque.
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48
Optimal Robot Speed
• The example value of 3 in-lb load on the
motor is due to the weight of the robot and
the radius of the wheel used.
• To increase the load on the motor to 4.3 inlb, use a gear train with a gear ratio of:
4.3 𝑖𝑛−𝑙𝑏
3 𝑖𝑛−𝑙𝑏
= 1.433
• Which would increase robot speed to
67.2
𝑓𝑡
𝑚𝑖𝑛
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49
Robot Weight
• The example value of 3 in-lb load on the
motor is due to the weight of the robot and
the radius of the wheel used.
• The weight of the robot can be calculated:
τ
𝑟
τ = F · r or F = =
3 𝑖𝑛−𝑙𝑏
1.375 𝑖𝑛
= 2.2 lb
• Assuming 2 drive wheels, the actual
example robot weight equals 4.4 lb
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50
Additional Examples
• The following slides show motor
specifications for the actual motors used in
the BEST robotic contest.
• Use these specifications for example
problems using real world examples.
• Graphs are included for visual clarity, but
students can be expected to create these
graphs themselves from information given.
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51
Motor 2 specs
•
•
•
•
Free Speed: 43 RPM
Stall Torque: 24 in-lbs
Stall Current: 3.34 amps
Free Current: 0.32 amps
All motor specifications are at 7.2 volts
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52
Example Motor 2
4.0
50
30
2.0
20
1.0
10
0
100
200
300
Torque (N-cm)
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Current (amps)
Speed (RPM)
3.0
40
53
Motor 3 specs
•
•
•
•
Free Speed: 90 RPM
Stall Torque: 8.9 in-lbs
Stall Current: 2.39 amps
Free Current: 0.21 amps
All motor specifications are at 7.2 volts
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54
Example Motor 3
2.4
2.0
150
100
1.2
.8
50
.4
0
25
50
75
100
Torque (N-cm)
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125
Current (amps)
Speed (RPM)
1.6