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Blacklight ravographs
These gizmos draw hypotrochoids just like Spirographs. They also draw hypotrochoids that Spirographs can't. And they draw them with light.
About this creation
Please feel free to look over the images and skip the verbiage.

When I was told that these Spirograph-like LEGOŽ gizmos produce blacklight effects straight out of a rave, I dubbed them "ravographs".



Please bear in mind that ravographic blacklight effects are very hard to capture in video, as most video cameras can't be forced into the required "persistence".

However, the effects are good in person and even better in long-exposure stills like these.



















It's nice to capture the entire hypotrochoid, as you generally would with a Spirograph on paper, but the fragments can have their own charm.





The setup, from front to back: (i) Different black ravograph heads for different effects. (ii) A 24-LED UV-A flashlight serving as portable blacklight. (iii) A motorized base to turn the heads under Power Functions remote control. (iv) A modified Power Functions IR speed control described in detail elsewhere.



Warning! Always wear eye protection when working or playing with high-speed LEGOŽ rotating machinery and keep valuables and bystanders (including pets) a safe distance away -- especially when testing new designs.

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Ravograph head design

Each ravograph head is a basically a single-stage planetary gear train with a long input shaft for the motorized base.





I sometimes drive the planet carrier with a sun gear on the input shaft, as on the right, but it's usually better to omit the sun and couple the input shaft directly to the carrier. (For more on LEGO planetary gear trains, click here.)



As the carrier is turned by hand or motor, the planet gears roll without slip around the 48-tooth "ring" (internal gear) inside the head's large black housing (hard plastic wheel with cleats and flanges, 64712). One of the planets then drives a counter-balanced "baton" with a strongly fluorescent curve "generator" at one or both ends.

NB: All of the heads used in the introductory video had just one generator, and the discussion will assume the same unless otherwise noted.

When the room is darkened, and the blacklight comes on, the brightly fluorescing generator appears to leave a "trail" of light as it traces out a plane curve known as a hypotrochoid. Spirographs draw their hypotrochoids in much the same way, but ravographs can make hypotrochoids that Spirographs can't.

As carrier speed increases, the generator's trail covers a greater portion of the hypotrochoid. The long exposures forced by darkening the room lengthen and brighten the video trails a good bit, but the effect is still better in person.

Here are close-ups of 4 different heads. In the labels, ZR and ZP are the ring and planet tooth counts, respectively, and RG is the distance from the center of the generator to the center of its planet along the baton. As explained below, these key parameters control every aspect of hypotrochoid size and structure.


ZR = 48, ZR = 8, ZP / ZR = 1/6, RG ≅ 12 mm.


ZR = 48, ZR = 12, ZP / ZR = 1/4, RG ≈ 16 mm.


ZR = 48, ZR = 16, ZP / ZR = 1/3, RG ≈ 56 mm.


ZR = 48, ZR = 20, ZP / ZR = 5/12, RG ≈ 30 mm.

Most of these heads run much more smoothly when their carriers are shimmed up 1-2 mm with small metal washers. Many good things come to those who embrace selective impurism.

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Generators, illumination, and contrast

The generators here are mostly 2x2 round bricks and 1x1 cones in trans-neon yellow, as they have axle holes and fluoresce very brightly under the UV-A output of a typical blacklight. The generators below are fluorescing under skylight, which contains a good bit of UV-A here in Denver.



Trans-neon orange parts also work, but they aren't as bright, as seen in these fluorescent spinning tops. Trans-neon green is comparable to trans-neon orange in brightness. Trans-medium blue also fluoresces strongly but less so than these.



Like most blacklights, mine puts out some visible light at blue to violet wavelengths. The contamination isn't bad and even adds a nice effect at times. Ambient light that can't be eliminated (e.g., in exhibition halls) is a much bigger problem, but the shade of a black umbrella sometimes helps.

To maximize generator/background constrast under the blacklight, I made the heads as black as possible, which meant shortening some black axles and harvesting some cheap black bushes from 3L bush pins (details here). After these photos were taken, I covered the motorized base in black as well.

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Hypotrochoid design

The hypotrochoids one can make with a given head are completely determined by 3 head parameters: (i) The pitch radius of the ring gear, RR. (ii) The pitch radius of the planet gear, RP. (iii) The radius of the generator's orbit around its planet, RG.

RG runs along the baton from the center of the planet to the center of the generator. The pitch radius R of any LEGOŽ gear is easily obtained from its tooth count Z via

R = Z / 2,

where R is in millimeters (mm).

All of my ravograph heads have the same RR = 24 mm, as there are no good alternatives to this 48-tooth ring, but each has its own RP and RG.



The ring accommodates LEGOŽ planets with 8, 12, 14, 16, and 20 teeth, while RG can range independently from ~12 mm to well over 96 mm. The maximum RG is limited only by vibration, the baton's ability to resist centrifugal force, and the space available.

Heads with more than 1 generator often have a different RG for each one. Heads with multiple RP values are also possible, but none are shown.



When RGRP, as is usually the case, the hypotrochoid will consist of 3 or more loops with no cusps.



However, if RG = RP, the head will produce a loop-free cusped hypotrochoid known as a hypocycloid.





Spirographs can't make hypocycloids, but I made the close approximations above with a ravograph head with 20-tooth planets and a small cone for a generator.

Together, RR, RP, and RG set the hypotrochoid's overall size. A hypotrochoid is always tangent to an outer bounding circle of radius

Rmax = RR - RP + RG

When RG < RR - RP, it also has an inner bounding circle of radius

Rmin = RR - RP - RG

At 6:13 in the introductory video, I fit the same single-generator head with RG values of increasing length to show the effect on the structure. The consequences for Rmax and Rmin are clear, but the widths of the loops are also affected. The sequence ends when the longest baton flies off at full throttle.

The "degree" of a hypotrochoid is just the number of cusps or loops in the completed figure. The degrees possible with a ravograph are 3, 4, 6, 12, and 24. To predict degree, we start with the planet/ring "radius ratio" given by

ρRP / RR = ZP / ZR,

where ZP and ZR are the respective planet and ring tooth counts. We then rewrite the radius ratio as

ρ = p / d,

where the whole numbers p and d are relative primes. The denominator d gives the degree and the numerator p gives the "period" -- i.e, the number of carrier revolutions needed to close the curve.

For example, when ZP = 20 and ZR = 48,

ρ = ZP / ZR = 20 / 48 = 5 / 12 = p / d.

Hence, all hypotrochoids drawn by this head will have 12 loops or cusps and will take 5 full carrier revolutions to complete, regardless of RG.

The periods possible with a 48-tooth ring and available planet gears are 1, 5, and 7. Hypotrochoids with p > 1 are especially hard to capture on video.

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Motorized base

The ungeared vertical L motor at the heart of the motorized base is good for carrier speeds of up to ~380 RPM under load. The fastest and slowest generators (in the 1/6 and 5/12 ravographs, respectively) revolve around their planets at 6 and 2.4 times carrier speed.







The heavy AA battery box damps out some of the vibrations left after counterbalancing the generator baton.

A "quick-release chuck" (rapid shooter magazine and trigger assembly, 18588c02) driven directly by the L motor takes all the muss and fuss out of exchanging ravograph heads.





The 4 DGB dogs in the yellow head receiver keep the head from spinning.

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Specifications

Overall dimensions:[] mm (LxWxH)
Overall mass:~[] kg excluding controller
Possible ring gears:48-tooth only
Possible planet gears:20, 16, 14, 12, 8 teeth
Possible planet/ring radius ratios:5/12, 1/3, 7/24, 1/4, 1/6
Minimum generator-planet separation:~8 mm
Maximum carrier speed:~380 RPM under load
Maximum generator speeds:2.4 to 6 times carrier speed
Modified LEGOŽ parts:Shortened black axles, bushes harvested from black bush pins
Non-LEGOŽ parts:UV-A flashlight, metal washers used as carrier shims
Credits:Original MOC inspired by the classic Spirograph drawing toy

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Comments

 I like it 
  October 8, 2016
Very nice Jeremy! I tried something different: http://www.moc-pages.com/moc.php/433485 I just saw this today, did you every see it? https://www.flickr.com/photos/53458657@N04/21558803343/in/dateposted/
 I made it 
  September 28, 2016
Quoting Walter Lee just in time for halloween! super cool!
Great idea, Walter!
 I like it 
  September 28, 2016
just in time for halloween! super cool!
 I made it 
  September 23, 2016
Quoting Oliver Becker Marvellousness all around here, Jeremy! Maybe I'm a little late to comment your great entertainment, but there was a little break because of the real work... ;)
Many thanks, Oliver! Never too late to hear from you, my friend. Glad your non-LEGO matters are caught up now. I'm also taking a break from MOCpages to work on some experiments with spinning top physics that I'm posting elsewhere.
 I like it 
  September 19, 2016
Marvellousness all around here, Jeremy! Maybe I'm a little late to comment your great entertainment, but there was a little break because of the real work... ;)
 I made it 
  August 18, 2016
Quoting Nick Barrett Amazing stuff, like your mind never stops.
Thanks, Nick! It has a mind of its own, I'm afraid.
 I like it 
  August 18, 2016
Amazing stuff, like your mind never stops.
 I made it 
  August 12, 2016
Quoting Nerds forprez Mesmerizing Jeremy. This is wonderful stuff. Creative and beautiful.
Many thanks, NFP!
 I made it 
  August 12, 2016
Quoting D H Wow, you never fail to create exceptional technical lego builds! I haven't even started to dive into the details yet but I'm already blown away by the beautiful images you've created using lego!
Deeply flattered, DH!
 I made it 
  August 12, 2016
Quoting Kira Redlof I had a lot fun reading this in-depth write-up, Jeremy, cool idea, well presented :)
Thank you, Kira! I'm especially glad you enjoyed the text.
 I like it 
  August 12, 2016
Wow, you never fail to create exceptional technical lego builds! I haven't even started to dive into the details yet but I'm already blown away by the beautiful images you've created using lego!
 I like it 
  August 12, 2016
I had a lot fun reading this in-depth write-up, Jeremy, cool idea, well presented :)
 I like it 
  August 11, 2016
Mesmerizing Jeremy. This is wonderful stuff. Creative and beautiful.
 I made it 
  August 11, 2016
Quoting Magma ! This is pretty sick. I have to buy myself a blacklight. Even pointing it towards stationary LEGO can make an amazing presentation, but what you did is just next level. Well done.
Many thanks, Magma! You can have a lot of fun with a blacklight flashlight. Lots of LEGO colors turn out to be slightly fluorescent (e.g., trans red and regular orange). They're also handy for finding out where your dog's been going on the carpet when you weren't looking. And I thought mine was such a perfect little angel!
 I made it 
  August 11, 2016
Quoting Geology Joe This is an awesome idea! I always learn so much reading your posts! Have you considered moving the mechanism through the field of view during a long exposure so that it creates a linear, braided trail of lights?
Very kind, Joe, and great idea! I'll have to see if any of the train folks in my LUG would be interested in a collaboration along those lines.
 I made it 
  August 11, 2016
Quoting jds 7777 Wow! Very impressive video! I never thought of putting lego pieces under a backlight before. My only use for backlights as a kid was to read invisible ink messages. I think there should be a disclaimer at the beginning of the video warning people of possible hypnoses. :)
Too kind, JDS! Agree, this kind of motion seems to be captivating. At Denver Brick Fest Live this weekend, they have a darkened tent with a blacklight just for MOCs built around fluorescent parts. Some of them are truly spectacular.
 I made it 
  August 11, 2016
Quoting David Roberts That's fascinating! The film with the lights on is as interesting as the film in the dark. I like watching the various gears move and trying to predict the pattern that will emerge. It's a shame that Lego don't make planetary ring gears in a more practical form.
Thanks, David! Couldn't agree more. A 48-tooth ring gear inside an 8x8 or 9x9 version of the 5x7 Technic frame would be a wonderful addition. So would a 72- or 96-tooth ring.
 I like it 
  August 11, 2016
This is pretty sick. I have to buy myself a blacklight. Even pointing it towards stationary LEGO can make an amazing presentation, but what you did is just next level. Well done.
 I like it 
  August 11, 2016
This is an awesome idea! I always learn so much reading your posts! Have you considered moving the mechanism through the field of view during a long exposure so that it creates a linear, braided trail of lights?
 I like it 
  August 11, 2016
Wow! Very impressive video! I never thought of putting lego pieces under a backlight before. My only use for backlights as a kid was to read invisible ink messages. I think there should be a disclaimer at the beginning of the video warning people of possible hypnoses. :)
 I like it 
  August 11, 2016
That's fascinating! The film with the lights on is as interesting as the film in the dark. I like watching the various gears move and trying to predict the pattern that will emerge. It's a shame that Lego don't make planetary ring gears in a more practical form.
 
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