DIY Moon Phase Dial

[Gina]

I have often wanted to know the phase of the moon when deciding astro matters but never used anything but computer software or the old eyeball of the sky.  I've often though it would be nice to have a moon phase display in my living room maybe added to a DIY analogue clock.  I know I could buy a clock but much more fun to make one   And the seemingly endless bad weather for anything astro or even outdoor jobs on observatories is giving me a "grasshopper mind" or maybe I should be kinder to myself and say encouraging lateral thinking

Of course nothing natural is convenient for us "mere mortals" and this applies well to the period of the moon wth respect to the earth's rotation and

our common clocks!

To quote from GEAR PATROL : The Moonphase Watch, Explained

Behind the dial of a typical moonphase watch is a disc with two identical moons on it. This disc rotates one complete cycle every twenty-nine and a half days, with the waxing and waning face of the moon accounted for by the curved edges of the dial aperture. The moon disc is driven by a 59-tooth gear that is advanced one notch by a mechanical finger every 24 hours, thus corresponding to one full rotation for the entire lunar cycle — almost.

In reality, the moon isn’t this cooperative. The true lunar cycle lasts 29 days, 12 hours and 44 minutes, or 29.53 days. While this accuracy is good enough for the average person, watchmakers are a precise lot and not content with rounding up or down. Being off by .03 days per month means that the entire moonphase cycle will be off by one full day every two years, seven and a half months. To overcome the discrepancy between the measured lunar cycle and the actual moon phases, a more sophisticated mechanism was developed that incorporates a 135-tooth gear to drive the moon disc. This improvement increases the accuracy of the movement so that the moonphase complication will only be off by a day once every 122 years, meaning that your grandson might need to do some adjustment, hopefully remembering your generosity when he does.

Further Googling has unearthed the following quote :-

They use 14,16:32:135, where the 32-tooth gear is an idler between the first shaft and the 135-tooth wheel on the edge of the two-disk lunar phase display. The 14-tooth gear is a ratchet which is advanced one tooth twice per day, thus turning at 1/7th of a turn per day

If I understand this correctly the 14 tooth rotates at 7 days per revolution and the ratio from that is 16:135 with the 32t idler just reversing the direction of rotation.  I calculate the rotation of the 135t gear as 7 x 135 / 16 days = 59.0625 and with the moon phase dial having two moons this means 29.53125 days per moon cycle.  That seems pretty accurate to me and not too difficult to implement

[Gina]

I don't think it's possible to represent the moon's phase with visual accuracy.  The curve of the terminator changes from a half circle at "new" and "old" moon to a straight line at half-moon ie. first and last quarter, other than by having separate pictures for each phase but I would prefer a continuous display even if it's not quite right.

Here are a few examples of moon phase dials - they all use the same principle.

[Gina]

A couple of examples of the moon phase disc used in clocks.  I prefer the first as might be expected but I'll probably use either something quite plain or a pair of prints from an image of the real moon.

[Stub Mandrel]

You can use a rotating ball painted black on one half to get a more accurate representation.

Some related but eccentric discussion on moon phase gearing half way down this page.

[Gina]

Thank you   I did come across a three dimensional moon phase display but using a rotating shield in front of a ball representing the moon.  This will only work correctly if viewed from the front - and deviation from straight in fromt produced the same error in moon phase angle.  I think this might work though as I will generally view the clock from my settee with a viewing angle close to 90° to the wall I plan to have the clock on.  I could 3D print two hemispheres, one in black and one in white and glue them together then put them on a vertical shaft driven from the clock mechanism.

That link shows another variation on gearing for moon phase   Accurate enough.  I'll see which gear set works out most convenient.  I shan't be using the crude and inaccurate 59 tooth ratchet wheel used in older long case clocks

[Gina]

I think I like the idea of a hemispherically coloured globe on a shaft.  The shaft will need to rotate once every 29.53 days so another factor of two to go in the gear train.  Also since the main clock gear shafts will be horizontal and the globe shaft vertical I shall want a pair of bevel gears to translate the motion.  I have 3D printed bevel gears in the past so no problem there.  OTOH there may be no need if I were to use the ratchet and paul differently - I could have the moon phase gear train horizontal.

I plan to add the moon phase display to a 3D printed wall clock and calendar so I will already have a 7 day motion driving the Day of Week dial (or other display).  So this will just need an 32:135 gear ratio to the moon phase shaft.  It was 16:135 for the two moon disc so the DoW gear now wants 32 teeth.  However, a gear with 135 teeth would need to be pretty big to get a decent tooth spacing for 3D printing (mod 1 is about the limit giving a diameter of just over 135mm - larger teeth are preferred making the gear even bigger).  I guess the gear could be on a horizontal axis like the clock gears and then use a separate pair of bevel gears with a 1:1 ratio.

An alternative would be the gear train mentioned in the link in post  #4  above.  This uses two pairs of gears from the DoW shaft rather than one with a slight error but it's only one day in 122 years - I can live with that

30:90,32:90, approximates the synodic month as 29.53125 days. The 30-tooth wheel is on the day-of-the-week shaft which is incremented once a day at local midnight by a ratchet, thus turning at 1/7th of a turn per day. The second 90-tooth wheel is on the edge of the lunar display disk, and turns at 1/59.0625th of a turn per day, producing an error of 1 day in 122 years.

This boils down to 1:3 and 16:45 to drive the standard twin moon disc so it will want changing to 1:3 and 32:45.  I can cover these ratios easily using teeth of mod 1.5 to mod 3, a good size for 3D printing.

[Stub Mandrel]

Hmm.. I'm looking for excuses to get a 3D printer - perhaps I need an Antikythera mechanism...

[Gina]

Perhaps you do   But there are dozens of things you can print out of plastic with astro uses.  Apart from gears and brackets

[Gina]

Looks like I shall be combining a clock with perpetual calendar with a moon phase display.  But no, I don't think I'll extend it to a planetarium display on the ceiling   OTOH....

Since this clock/calendar will be going on the living room wall where space is limited it will not have a pendulum nor be weight driven - I shall drive it from a small stepper motor run from an Arduino.  Nor will it be as big as my Giant Wall Clock.  But most of it will be 3D printed.  I think I shall have a sweep second hand so there will be three motions carried by concentric shafts - an inner one probably of stainless steel and the outer two of printed plastic.  It will probably have a spur gear reduction from the stepper motor to the seconds shaft.  Then 60:1 gears to the minutes shaft and 12:1 to the hours.  These will be accomplished with one intermediate gear for each with gear ratios of 6:1 and 10:1 seconds to minutes, and 3:1 and 4:1 for minutes to hours.

For the calendar and moon phase, there will be a further 2:1 step down from the hours shaft to provide a days shaft which will drive the DoW with a ratchet.  From that gear ratios of 3:1 and 32:45 will drive the moon globe shaft. 

I have yet to decide how I shall display the DoW and date.  The former could be a dial and pointer/hand or a drum behind a rectangular opening, the drum being labelled with MON, TUE, WED etc.  I don't fancy a dial type Day of Month display - far too difficult to read from a distance so that will probably be digits.  For the Month, a dial might be just about alright but a 12 faced drum with the months on in text would be nicer.  Unfortunately, a duodeconal drum would be pretty darn big so something else would be better.  But NO I don't want an LCD display.  OK I know I'm using an Arduino for the clock drive but I would prefer the display to be less electronic - more rustic

I need to get thinking about the calendar display issue.  The clock will be the standard analogue with dial and hands and (as I said) I think the moon phase with a two colour globe.  Now where's my "Heath-Robinson Hat"? 

[Garethr]

Hi Gina,

I have this in the Obsy or a version of showing time temp and moon phase.

Using you ability to manufacture cogs and gears would this work as a simple represntation of the moon phase

http://www.firstlightoptics.com/moon-phase-clocks/moon-phase-clock.html

Gareth 

[Gina]

Hi Gareth, yes I could do that but I decided I didn't really like it, but thanks for the suggestion   The hand would be driven from the moon phase shaft the same as the globe but without needing bevel gears.

I'm planning to have temperature, humidity and wind speed displays alongside the clock but I need to finish my weather station first.

[Garethr]

Sorry Gina,

My bad. Our posts crossed and when I read your plans I realised we were back on another "Gina" project.

Far to simple a suggestion I should have realised. Looking forward to seeing the plans and build develop

Gareth

[Gina]

Thank you Gareth

[Gina]

I have designed a 100mm diameter hemisphere in SketchUp and now printing it.  One of these in white and the other in black will be glued together to form the moon globe.  Then an axle will be fed through the hole.

[Gina]

Here are sme photos of the print using my little UP! Plus 2 3D printer.  Specially set to print shell only and using transparent ABS filament.  The white filament jams in the extruder (this printer is very fussy about filament).

[Stu]

Looks a very impressive and accurate hemisphere Gina, can't be an easy thing to print.

Just out of interest, what caused the change in colour/opacity towards the top?

[Spikey]

This looks fascinating Gina, I'm looking forward to seeing the results.

[Gina]

Looks a very impressive and accurate hemisphere Gina, can't be an easy thing to print.

Just out of interest, what caused the change in colour/opacity towards the top?

Thank you   I was tempting fate by printing a hemisphere with shell only ie. no support for the inside top where the angle is approaching horizontal.  In fact the very top is horizontal.  But the UP Plus 2 is an excellent little printer.

As the angle from vertical increases the overhang increases and reaches a point where the filament threads no longer bond well to their neighbours.  This means the plastic is no longer homogenous and turns translucent to opaque.

[Gina]

I have now printed the black hemisphere.  Actually, looking at the results, I've realised that the black half is not really necessary.  The flat side of the white hemisphere could be painted matt black and presented in front of a matt black background.  OTOH there is no such thing as zero reflection from any black surface and the illusion will be spoilt in a good light.  I thibk I might paint the black hemisphere with matt black paint.  As for the white one, I could paint this white or I could print a real white one with white filament on my Titan printer ot Pilot when I get that going again).

[Starlight 1]

 Only just seen this one, What will you think of next Gina.

[Gina]

Now to the clock design.  As mentioned above the clock will be driven from a small stepper motor controlled by an Arduino to provide accurate timekeeping.  The stepper motor will either drive the seconds shaft directly or via a pair of gears.  To make construction simpler, I propose to have the clock gears on two axles - the main hours, minutes and seconds concentric shafts and a second axle for the intermediate gears.  From some juggling with figures, I plan to space the axles at 120mm.  This will fit in well with the printing size of the UP Plus 2 printer, currently the highest precision 3D printer I have.

The 3:1 & 4:1 minutes to hours gear ratios fit perfectly with this with gear teeth of mod 2 but the seconds to minutes ratios of 6:1 and 10:1 will need fractional mod figures.  This is no great problem - just non-integral arithmetic.  With the Involute Gear add-on in SketchUp dealing with Pitch Radius rather than diameter the sum of radii of each gear pair will have to add up to 60mm so that the gears fit.  I have worked out all the dimensions and now present them in a table.  I shall want a Day shaft too, for driving the Day of Week display and moon phase gear train, this can be on  the intermediate gear axle so that adds a 2:1 ratio as well as the usual clock ones.

[Gina]

Made a mistake above.  The axles are separated by the sum of the radii of the gears NOT the diameters so the axles will be 60mm apart rather than 120mm.

[Gina]

This exploded diagram shows the gear train from seconds shaft to once-per-day gear.  The gears are shown as discs but with diameters to scale.

[Stub Mandrel]

If you want to do gears google 'Gearotic'.

[Gina]

I'll think about the calendar part later but now to the moon phase drive.

From the DoW shaft which rotates once per week, ratios of 1:3 and 32:45 will drive the moon globe shaft.

So we want to start with a shaft rotating once per week which is 1:7 from the once per day gear and then gear that down by 1:3 and 32:45.  Alternatively, the hour shaft could have a paul driving a ratchet wheel with 14 teeth and then have gearing to the moon phase shaft.  This could achieve two operations in one go viz. step down the shaft rotation speed and cahnge the rotation from horizontal to vertical.