(r5) Lecture9:SteppingMotors < Embedded

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---+ Stepping Motors
<h2 align="center">Lecture 9</h2> <h2 align="center">Uli Raich</h2> <h2 align="center">UCC semester 2017/2018</h2>

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---+ The 27BJY-48 stepper motor and its ULN-2803 driver module

<img alt="stepping.png" height="453" src="%ATTACHURL%/stepping.png" title="stepping.png" width="703" />

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---+ A lecture on youtube

There is an excellent [[%20https://www.youtube.com/watch?v=Dc16mKFA7Fo][ lecture]] describing the usage of exactly our stepper motor setup on youtube

---+ Stepping Motors versus DC Motors

While DC motors simply spin when they are powered,

stepping motors can be moved in defined steps and thus positioned very precisely.

They contain 2 coils which can be powered in positive or negative

direction making the current flow in normal or reverse direction

and thus creating magnetic fields of opposite polarity

The rotor has a series of magnets (16 in case of the 28BYJ-48 which we are using)

with alternating opposite polarization.

A north pole followed by a south pole followed by a north pole and so on.

The motor base has 2*16 teeth which can be polarized as

north or south poles depending on the direction of the coil current.

Here is the data sheet of the [[http://robocraft.ru/files/datasheet/28BYJ-48.pdf][28BYJ-48]]

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---+ The Driver Card

The maximum current that a GPIO pin on the Raspberry Pi can deliver is 60 mA

which is insufficient to power the motor coils.

We therefore need a driver circuit (Darlington stage) to amplify

this current. In our case we use the [[http://www.ti.com/lit/ds/symlink/uln2803a.pdf][ULN-2803]] chip

The little PCB has 4 LEDs on it to show which of the 2 coils is

powered and in which direction. This is very useful to demonstrate which signals

are sent to the motor and it illustrates nicely the functioning of the motor.

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---+ Connecting the Driver to the Motor

<img alt="connections.png" height="356" src="%ATTACHURL%/connections.png" title="connections.png" width="418" />

We can see from the connections that when powering the pink line

the coil current is flowing in one direction while when

powering the orange line it is flowing in the opposite direction

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---+ Motor Movement

First we power the first coil in such a way the the first tooth has a

south pole and the second one a north pole, which

makes the rotor (whose north magnet is considered) moves to the first tooth.

Then we switch off the first coil and power the second coil such that

the first tooth of the lower row has a south pole.

This makes the rotor move to this tooth.

Now switch off the second coil and switch the first one on again,

however this time with reverse current. The second tooth of the

upper row now has the south pole

(the poles are inversed with respect to the first step).

Now we switch on only the second coil with inverse current to make

the rotor move to the forth tooth. From now on the whole cycle repeats.<br /><br />
| <img alt="step1.png" height="195" src="%ATTACHURL%/step1.png" title="step1.png" width="198" /> | <img alt="step2.png" height="192" src="%ATTACHURL%/step2.png" title="step2.png" width="211" /> | <img alt="step3.png" height="190" src="%ATTACHURL%/step3.png" title="step3.png" width="196" /> | <p><img alt="step4.png" height="185" src="%ATTACHURL%/step4.png" title="step4.png" width="185" /></p> <p> </p> |
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---+ Signal Table for Single Phase Forward

We have seen in the last slide how we have to power the coils to

make the stepping motor move by 1 cycle, which is 4 steps in case of

Single Phase Forward stepping

How does this translate into a program?

We connect the 4 phases (coil 1 forward, coil 2 backward, coil 1 backward, coil 2 forward)

to 4 GPIO pins on the Raspberry Pi cobbler

Then we create the following signal table, which is a 2-dimensional array of booleans:<br /><br /><img alt="" height="188" 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" width="433" />
---++ 
---+ Sending the pulses to the hardware

Now all we have to do is to go through this table and, for each step,

send a high level to the GPIO pin to which we connected the coils.

<img alt="stepTable.png" height="303" src="%ATTACHURL%/stepTable.png" title="stepTable.png" width="454" />
---++ 

---++ 
---+ Going through one step cycle

<img alt="oneCycle.png" height="196" src="%ATTACHURL%/oneCycle.png" title="oneCycle.png" width="567" />

---++ 
---+ Other modes of operation

Single Step forward (and backward) works fine but we can do better.

Up to now we have always powered only one coil at a time.

It is however possible to power both coils at the same time.

This will draw of course more current but the motor will get

a higher torque and can therefore handle bigger loads.

---+ Movement Double Phase Forward
| <img alt="doubleStep1.png" height="185" src="%ATTACHURL%/doubleStep1.png" title="doubleStep1.png" width="205" /> | <img alt="doubleStep2.png" height="212" src="%ATTACHURL%/doubleStep2.png" title="doubleStep2.png" width="234" /> | <img alt="doubleStep3.png" height="182" src="%ATTACHURL%/doubleStep3.png" title="doubleStep3.png" width="189" /> | <img alt="doubleStep4.png" height="190" src="%ATTACHURL%/doubleStep4.png" title="doubleStep4.png" width="189" /> |
---++ 

---++ 
---+ Double Step Forward Table

Of course our signal table must change correspondingly,

our program to send out the signals for one full cycle stays the same however.
---++ <img alt="" height="164" 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" width="379" />

---++ 
---+ Programming double step forward mode

For this, nothing much is to be said:<br /><br />We change the table, but since the program is independent

from the contents of the stepping table, the code stays strictly the same
---++ 
---+ Position of rotor in doubleStepForward mode

An important point to note is that the rotor moves half a step

further than in single Step Forward because its north pole

is now attracted by the top and the bottom south poles.

By first powering only the upper coil, then powering both coils

then powering again only one pole of the lower coil it should

be possible to move the motor by half steps only

and by doing so increase its resolution.

This is what we call half step mode and it is a combination

of single and double step forward modes.

The torque of the motor is less than in double step forward

and the speed is only about half because now we need 8 steps for a full cycle.

---++ 
---+ Movement Half Step Forward
| <img alt="step1.png" height="195" src="%ATTACHURL%/step1.png" title="step1.png" width="198" /> | <img alt="doubleStep1.png" height="185" src="%ATTACHURL%/doubleStep1.png" title="doubleStep1.png" width="205" /> | <img alt="step2.png" height="192" src="%ATTACHURL%/step2.png" title="step2.png" width="211" /> | <img alt="doubleStep2.png" height="212" src="%ATTACHURL%/doubleStep2.png" title="doubleStep2.png" width="234" /> |
| <img alt="step3.png" height="190" src="%ATTACHURL%/step3.png" title="step3.png" width="196" /> | <img alt="doubleStep3.png" height="182" src="%ATTACHURL%/doubleStep3.png" title="doubleStep3.png" width="189" /> | <img alt="step4.png" height="185" src="%ATTACHURL%/step4.png" title="step4.png" width="185" /> | <img alt="doubleStep4.png" height="190" src="%ATTACHURL%/doubleStep4.png" title="doubleStep4.png" width="189" /> |
---++ 
---+ Half Step Forward Table

<img alt="" height="182" 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" width="669" />

---++ 
---+ Programming Half Step Mode

Again, apart from the fact that we must now pass through

a table of 8 entries instead of 4 the program does not change.

If we use the signature of all bits being zero

as end of table indicator then no change at all is required.

---++ 
---+ The pigpio library

Up to now we always used wiringPi to access our GPIO pins.

I explained in the first lecture on the Raspberry Pi

that there are 2 independent libraries available:<br /><br />
   * wiringPi
   * wigpio
Why would we be interested to use a different library?

---++ 
---+ Advantages of pigpio

The pigpio library comes in 2 versions:<br /><br />
   * The standard one where calls to the library code <br />results in direct access to the hardware
   * The daemon version where first a daemon (pigpiod)<br />is started and then the hardware access is only made in this daemon
---++ 
---+ Accessing the daemon

The daamon is started once before we make any hardware access:

_sudo pigpiod_

After this all hardware access can be make by a normal user

The program communicates with the deamon through library calls

which connect to the daemon through <br /><br />
   * pipes (when running on the Raspberry Pi) or<br /><br />
   * through sockets when running on a remote system <br />like our Ubuntu PC
There is a library version that runs on the PC

We can write C programs on the PC with hardware access

to our devices on the bread board through pigpio calls to the

PC version of the library which communicates

with the pigpio daemon on the Raspberry Pi

---++ 
---+ Documentation of pigpio

%SLIDESHOWSTART%
---+ Stepping Motors
<h2 align="center">Lecture 9</h2> <h2 align="center">Uli Raich</h2> <h2 align="center">UCC semester 2017/2018</h2>

---++ 
---+ The 27BJY-48 stepper motor and its ULN-2803 driver module

<img alt="stepping.png" height="453" src="%ATTACHURL%/stepping.png" title="stepping.png" width="703" />

---++ 
---+ Stepping Motors versus DC Motors

While DC motors simply spin when they are powered,

stepping motors can be moved in defined steps and thus positioned very precisely.

They contain 2 coils which can be powered in positive or negative

direction making the current flow in normal or reverse direction

and thus creating magnetic fields of opposite polarity

The rotor has a series of magnets (16 in case of the 28BYJ-48 which we are using)

with alternating opposite polarization.

A north pole followed by a south pole followed by a north pole and so on.

The motor base has 2*16 teeth which can be polarized as

north or south poles depending on the direction of the coil current.

Here is the data sheet of the [[http://robocraft.ru/files/datasheet/28BYJ-48.pdf][28BYJ-48]]

---++ 
---+ The Driver Card

The maximum current that a GPIO pin on the Raspberry Pi can deliver is 60 mA

which is insufficient to power the motor coils.

We therefore need a driver circuit (Darlington stage) to amplify

this current. In our case we use the [[http://www.ti.com/lit/ds/symlink/uln2803a.pdf][ULN-2803]] chip

The little PCB has 4 LEDs on it to show which of the 2 coils is

powered and in which direction. This is very useful to demonstrate which signals

are sent to the motor and it illustrates nicely the functioning of the motor.

---++ 
---+ Connecting the Driver to the Motor

<img alt="connections.png" height="356" src="%ATTACHURL%/connections.png" title="connections.png" width="418" />

We can see from the connections that when powering the pink line

the coil current is flowing in one direction while when

powering the orange line it is flowing in the opposite direction

---++ 
---+ Motor Movement

First we power the first coil in such a way the the first tooth has a

south pole and the second one a north pole, which

makes the rotor (whose north magnet is considered) moves to the first tooth.

Then we switch off the first coil and power the second coil such that

the first tooth of the lower row has a south pole.

This makes the rotor move to this tooth.

Now switch off the second coil and switch the first one on again,

however this time with reverse current. The second tooth of the

upper row now has the south pole

(the poles are inversed with respect to the first step).

Now we switch on only the second coil with inverse current to make

the rotor move to the forth tooth. From now on the whole cycle repeats.<br /><br />
| <img alt="step1.png" height="195" src="%ATTACHURL%/step1.png" title="step1.png" width="198" /> | <img alt="step2.png" height="192" src="%ATTACHURL%/step2.png" title="step2.png" width="211" /> | <img alt="step3.png" height="190" src="%ATTACHURL%/step3.png" title="step3.png" width="196" /> | <p><img alt="step4.png" height="185" src="%ATTACHURL%/step4.png" title="step4.png" width="185" /></p> <p> </p> |
---++ 
---+ Signal Table for Single Phase Forward

We have seen in the last slide how we have to power the coils to

make the stepping motor move by 1 cycle, which is 4 steps in case of

Single Phase Forward stepping

How does this translate into a program?

We connect the 4 phases (coil 1 forward, coil 2 backward, coil 1 backward, coil 2 forward)

to 4 GPIO pins on the Raspberry Pi cobbler

Then we create the following signal table, which is a 2-dimensional array of booleans:<br /><br /><img alt="" height="188" src="data:image/png;base64,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" width="433" />

---+ Sending the pulses to the hardware

Now all we have to do is to go through this table and, for each step,

send a high level to the GPIO pin to which we connected the coils.

<img alt="stepTable.png" height="303" src="%ATTACHURL%/stepTable.png" title="stepTable.png" width="454" />
---++ 

---++ 
---+ Going through one step cycle

<img alt="oneCycle.png" height="196" src="%ATTACHURL%/oneCycle.png" title="oneCycle.png" width="567" />

---++ 
---+ Other modes of operation

Single Step forward (and backward) works fine but we can do better.

Up to now we have always powered only one coil at a time.

It is however possible to power both coils at the same time.

This will draw of course more current but the motor will get

a higher torque and can therefore handle bigger loads.

---+ Movement Double Phase Forward
| <img alt="doubleStep1.png" height="185" src="%ATTACHURL%/doubleStep1.png" title="doubleStep1.png" width="205" /> | <img alt="doubleStep2.png" height="212" src="%ATTACHURL%/doubleStep2.png" title="doubleStep2.png" width="234" /> | <img alt="doubleStep3.png" height="182" src="%ATTACHURL%/doubleStep3.png" title="doubleStep3.png" width="189" /> | <img alt="doubleStep4.png" height="190" src="%ATTACHURL%/doubleStep4.png" title="doubleStep4.png" width="189" /> |
---++ 

---++ 
---+ Double Step Forward Table

Of course our signal table must change correspondingly,

our program to send out the signals for one full cycle stays the same however.
---++ <img alt="" height="164" 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" width="379" />

---++ 
---+ Programming double step forward mode

For this, nothing much is to be said:<br /><br />We change the table, but since the program is independent

from the contents of the stepping table, the code stays strictly the same
---++ 
---+ Position of rotor in doubleStepForward mode

An important point to note is that the rotor moves half a step

further than in single Step Forward because its north pole

is now attracted by the top and the bottom south poles.

By first powering only the upper coil, then powering both coils

then powering again only one pole of the lower coil it should

be possible to move the motor by half steps only

and by doing so increase its resolution.

This is what we call half step mode and it is a combination

of single and double step forward modes.

The torque of the motor is less than in double step forward

and the speed is only about half because now we need 8 steps for a full cycle.

---++ 
---+ Movement Half Step Forward
| <img alt="step1.png" height="195" src="%ATTACHURL%/step1.png" title="step1.png" width="198" /> | <img alt="doubleStep1.png" height="185" src="%ATTACHURL%/doubleStep1.png" title="doubleStep1.png" width="205" /> | <img alt="step2.png" height="192" src="%ATTACHURL%/step2.png" title="step2.png" width="211" /> | <img alt="doubleStep2.png" height="212" src="%ATTACHURL%/doubleStep2.png" title="doubleStep2.png" width="234" /> |
| <img alt="step3.png" height="190" src="%ATTACHURL%/step3.png" title="step3.png" width="196" /> | <img alt="doubleStep3.png" height="182" src="%ATTACHURL%/doubleStep3.png" title="doubleStep3.png" width="189" /> | <img alt="step4.png" height="185" src="%ATTACHURL%/step4.png" title="step4.png" width="185" /> | <img alt="doubleStep4.png" height="190" src="%ATTACHURL%/doubleStep4.png" title="doubleStep4.png" width="189" /> |
---++ 
---+ Half Step Forward Table

<img alt="" height="182" 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" width="669" />

---++ 
---+ Programming Half Step Mode

Again, apart from the fact that we must now pass through

a table of 8 entries instead of 4 the program does not change.

If we use the signature of all bits being zero

as end of table indicator then no change at all is required.

---++ 
---+ The pigpio library

Up to now we always used wiringPi to access our GPIO pins.

I explained in the first lecture on the Raspberry Pi

that there are 2 independent libraries available:<br /><br />
   * wiringPi
   * wigpio
Why would we be interested to use a different library?

---++ 
---+ Advantages of pigpio

The pigpio library comes in 2 versions:<br /><br />
   * The standard one where calls to the library code <br />results in direct access to the hardware
   * The daemon version where first a daemon (pigpiod)<br />is started and then the hardware access is only made in this daemon
---++ 
---+ Accessing the daemon

The daamon is started once before we make any hardware access:

_sudo pigpiod_

After this all hardware access can be make by a normal user

The program communicates with the deamon through library calls

which connect to the daemon through <br /><br />
   * pipes (when running on the Raspberry Pi) or<br /><br />
   * through sockets when running on a remote system <br />like our Ubuntu PC
There is a library version that runs on the PC

We can write C programs on the PC with hardware access

to our devices on the bread board through pigpio calls to the

PC version of the library which communicates

with the pigpio daemon on the Raspberry Pi

---++ 
---+ Documentation of pigpio

%SLIDESHOWSTART%
---+ Stepping Motors
<h2 align="center">Lecture 9</h2> <h2 align="center">Uli Raich</h2> <h2 align="center">UCC semester 2017/2018</h2>

---++ 
---+ The 27BJY-48 stepper motor and its ULN-2803 driver module

<img alt="stepping.png" height="453" src="%ATTACHURL%/stepping.png" title="stepping.png" width="703" />

---++ 
---+ Stepping Motors versus DC Motors

While DC motors simply spin when they are powered,

stepping motors can be moved in defined steps and thus positioned very precisely.

They contain 2 coils which can be powered in positive or negative

direction making the current flow in normal or reverse direction

and thus creating magnetic fields of opposite polarity

The rotor has a series of magnets (16 in case of the 28BYJ-48 which we are using)

with alternating opposite polarization.

A north pole followed by a south pole followed by a north pole and so on.

The motor base has 2*16 teeth which can be polarized as

north or south poles depending on the direction of the coil current.

Here is the data sheet of the [[http://robocraft.ru/files/datasheet/28BYJ-48.pdf][28BYJ-48]]

---++ 
---+ The Driver Card

The maximum current that a GPIO pin on the Raspberry Pi can deliver is 60 mA

which is insufficient to power the motor coils.

We therefore need a driver circuit (Darlington stage) to amplify

this current. In our case we use the [[http://www.ti.com/lit/ds/symlink/uln2803a.pdf][ULN-2803]] chip

The little PCB has 4 LEDs on it to show which of the 2 coils is

powered and in which direction. This is very useful to demonstrate which signals

are sent to the motor and it illustrates nicely the functioning of the motor.

---++ 
---+ Connecting the Driver to the Motor

<img alt="connections.png" height="356" src="%ATTACHURL%/connections.png" title="connections.png" width="418" />

We can see from the connections that when powering the pink line

the coil current is flowing in one direction while when

powering the orange line it is flowing in the opposite direction

---++ 
---+ Motor Movement

First we power the first coil in such a way the the first tooth has a

south pole and the second one a north pole, which

makes the rotor (whose north magnet is considered) moves to the first tooth.

Then we switch off the first coil and power the second coil such that

the first tooth of the lower row has a south pole.

This makes the rotor move to this tooth.

Now switch off the second coil and switch the first one on again,

however this time with reverse current. The second tooth of the

upper row now has the south pole

(the poles are inversed with respect to the first step).

Now we switch on only the second coil with inverse current to make

the rotor move to the forth tooth. From now on the whole cycle repeats.<br /><br />
| <img alt="step1.png" height="195" src="%ATTACHURL%/step1.png" title="step1.png" width="198" /> | <img alt="step2.png" height="192" src="%ATTACHURL%/step2.png" title="step2.png" width="211" /> | <img alt="step3.png" height="190" src="%ATTACHURL%/step3.png" title="step3.png" width="196" /> | <p><img alt="step4.png" height="185" src="%ATTACHURL%/step4.png" title="step4.png" width="185" /></p> <p> </p> |
---++ 
---+ Signal Table for Single Phase Forward

We have seen in the last slide how we have to power the coils to

make the stepping motor move by 1 cycle, which is 4 steps in case of

Single Phase Forward stepping

How does this translate into a program?

We connect the 4 phases (coil 1 forward, coil 2 backward, coil 1 backward, coil 2 forward)

to 4 GPIO pins on the Raspberry Pi cobbler

Then we create the following signal table, which is a 2-dimensional array of booleans:<br /><br /><img alt="" height="188" src="data:image/png;base64,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" width="433" />
---++ 
---+ Sending the pulses to the hardware

Now all we have to do is to go through this table and, for each step,

send a high level to the GPIO pin to which we connected the coils.

<img alt="stepTable.png" height="303" src="%ATTACHURL%/stepTable.png" title="stepTable.png" width="454" />
---++ 

---++ 
---+ Going through one step cycle

<img alt="oneCycle.png" height="196" src="%ATTACHURL%/oneCycle.png" title="oneCycle.png" width="567" />

---++ 
---+ Other modes of operation

Single Step forward (and backward) works fine but we can do better.

Up to now we have always powered only one coil at a time.

It is however possible to power both coils at the same time.

This will draw of course more current but the motor will get

a higher torque and can therefore handle bigger loads.

---+ Movement Double Phase Forward
| <img alt="doubleStep1.png" height="185" src="%ATTACHURL%/doubleStep1.png" title="doubleStep1.png" width="205" /> | <img alt="doubleStep2.png" height="212" src="%ATTACHURL%/doubleStep2.png" title="doubleStep2.png" width="234" /> | <img alt="doubleStep3.png" height="182" src="%ATTACHURL%/doubleStep3.png" title="doubleStep3.png" width="189" /> | <img alt="doubleStep4.png" height="190" src="%ATTACHURL%/doubleStep4.png" title="doubleStep4.png" width="189" /> |
---++ 

---++ 
---+ Double Step Forward Table

Of course our signal table must change correspondingly,

our program to send out the signals for one full cycle stays the same however.
---++ <img alt="" height="164" 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" width="379" />

---++ 
---+ Programming double step forward mode

For this, nothing much is to be said:<br /><br />We change the table, but since the program is independent

from the contents of the stepping table, the code stays strictly the same
---++ 
---+ Position of rotor in doubleStepForward mode

An important point to note is that the rotor moves half a step

further than in single Step Forward because its north pole

is now attracted by the top and the bottom south poles.

By first powering only the upper coil, then powering both coils

then powering again only one pole of the lower coil it should

be possible to move the motor by half steps only

and by doing so increase its resolution.

This is what we call half step mode and it is a combination

of single and double step forward modes.

The torque of the motor is less than in double step forward

and the speed is only about half because now we need 8 steps for a full cycle.

---++ 
---+ Movement Half Step Forward
| <img alt="step1.png" height="195" src="%ATTACHURL%/step1.png" title="step1.png" width="198" /> | <img alt="doubleStep1.png" height="185" src="%ATTACHURL%/doubleStep1.png" title="doubleStep1.png" width="205" /> | <img alt="step2.png" height="192" src="%ATTACHURL%/step2.png" title="step2.png" width="211" /> | <img alt="doubleStep2.png" height="212" src="%ATTACHURL%/doubleStep2.png" title="doubleStep2.png" width="234" /> |
| <img alt="step3.png" height="190" src="%ATTACHURL%/step3.png" title="step3.png" width="196" /> | <img alt="doubleStep3.png" height="182" src="%ATTACHURL%/doubleStep3.png" title="doubleStep3.png" width="189" /> | <img alt="step4.png" height="185" src="%ATTACHURL%/step4.png" title="step4.png" width="185" /> | <img alt="doubleStep4.png" height="190" src="%ATTACHURL%/doubleStep4.png" title="doubleStep4.png" width="189" /> |
---++ 
---+ Half Step Forward Table

<img alt="" height="182" 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" width="669" />

---++ 
---+ Programming Half Step Mode

Again, apart from the fact that we must now pass through

a table of 8 entries instead of 4 the program does not change.

If we use the signature of all bits being zero

as end of table indicator then no change at all is required.

---++ 
---+ The pigpio library

Up to now we always used wiringPi to access our GPIO pins.

I explained in the first lecture on the Raspberry Pi

that there are 2 independent libraries available:<br /><br />
   * wiringPi
   * wigpio
Why would we be interested to use a different library?

---++ 
---+ Advantages of pigpio

The pigpio library comes in 2 versions:<br /><br />
   * The standard one where calls to the library code <br />results in direct access to the hardware
   * The daemon version where first a daemon (pigpiod)<br />is started and then the hardware access is only made in this daemon
---++ 
---+ Accessing the daemon

The daamon is started once before we make any hardware access:

_sudo pigpiod_

After this all hardware access can be make by a normal user

The program communicates with the deamon through library calls

which connect to the daemon through <br /><br />
   * pipes (when running on the Raspberry Pi) or<br /><br />
   * through sockets when running on a remote system <br />like our Ubuntu PC
There is a library version that runs on the PC

We can write C programs on the PC with hardware access

to our devices on the bread board through pigpio calls to the

PC version of the library which communicates

with the pigpio daemon on the Raspberry Pi

---++ 
---+ Documentation of pigpio

<br />%SLIDESHOWEND%

--

%SLIDESHOWSTART%
---+ Stepping Motors
<h2 align="center">Lecture 9</h2> <h2 align="center">Uli Raich</h2> <h2 align="center">UCC semester 2017/2018</h2>

---++ 
---+ The 27BJY-48 stepper motor and its ULN-2803 driver module

<img alt="stepping.png" height="453" src="%ATTACHURL%/stepping.png" title="stepping.png" width="703" />

---++ 
---+ Stepping Motors versus DC Motors

While DC motors simply spin when they are powered,

stepping motors can be moved in defined steps and thus positioned very precisely.

They contain 2 coils which can be powered in positive or negative

direction making the current flow in normal or reverse direction

and thus creating magnetic fields of opposite polarity

The rotor has a series of magnets (16 in case of the 28BYJ-48 which we are using)

with alternating opposite polarization.

A north pole followed by a south pole followed by a north pole and so on.

The motor base has 2*16 teeth which can be polarized as

north or south poles depending on the direction of the coil current.

Here is the data sheet of the [[http://robocraft.ru/files/datasheet/28BYJ-48.pdf][28BYJ-48]]

---++ 
---+ The Driver Card

The maximum current that a GPIO pin on the Raspberry Pi can deliver is 60 mA

which is insufficient to power the motor coils.

We therefore need a driver circuit (Darlington stage) to amplify

this current. In our case we use the [[http://www.ti.com/lit/ds/symlink/uln2803a.pdf][ULN-2803]] chip

The little PCB has 4 LEDs on it to show which of the 2 coils is

powered and in which direction. This is very useful to demonstrate which signals

are sent to the motor and it illustrates nicely the functioning of the motor.

---++ 
---+ Connecting the Driver to the Motor

<img alt="connections.png" height="356" src="%ATTACHURL%/connections.png" title="connections.png" width="418" />

We can see from the connections that when powering the pink line

the coil current is flowing in one direction while when

powering the orange line it is flowing in the opposite direction

---++ 
---+ Motor Movement

First we power the first coil in such a way the the first tooth has a

south pole and the second one a north pole, which

makes the rotor (whose north magnet is considered) moves to the first tooth.

Then we switch off the first coil and power the second coil such that

the first tooth of the lower row has a south pole.

This makes the rotor move to this tooth.

Now switch off the second coil and switch the first one on again,

however this time with reverse current. The second tooth of the

upper row now has the south pole

(the poles are inversed with respect to the first step).

Now we switch on only the second coil with inverse current to make

the rotor move to the forth tooth. From now on the whole cycle repeats.<br /><br />
| <img alt="step1.png" height="195" src="%ATTACHURL%/step1.png" title="step1.png" width="198" /> | <img alt="step2.png" height="192" src="%ATTACHURL%/step2.png" title="step2.png" width="211" /> | <img alt="step3.png" height="190" src="%ATTACHURL%/step3.png" title="step3.png" width="196" /> | <p><img alt="step4.png" height="185" src="%ATTACHURL%/step4.png" title="step4.png" width="185" /></p> <p> </p> |
---++ 
---+ Signal Table for Single Phase Forward

We have seen in the last slide how we have to power the coils to

make the stepping motor move by 1 cycle, which is 4 steps in case of

Single Phase Forward stepping

How does this translate into a program?

We connect the 4 phases (coil 1 forward, coil 2 backward, coil 1 backward, coil 2 forward)

to 4 GPIO pins on the Raspberry Pi cobbler

Then we create the following signal table, which is a 2-dimensional array of booleans:<br /><br /><img alt="" height="188" src="data:image/png;base64,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" width="433" />
---++ 
---+ Other modes of operation

Single Step forward (and backward) works fine but we can do better.

Up to now we have always powered only one coil at a time.

It is however possible to power both coils at the same time.

This will draw of course more current but the motor will get

a higher torque and can therefore handle bigger loads.

---+ Movement Double Phase Forward
| <img alt="doubleStep1.png" height="185" src="%ATTACHURL%/doubleStep1.png" title="doubleStep1.png" width="205" /> | <img alt="doubleStep2.png" height="212" src="%ATTACHURL%/doubleStep2.png" title="doubleStep2.png" width="234" /> | <img alt="doubleStep3.png" height="182" src="%ATTACHURL%/doubleStep3.png" title="doubleStep3.png" width="189" /> | <img alt="doubleStep4.png" height="190" src="%ATTACHURL%/doubleStep4.png" title="doubleStep4.png" width="189" /> |
---++ 

---++ 
---+ Double Step Forward Table

Of course our signal table must change correspondingly,

our program to send out the signals for one full cycle stays the same however.
---++ <img alt="" height="164" 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" width="379" />

---++ 
---+ Programming double step forward mode

For this, nothing much is to be said:<br /><br />We change the table, but since the program is independent

from the contents of the stepping table, the code stays strictly the same
---++ 
---+ Position of rotor in doubleStepForward mode

An important point to note is that the rotor moves half a step

further than in single Step Forward because its north pole

is now attracted by the top and the bottom south poles.

By first powering only the upper coil, then powering both coils

then powering again only one pole of the lower coil it should

be possible to move the motor by half steps only

and by doing so increase its resolution.

This is what we call half step mode and it is a combination

of single and double step forward modes.

The torque of the motor is less than in double step forward

and the speed is only about half because now we need 8 steps for a full cycle.

---++ 
---+ Movement Half Step Forward
| <img alt="step1.png" height="195" src="%ATTACHURL%/step1.png" title="step1.png" width="198" /> | <img alt="doubleStep1.png" height="185" src="%ATTACHURL%/doubleStep1.png" title="doubleStep1.png" width="205" /> | <img alt="step2.png" height="192" src="%ATTACHURL%/step2.png" title="step2.png" width="211" /> | <img alt="doubleStep2.png" height="212" src="%ATTACHURL%/doubleStep2.png" title="doubleStep2.png" width="234" /> |
| <img alt="step3.png" height="190" src="%ATTACHURL%/step3.png" title="step3.png" width="196" /> | <img alt="doubleStep3.png" height="182" src="%ATTACHURL%/doubleStep3.png" title="doubleStep3.png" width="189" /> | <img alt="step4.png" height="185" src="%ATTACHURL%/step4.png" title="step4.png" width="185" /> | <img alt="doubleStep4.png" height="190" src="%ATTACHURL%/doubleStep4.png" title="doubleStep4.png" width="189" /> |
---++ 
---+ Half Step Forward Table

<img alt="" height="182" 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" width="669" />

---++ 
---+ Programming Half Step Mode

Again, apart from the fact that we must now pass through

a table of 8 entries instead of 4 the program does not change.

If we use the signature of all bits being zero

as end of table indicator then no change at all is required.

---++ 
---+ The pigpio library

Up to now we always used wiringPi to access our GPIO pins.

I explained in the first lecture on the Raspberry Pi

that there are 2 independent libraries available:<br /><br />
   * wiringPi
   * wigpio
Why would we be interested to use a different library?

---++ 
---+ Advantages of pigpio

The pigpio library comes in 2 versions:<br /><br />
   * The standard one where calls to the library code <br />results in direct access to the hardware
   * The daemon version where first a daemon (pigpiod)<br />is started and then the hardware access is only made in this daemon
---++ 
---+ Accessing the daemon

The daamon is started once before we make any hardware access:

_sudo pigpiod_

After this all hardware access can be make by a normal user

The program communicates with the deamon through library calls

which connect to the daemon through <br /><br />
   * pipes (when running on the Raspberry Pi) or<br /><br />
   * through sockets when running on a remote system <br />like our Ubuntu PC
There is a library version that runs on the PC

We can write C programs on the PC with hardware access

to our devices on the bread board through pigpio calls to the

PC version of the library which communicates

with the pigpio daemon on the Raspberry Pi

---++ 
---+ Documentation of pigpio

The WEB page of pigpio can be found [[http://abyz.me.uk/rpi/pigpio/][here<br />]]<br /><img alt="pigpioPage.png" height="352" src="%ATTACHURL%/pigpioPage.png" title="pigpioPage.png" width="650" />

---++ 
---+ Features of pigpio

<img alt="features.png" height="471" src="%ATTACHURL%/features.png" title="features.png" width="496" />

---++ 
---+ This is how to use the library

<img alt="usage.png" height="273" src="%ATTACHURL%/usage.png" title="usage.png" width="592" />

Please convert this to what will be required in your source code.

---++ 

---+ Sending the pulses to the hardware

Now all we have to do is to go through this table and, for each step,

send a high level to the GPIO pin to which we connected the coils.

<img alt="stepTable.png" height="303" src="%ATTACHURL%/stepTable.png" title="stepTable.png" width="454" />
---++ 

---++ 
---+ Going through one step cycle

<img alt="oneCycle.png" height="196" src="%ATTACHURL%/oneCycle.png" title="oneCycle.png" width="567" />

---++ 

%SLIDESHOWEND%

-- %USERSIG{UliRaich - 2017-10-16}%

---++ Comments

The youtube video on stepping motors has been taken out of the lecture slides (lecture_9_upload.odt) because it would make the file too big for upload and I am not sure about copyright issues. However, you have the link to the video in the slides on this page.

-- %BUBBLESIG{UliRaich - 2017-11-01}%

%COMMENT%
Attachments
Topic attachments
I	Attachment	History	Action	Size	Date	Who
png	connections.png	r1	manage	29.9 K	2017-10-16 - 13:58	UnknownUser
png	daemon.png	r1	manage	17.0 K	2017-10-26 - 13:43	UnknownUser
png	doubleStep1.png	r1	manage	5.3 K	2017-10-17 - 09:20	UnknownUser
png	doubleStep2.png	r1	manage	5.6 K	2017-10-17 - 09:20	UnknownUser
png	doubleStep3.png	r1	manage	5.2 K	2017-10-17 - 09:20	UnknownUser
png	doubleStep4.png	r1	manage	5.5 K	2017-10-17 - 09:20	UnknownUser
png	features.png	r1	manage	40.2 K	2017-10-26 - 13:43	UnknownUser
png	gpioI2C.png	r1	manage	76.7 K	2017-10-26 - 13:43	UnknownUser
odp	lecture_9_upload.odp	r1	manage	695.0 K	2017-11-01 - 09:29	UnknownUser
png	oneCycle.png	r1	manage	18.6 K	2017-10-17 - 09:20	UnknownUser
png	pigpioCalls.png	r1	manage	65.6 K	2017-10-26 - 13:43	UnknownUser
png	pigpioLib.png	r1	manage	60.9 K	2017-10-26 - 13:43	UnknownUser
png	pigpioPage.png	r1	manage	228.8 K	2017-10-26 - 13:43	UnknownUser
png	pigpioVariants.png	r1	manage	20.7 K	2017-10-26 - 13:43	UnknownUser
png	step1.png	r1	manage	4.8 K	2017-10-16 - 13:41	UnknownUser
png	step2.png	r1	manage	4.7 K	2017-10-16 - 13:41	UnknownUser
png	step3.png	r1	manage	4.8 K	2017-10-16 - 13:41	UnknownUser
png	step4.png	r1	manage	4.6 K	2017-10-16 - 13:41	UnknownUser
png	stepTable.png	r1	manage	18.3 K	2017-10-17 - 09:20	UnknownUser
png	stepperUsage.png	r1	manage	37.5 K	2017-10-26 - 14:38	UnknownUser
png	stepping.png	r1	manage	182.9 K	2017-10-16 - 12:46	UnknownUser
png	usage.png	r1	manage	16.9 K	2017-10-26 - 14:38	UnknownUser
Topic revision: r5 - 2017-11-01 - uli