Thank you Whit !
If you have time put a pen in your S2 upload the next spin code and see the result!
The S2 will draw a Greek dancer dancing "The Evdokia's Zeibekiko" and simultaneously plays the song!

The "Artist" performs the same activity more impresive due to the SD card and the vecho speaker, but the accuracy of the S2 is remarkable!

Another video with "Artist", dancing and singing the "Evdokias Zeibekiko" (Rock edition), during the 3rd day of 5th digital student's festival in Patras-Greece 2015

The drawing has some improvements: The figure "8" s are symetrical and smaller in order to fit the entire shape in the 2 X2,5m black moquette That I bought for this purpose....

Nicely done, and way to display the Parallax banner!

Thank you Erco!
I displayed the Parallax banner and in a second event (the same day) :

Saturday 5 April 2015, after the 5th student’s digital festival, another festival took place in Patras city.
The “Annual student’s festival”, that is supported mostly from young with strong political interest and political parts against the European Union.
One of my students (Tassos), a politically active student, asked me to present the “Artist” and the “Parallax S2 robot” in this festival.
Although I totally disagree with politics, I accepted this challenge because I believe that robots must be beyond politics and they consist a great way for a better future for young people.
It was a great opportunity to make a contact of that part of youth with robotics and Parallax.

After the Show, “Artist” and S2 robot got the applauses from the audience, and I accepted a lot of questions about Parallax and robots in general. I realized that many graduated student’s had a totally ignorance about robotics because of their only interest in politics!

The last part of this project is the drawings. Except from the figure 8s and the flowers( post #106), the robot must be able to make and other shapes like triangles, rectangles, polygons, curves , straight lines and Letters!!!

So it is very important to program it, in order to turning in place with accuracy.
In order to test the robots behavior, I made a square ring divided in 36 sectors with degrees from 0 to 360. Each sector is equal to 10 degrees.
I also added an indicator from cardboard on the front of the Artist in order to measure the turns.

I used the command drive speed (25, -25) and I found the certain amount of time that is needed for the various angles.
This time is given by the formula: time=Round(angle*14,7778)

The use of the drive_speed command gave me a very good result and accuracy! I have to say that using the drive_goto command, I had some problems......

Lets take a closer look at the drive_speed(a,b) command.
This command can make the robot to go at straight lines when (a=b), or make curves and circles when (a>b).

The calculations for straight lines in curtains distances are very easy as the distances are proportional to the amount of time on the Pause () command.

The question is how can we make certain circles (if we know the radius R of the circle) using the drive_speed (a,b) command? Can we have a formula to calculate the (a) and (b)?
The answer is yes. The remarkable is although (a) and (b) represent ticks per second of left and right wheel, their quotient is independent from encoders ticks and it depends only from the distance (d) between the two wheels of the robot.
So if we want for example to draw a circle with radius R=40cm with the Artist that has d=28,5cm (distance between the two wheels).

We use the Drive_speed(a,b) and we choose for a= 25 (or any other integer).Then the b=a*(2*R-d)/(2*R+d)=25*(2*40-28,5)/(2*40+28,5)=12 . So the right command is : drive_speed(25,12)
Lets see why:

After some tests I verified in practice all the above formulas and I am convinced that we can draw everything using only the drive_speed command.

The next step will be the creation of an ALPHABET for artist or ARLO robots in propeller C!

This thread and the information contained here just keeps getting better and better Nikos - Thanks again for your great documentation and willingness to share!

Ευχαριστώ!

P.S. - Even though I knew this - It is still fascinating to me that "Thank you" in Greek is essentially the same word as Eucharist!

Thank you Whit!
I hope you'll find interest and the next example:

Trying to verify the avove theory and formulas, I tried to draw 10 circles with gradually grow up the radius from 5 cm to 50 cm with step 5.

I found the appropriate drive_speed(a,b) commands, (the first parameter was a=25 and I changed only the b).
and I also found the time for the Pause command in order to complete every circle. And here it is:

Nikos, Is this a hobby or what you do for a living? Either way, you do awesome work.

Thank you Andy,
I am an ICT teacher, but I prefer to see my job as a hobby!.
So Parallax and robotics is a great way to show my students the beauty of programming and algorithms.!

For the next example the only we have to do is to make a copy of the above commands,
and change the position of "a" and "b" variables in every drive_speed(a,b).
Then we'll have the next:

I think it could be an "advanced erco's figure 8 challenge".....

Yes, erco loves it! Awesome job Nikos! Makes me want to try my Trike Bot on a course like that!

In real situations I had not a 100% symmetry as the theoretical drawings......
Maybe because the robot makes first the entire right group of circles, and then the entire left group and not sequential figure 8s

thank you (very much) in Greek is "Efharisto" (poli). I guess you meant the Greek letters resemble "Eucharist" back in #130?

... Not only the letters resemble "Eucharist". The meaning of the Greek "Ευχαριστώ" can be very similar to "Eucharist". Using the adjective "Θεία"=holy before "Ευχαριστώ" they have exactly the same meaning: "Θεία Ευχαριστία"="Eucharist"! (and the sound is also very similar)

Just saw the photo of facebook, but the video is incredible! Great work as always friend!

Your robot is an Artist and so are you.

Thank you Whit,
From a short research about spirals, I found that except from the artistic interest (as drawings), spirals also have an extremely mathematical interest (much more than I initially thought)! Maybe I must spend some more time with them .. (It would be very interesting because all this theory can be applied to the S2 Robot too!). The spiral I made, is a type of Archimedean Spiral but there are many other types of spirals with different mathematic features ..

In order to make an Archimedean Spiral, you must draw sequential semicircles and gradually you must increase the radius in a constant amount.
So the 1st semicircle has radius r=5, the 2nd r=10, the 3rd r=15, the 4rth r=20, the 5th r=25, the 6th r=30 and son on ….
So we must calculate the appropriate “a”, “b” parameters for the Drive_speed(a,b) commands, according the formula from post#128. We must also calculate the time for the “pause” command in order to achieve a semicircle, taking into account that every semicircle is an arc with 180 degrees angle. So using the formula from post#129. we have :

For the double spiral in order to draw the 2nd spiral we write down the same commands as the 1rst spiral but reversely,
and we also change the order between “a” and “b” inside the drive_speed(a,b) commands…

Spirals are great. Makes me want to try some on servo-steered trikebot, except tracing the path might be difficult. It weighs so little that simply dragging a marker might throw off the steering/tracking.

Spirals are great. Makes me want to try some on servo-steered trikebot, except tracing the path might be difficult. It weighs so little that simply dragging a marker might throw off the steering/tracking.

Spirals are great indeed! It is amazing that people from different places of the planet without internet or any type of communication, thousands years ago (like the Greek Archimedes and Indians from Chaco Canyon) had spirals in the center of their research!
Another interesting point is that “Fibonacci spiral” is connected also with the number “Phi” (the golden ratio) that is always in nature.

Some people call that number as the “fingerprint of God”.
In the next posts I’ll try to make a connection between Fibonacci spiral algorithm and Parallax robots

In order to make a Fibonacci spiral using a robot you must draw sequential arcs and not semicircles as the Archimedean spiral.
The radius of each arc must be a number from the Fibonacci sequence 0,1,1,2,3,5,8,13,,21,34,55,89,144, (We start with 0 and 1 and then each subsequent number is the sum of the previous two). The angle of each arc must be 90 degrees.
The only we have to do is to calculate the appropriate a, b for drive_speed(a,b) commands, and time for the Pause commands using the formulas from post #128 and post #129....

Inspired by Nikos "Artist," little brother wanted to get in on the fun. Thanks to Phil's S2 Object - it really wasn't that hard. I did end up going counter-clock-wise, but that is easy to change too!

Bravo and thanks Nikos for the fun idea!

Spin for the S2 is attached also. Use at will! And have fun!

Well done Whit! Now you're just shaming me into doing a spiral with my trike. Should be simple, just drive and slowly increment the steering servo, but I'm swamped right now, it will have to wait a few days.

You guys are having all the fun. Maybe Nikos' spiral challenge is the new figure 8! Certainly a companion challenge.

## Comments

705Thank you Whit !

If you have time put a pen in your S2 upload the next spin code and see the result!

The S2 will draw a Greek dancer dancing "The Evdokia's Zeibekiko" and simultaneously plays the song!

The "Artist" performs the same activity more impresive due to the SD card and the vecho speaker, but the accuracy of the S2 is remarkable!

705The drawing has some improvements: The figure "8" s are symetrical and smaller in order to fit the entire shape in the 2 X2,5m black moquette That I bought for this purpose....

20,194705Thank you Erco!

I displayed the Parallax banner and in a second event (the same day) :

Saturday 5 April 2015, after the 5th student’s digital festival, another festival took place in Patras city.

The “Annual student’s festival”, that is supported mostly from young with strong political interest and political parts against the European Union.

One of my students (Tassos), a politically active student, asked me to present the “Artist” and the “Parallax S2 robot” in this festival.

Although I totally disagree with politics, I accepted this challenge because I believe that robots must be beyond politics and they consist a great way for a better future for young people.

It was a great opportunity to make a contact of that part of youth with robotics and Parallax.

After the Show, “Artist” and S2 robot got the applauses from the audience, and I accepted a lot of questions about Parallax and robots in general. I realized that many graduated student’s had a totally ignorance about robotics because of their only interest in politics!

20,194705Drawings: The last part of the Artists projectThe last part of this project is the drawings. Except from the figure 8s and the flowers( post #106), the robot must be able to make and other shapes like triangles, rectangles, polygons, curves , straight lines and Letters!!!

So it is very important to program it, in order to turning in place with accuracy.

In order to test the robots behavior, I made a square ring divided in 36 sectors with degrees from 0 to 360. Each sector is equal to 10 degrees.

I also added an indicator from cardboard on the front of the Artist in order to measure the turns.

I used the command drive speed (25, -25) and I found the certain amount of time that is needed for the various angles.

This time is given by the formula:

time=Round(angle*14,7778)The use of the

drive_speedcommand gave me a very good result and accuracy! I have to say that using thedrive_gotocommand, I had some problems......705drive_speed(a,b)command.This command can make the robot to go at straight lines when (a=b), or make curves and circles when (a>b).

The calculations for straight lines in curtains distances are very easy as the distances are proportional to the amount of time on the

Pause ()command.The question is how can we make certain circles (if we know the radius R of the circle) using the

drive_speed (a,b)command? Can we have a formula to calculate the(a)and(b)?The answer is yes. The remarkable is although

(a)and(b)represent ticks per second of left and right wheel, their quotient is independent from encoders ticks and it depends only from the distance(d)between the two wheels of the robot.So if we want for example to draw a circle with radius R=40cm with the Artist that has d=28,5cm (distance between the two wheels).

We use the Drive_speed(a,b) and we choose for a= 25 (or any other integer).Then the b=a*(2*R-d)/(2*R+d)=25*(2*40-28,5)/(2*40+28,5)=12 . So the right command is :

drive_speed(25,12)Lets see why:

After some tests I verified in practice all the above formulas and I am convinced that we can draw everything using only the

drive_speedcommand.The next step will be the creation of an ALPHABET for artist or ARLO robots in propeller C!

705The answer is in the next image:

if you use the above formula on your robot the only thing that maybe must change is the constant 59,94.

That 59,94 is the time we put on Pause command after a drive_speed(25,25) in order to make the robot move straight for 1cm

Tip: find the time in order to move the robot straight 1m=100cm and then divide with 100.

You can trust all the above formulas as I have allready tested them.( I can explain if you have any question)

I tried to draw the letters "A" and "B" using the above theory. The letter "B" had curves that were arcs with radius 5 and angle 180

Although I didn't use Pen Up and Pen Down commands I think the result is right.

Any volunteer for the letter's design?

4,190Ευχαριστώ!

P.S. - Even though I knew this - It is still fascinating to me that "Thank you" in Greek is essentially the same word as Eucharist!

705I hope you'll find interest and the next example:

Trying to verify the avove theory and formulas, I tried to draw 10 circles with gradually grow up the radius from 5 cm to 50 cm with step 5.

I found the appropriate drive_speed(a,b) commands, (the first parameter was a=25 and I changed only the b).

and I also found the time for the Pause command in order to complete every circle. And here it is:

The result was exactly as i expected !

4,1903,629705Thank you Andy,

I am an ICT teacher, but I prefer to see my job as a hobby!.

So Parallax and robotics is a great way to show my students the beauty of programming and algorithms.!

For the next example the only we have to do is to make a copy of the above commands,

and change the position of "a" and "b" variables in every drive_speed(a,b).

Then we'll have the next:

I think it could be an "advanced erco's figure 8 challenge".....

4,19020,194BTW Whit, thank you (very much) in Greek is "Efharisto" (poli). I guess you meant the Greek letters resemble "Eucharist" back in #130?

705Maybe because the robot makes first the entire right group of circles, and then the entire left group and not sequential figure 8s

However I had enough accuracy with spirals.....

... Not only the letters resemble "Eucharist". The meaning of the Greek "Ευχαριστώ" can be very similar to "Eucharist". Using the adjective "Θεία"=holy before "Ευχαριστώ" they have exactly the same meaning: "Θεία Ευχαριστία"="Eucharist"! (and the sound is also very similar)

70520,194When the robots come to kill us all, I hope they will play some nice music as you have demonstrated. It's the least they can do.

Great job, Boss!

4,190Your robot is an Artist and so are you.

705Thank you Whit,

From a short research about spirals, I found that except from the artistic interest (as drawings), spirals also have an extremely mathematical interest (much more than I initially thought)! Maybe I must spend some more time with them .. (It would be very interesting because all this theory can be applied to the S2 Robot too!). The spiral I made, is a type of Archimedean Spiral but there are many other types of spirals with different mathematic features ..

705So the 1st semicircle has radius r=5, the 2nd r=10, the 3rd r=15, the 4rth r=20, the 5th r=25, the 6th r=30 and son on ….

So we must calculate the appropriate “a”, “b” parameters for the Drive_speed(a,b) commands, according the formula from post#128. We must also calculate the time for the “pause” command in order to achieve a semicircle, taking into account that every semicircle is an arc with 180 degrees angle. So using the formula from post#129. we have :

For the double spiral in order to draw the 2nd spiral we write down the same commands as the 1rst spiral but reversely,

and we also change the order between “a” and “b” inside the drive_speed(a,b) commands…

A special interest has the " Fibonacci or Golden spiral"....

12,362I am always amazed at your mathematical abilities, and the way that it shows the children how they relate to a direct output.

Excellent work again!

Jim

4,19020,194Of course, I've been a sucker for the magic of spirals since I learned about the sun dagger in Chaco Canyon. Jump to 1:00 at https://www.youtube.com/watch?v=sS73UpIy7zs

705Another interesting point is that “Fibonacci spiral” is connected also with the number “Phi” (the golden ratio) that is always in nature.

Some people call that number as the “fingerprint of God”.

In the next posts I’ll try to make a connection between Fibonacci spiral algorithm and Parallax robots

705The radius of each arc must be a number from the Fibonacci sequence 0,1,1,2,3,5,8,13,,21,34,55,89,144, (We start with 0 and 1 and then each subsequent number is the sum of the previous two). The angle of each arc must be 90 degrees.

The only we have to do is to calculate the appropriate a, b for drive_speed(a,b) commands, and time for the Pause commands using the formulas from post #128 and post #129....

4,190Bravo and thanks Nikos for the fun idea!

Spin for the S2 is attached also. Use at will! And have fun!

Edit: Side by side comparison...

20,194You guys are having all the fun. Maybe Nikos' spiral challenge is the new figure 8! Certainly a companion challenge.

12,36220,194Which type of spiral shall I attempt?

Archimedes, Fibonacci, Logarithmic, Parabolic, or Hyperbolic? http://science.jrank.org/.../6396/Spiral-Types-spirals.html