INTRODUCTION TO ROBOTICS Part 3: Propulsion System Robotics and Automation Copyright © Texas...

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INTRODUCTION TO ROBOTICSPart 3: Propulsion System

Robotics and AutomationCopyright © Texas Education Agency, 2012. All rights reserved.

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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

Copyright © Texas Education Agency, 2012. All rights reserved.

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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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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.Copyright © Texas Education Agency, 2012. All rights reserved.

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Gear Calculations

• The ratio of the number of gear teeth equals the ratio of the torque.

{ Assume gear one (g1) driving gear two (g2) }

=

• The ratio of gear teeth equals the inverse ratio of the speed.

=


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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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More Gear Info

• For further information, there are some great gear video tutorials available on-line.


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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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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.


Photo Credit: VEX Robotics, Inc.

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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 specific structural system:• Drive shaft connection

• Mounting connectionsNote screw connections sizes such as 6-32 or 8-32Copyright © Texas Education Agency, 2012. All rights reserved.

Photo Credit: VEX Robotics, Inc.

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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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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.Copyright © Texas Education Agency, 2012. All rights reserved.

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• 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.

• W w


Motor Specs

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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


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Conversion Practice

1. Convert 150 RPM to

2. Convert 12π to RPM

3. Convert 85 to RPM

4. A motor rotates 120 times in 200 min. Convert this speed to .

5. A motor rotates 1 radian in 2.5 sec. Convert this speed to RPM.


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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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Permanent Magnet DC Motor


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Stator

Rotor


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Armature

Bearings

Commutator


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Armature Electromagnetic Field Coil Windings

Field CoilPoles


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PermanentMagnetField Poles

Brushes

The positive and negative DC voltage on these wires connectsto 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.Copyright © Texas Education Agency, 2012. All rights reserved.

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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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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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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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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 CurvesAll motor specifications are at 7.2 volts


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Motor Current and Torque

Torque (N-cm)

150

100

50

0

Speed (RPM) Current (amps)

.4

.8

2.0

1.2

1.6

5.02.5 7.5 10

This line shows that current and torque are directly proportional


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Motor Speed and Torque

Torque (N-cm)

150

100

50

0


.4

.8

2.0

1.2

1.6

5.02.5 7.5 10

This line shows that current and speed are inversely proportional, meaning that as torque goes up, speed goes down


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Motor Characteristic Curves

No-Load Speed ωn

No-Load Current


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Motor Characteristic Curves

Stall Current

Stall Torque τs Copyright © Texas Education Agency, 2012. All rights reserved.

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Motor Characteristic Formulas

τmotor = τs - τs = τs (1 - )

ωmotor = ωn ( 1 - ) τmotor () and ωmotor (m) are actual

motor operating torque and speed Copyright © Texas Education Agency, 2012. All rights reserved.

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• 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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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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Motor Formulas

• From Ohms Law:

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 = ke·ω

I =


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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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• Φ = μAI

• 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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Additional Formulas

• Speed equals cemf over shunt field flux

• N =

• 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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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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Example 1

• Use the specs for the motor given on slide 8• Free Speed: 100 rpm


• 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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Example 1

• Calculate R from stall current (ω = 0, Ve = 0)• Calculate Ve from free running current

• Calculate ke from Ve (use free running speed)

Ve = ke · ω, ke = = = 0.067

I = Solve for R, R = = = 2.77 Ω

Ve = VS – IR = 7.2 V – (.18 A · 2.77 Ω) = 7.2 - .5 = 6.7 V


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Example 1 continued

• Calculate motor speed from load

• To calculate current, you need Ve

ωmotor = ωn ( 1 - ) = 100 RPM ( 1 - )

= 65.1 RPM

Ve = ke · ω = 0.067 · 65.1 = 4.36 V

I = = = 1.02 A


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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 = x 100 =

=


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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 • Metric Units: Ѵ = ω · rUnits for ω in RPM, C is circumference of the wheel = 2πr

Units for ω in radians per second, r is radius of the wheel


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Calculating Linear Speed

• Wheel diameter equals 2.75 inches.

Ѵ = ω · C = ω · π d= 65.1 RPM · π · 2.75 in

= 562.4 = 46.87

• 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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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 in-lb, use a gear train with a gear ratio of:

= 1.433

• Which would increase robot speed to 67.2


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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:

• Assuming 2 drive wheels, the actual example robot weight equals 4.4 lb

τ = F · r or F = = = 2.2 lb


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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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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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Example Motor 2

Torque (N-cm)

50

40

10

0


1.0

4.0

2.0

3.0

100 200 300

30

20


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Motor 3 specs

• Free Speed: 90 RPM


• Stall Current: 2.39 amps

• Free Current: 0.21 amps

All motor specifications are at 7.2 volts


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Example Motor 3

Torque (N-cm)

150

100

50

0


.4

.8

2.0

1.2

1.6

5025 75 100 125

2.4


INTRODUCTION TO ROBOTICS Part 3: Propulsion System Robotics and Automation Copyright © Texas...

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Transcript of INTRODUCTION TO ROBOTICS Part 3: Propulsion System Robotics and Automation Copyright © Texas...