Old 09-16-2015, 01:36 AM #1
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Default Mathematics behind Laser Spirograph

I built a laser spirograph and am wondering if anybody can help with the mathematics behind it?

Spirograph -- from Wolfram MathWorld

The above link shows hypotrochoids, which are generated by a fixed point on a circle rolling inside a fixed circle. The various diagrams are exactly what my laser spirograph can make shape wise.

How can I relate the speed of the motors and the angle that the mirrors are tilted at to the hypotrochoid?


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Old 09-16-2015, 04:47 AM #2
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Default Re: Mathematics behind Laser Spirograph

Quote:
Originally Posted by electricity440 View Post
I built a laser spirograph and am wondering if anybody can help with the mathematics behind it?

Spirograph -- from Wolfram MathWorld

The above link shows hypotrochoids, which are generated by a fixed point on a circle rolling inside a fixed circle. The various diagrams are exactly what my laser spirograph can make shape wise.

How can I relate the speed of the motors and the angle that the mirrors are tilted at to the hypotrochoid?
You can do all kinds of stuff, you can vary motor speed independent of each other, pulse the laser, add a 2nd laser, add a 4th spinning mirror, change mirror angles, you will be amazed how much fun it is. But play safe, protect your eyes.
Here's just a few I pulled up, not my best at all.
This is an early basic setup, fan motors are pulse width modulation controlled so I build drivers on a proto board, the blue boxes are multi turn pots to control speed, I should build some multi channel laser drivers but I've been lazy about it, I'm kinda waiting to see how things evolve.







The last one is with a 4th mirror, you have to arrange them creatively so the beans cross over but the shapes can expand and collapse, it's a lot of fun, I even made a portable multi color to project into the tree tops but it was years ago and my cell phone videos are not very good quality, anyway it's a lot of fun experimenting, just always be safe.

DAM...sorry I totally ignored your question. There is the angle your mirror is attached to the motor and then the angle the motor is placed, also the distance between as the shape diverges.

p.s. I can see exactly how that would be drawn with a pencil in a Spirograph wheel/gear, you will need a slow turning and very large third mirror.
Something like the fifth shape on the top line of your chart 1,3 but it has to slowly advance on a third large final output mirror.

1 spinning mirror at attached at an angle makes a circle, with a 2nd mirror you can make the basic shape such as the 5th on the top line of your chart and the 3rd slower turning mirror advances the shape being produced by the 1st and 2nd, but the 3rd mirror will need to be larger as the shape will grow with each spinning mirror added.

Last edited by RedCowboy; 09-16-2015 at 11:55 AM.
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Old 09-16-2015, 02:26 PM #3
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Default Re: Mathematics behind Laser Spirograph

The knowledge and experience of many members on here is fantastic.
Sorry I do not have any help to add electricity440 on this particular subject but I sure do support you in the advancement of knowledge in the arena of lasers
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Old 09-18-2015, 01:15 AM #4
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Default Re: Mathematics behind Laser Spirograph

These things are so called lissajous figures. They basically are exactly what you can draw with a spirograph, but also with simple angled mirrors in the path of a laser.

Whilst very simple in nature they can provide pretty nice effects - nothing compared to what a set of real galvo's can do, but still able to impress some audiences surely.
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Old 09-18-2015, 04:18 AM #5
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Default Re: Mathematics behind Laser Spirograph

Quote:
Originally Posted by Benm View Post
These things are so called lissajous figures. They basically are exactly what you can draw with a spirograph, but also with simple angled mirrors in the path of a laser.

Whilst very simple in nature they can provide pretty nice effects - nothing compared to what a set of real galvo's can do, but still able to impress some audiences surely.
Oh yes Glavos are the way to go, even a cheap ebay show with DMX controller and laptop software is fun.

Here's a old cell phone clip showing what can happen with a 4th spinning mirror, a spirograph can't do this. It's a short clip and low quality, but you can get the idea.



Last edited by RedCowboy; 10-01-2015 at 02:54 AM.
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Old 10-01-2015, 02:25 AM #6
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Default Re: Mathematics behind Laser Spirograph

Harmonograph: A Visual Guide to the Mathematics of Music (Wooden Books): Anthony Ashton: 9780802714091: Amazon.com: Books

Just buy the book, it has most of the ratios plotted.

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