Wooden astrolabe

I have wanted an astrolabe for a long time and decided to make one as a small project.  After reading Chaucer's Treatise on the Astrolabe -- which is still a very clear manual for the instrument's use -- I had the plan fixed in my mind.

The finished product works nicely and looks smart.  I can usually measure the time from the stars or sun to within about 10 minutes, and can measure true north within about 5 degrees or so.

As many sources on the internet point out (correctly!) that the astrolabe is a stereographic projection of the sky onto a plane that is tangent to the earth at one of the poles.  For northern hemisphere astrolabes, such as mine, the plane is tangent to the north pole, and the projection point is the south pole.  That makes the north pole (and the north star) the center of the instrument.  Since stereographic projection turns circles on the earth into circles on the projection plane, nearly everything sketched on the astrolabe is also a circle.  For instance, both the equator and the ecliptic, which is the path that the sun appears to move through the sky, are both circles.  Since the ecliptic is almost concentric with the equator, but twisted off the equator by about 23.5 degrees (the tropics!), the ecliptic looks like an offset circle on the astrolabe.

I could do all these projections by geometric constructions, but decided that merely projecting points was easier.  This I did in python, and to keep organized, I chose to design all of the curves and scales in a Jupyter notebook.  The notebook produces SVG files as output that contain the various curves, stars, and scales, all at a fixed scale for printing.  I edited each of the files by hand to add some more difficult annotations or to make aesthetic adjustments.  For instance, the back of the instrument has an equation of time, to which I added some small glosses for "sun fast" and "sun slow" as well as the build date.

The front of the instrument consists of the rete (a simplified star chart), the tympan (a replaceable model of the sky's azimuth and elevation curves for local latitude), and a scale around the outer edge for time and compass directions.  I used this file as the source of my star chart, from which I produced the rete file.

With the rete file in hand, I manually selected the ten brightest stars, and shaped the pointers.  The idea is that the outer two rings go on the body of the instrument, while the rete, proper, starts at the inner two rings.  The picture below is an earlier revision, with somewhat different scales on the rete.  It also contains both front and back pointers.

This earlier revision uses mean solar time, from which the true position of the sun cannot be read directly.  You need to use the equation of time to make this adjustment.  I found that was too error prone.  I prefer to have the front of the astrolabe show the true position of everything, and then correct for mean solar time afterwards if desired. 

I printed two copies of this file, so that I would have clean copies of each for construction.

You need one tympan for each latitude.  This one is for my local latitude.

This file contains the same outer scales as the rete so that the pages can all be scaled the same.  These outer two scales are cut off and disposed, which is why I left some intersections.  The bright red mark is the location of true north, common to all files.

It wasn't too difficult to arrange the lines of constant azimuth and elevation, though I noticed that there is very little documentation about how the "unequal hours" lines are traced.  After playing with the models a bit, I realized that these lines are the horizon line rotated about the local north direction, not rotated about true north. 

The unequal hours aren't particularly in a modern instrument, but were used for reckoning time in Italy until the introduction of weight-driven clocks.  The idea is that day and night are divided into twelve hours of equal length, starting at sunset.  The hours are therefore of unequal length throughout the year.  During the day, the unequal hours can be read from the position of the sun.  At night, the astrolabe is more useful.  By turning the rete so that the stars are oriented correctly, the position of the sun in one of the unequal hours tells you the time.  At least on my instrument, the sketching the unequal hours seemed to occupy unused space in a pleasing way. 

The instrument was built using my usual paper-on-wood scroll saw technique.  I used 1/8" birch plywood for the flat pieces.  The tympan is merely a laminated sheet of paper, so that it is thin and sturdy.  The two pointers were cut from oak. 

Here is the astrolabe disassembled.

The instrument has a brass pin that holds all the parts on the common center (the north pole).  The back pointer has a cutout that sets the pin into place.

This is important because you simultaneously want one edge of the pointer to align with the center of the mounting hole -- so that you can sight across it and then read an elevation on the scale -- and you want the pin there too.  The pin has to fit back into the pointer to give clearance for the sight line.

The front pointer has a similar construction, but I made a small brass button to keep the pin end.  Once the pin is installed, you merely bend the tip of the pin to retain it.  The marks along the front pointer measure declination -- angular distance from the celestial equator.

Finally, I added a thumb ring that sets through a larger pin.  I turned this with a small flourish, and silver soldered the ring closed.

Clock 4 detent issues

I installed a new(er) 1/3 hp 1725 rpm motor on my lathe since the bearings on the old one were dead.  It runs much better than before!

The detent mechanism for Clock 4 uses a gate invented by Philip Woodward (I think).  The detent sits on a pivot near the pin escape wheel.

The detent is fairly long, but just press fit into the frame.

The detent is cut from a small piece of white oak.

Here is the detent after shaping.

There are many issues with the detent, and it doesn't run at the moment:

• The gate is very thin.  I broke two detents already
• Woodward didn't seem to bank his detent, but it looks like I need to since wood has more flexibility than metal
• The catch for holding the pin is very touchy as to how deep it is.  Woodward suggests that it might work as just a small depression, but this caused the pins to jump out.  Too deep, and they can't clear when the escape wheel recoiled... in which case the pins stick.
• The pins of the escape wheel are too inaccurate in their placement
• The pins of the escape wheel are too inaccurate in their vertical alignment
• The pins of the escape wheel are not all the same diameter (because some of them split in the process of being installed).
• The relative positioning of the catch and the gate slot is quite delicate, and there isn't much clearance.
• The counterweight portion of the detent governs how much weight is needed to run the escapement.  This needs to be very light.

A few times, I could feel the escapement "almost working" under my hand, but it wasn't consistent enough to run under a weight.

Clock 4 mounting and clicks

Unlike Clocks 1 and 3, but like Clock 2, I plan to make Clock 4 wall mounted.

 
My wall mounting plans are to use a French cleat, since this makes it easy to remove the clock, and it's sturdy.  I attached a cleat to the back of the clock...

... but it was unstable since the plate is wide and the pendulum is off center.  So to stabilize, I added a small dowel to the back of the plate that grips the bottom of the cleat on the wall.

This means that I'm confined to use a particular size cleat (on the wall), but other dowel locations can be added easily.

The other thing I wanted was for the clicks and click springs to be carved from a single piece of wood.  I tried this on Clock 3 with oak springs, but they were very stiff and eventually broke.  Now I'm trying a pair of walnut springs, each a little lighter than the single oak I used previously. 

They're glued to the drive wheel.  I thought about offsetting them, which would lead to smoother winding, but I had trouble keeping the mechanism stable while setting up the glue. Hopefully they'll stand up to use.

Clock 4 drive assembly

Previously, I haven't made key-wound mechanisms, so Clock 4 is to be driven by a roughly 1" barrel wound with a key.  The drive wheel rides loosely on the barrel arbor, which is (at least for now) friction-locked onto the barrel. 

The barrel arbor has a 1/8" plain pivot that fits a hole in the back plate.  To engage the key, there is a cross drilling for a steel pin.  The drive wheel is supported in a cock screwed onto the back plate.

The drive wheel meshes with a pinion that directly drives the escape wheel. 

The pinion rides on a small arbor that itself screws into the back plate.

I will cut away some of the cock to allow clearance for the escape wheel, which also will carry the minute hand (directly).  I also plan to try Aaron Dodd Crane's daisy wheel motion work to drive the hour hand coaxially.

Clock 3 escapement adjustments

By using the strategy of topping-within-the-frame, I got the escapement wheel for clock 3 round.  That helped a bit.

By filing the foot spring on the detent thinner, I got it so that 2 lb tangential force on the center wheel got the clock to run.  Still way too much.  So I kept filing, and the spring got very delicate.  I didn't break it, but it was no longer stiff enough to stay vertical.  So, time to make a new detent. 

Figuring that detents were delicate, I made two: a spring one like the one I over-thinned, and a pivoted one. The pivoted detent consists of two parts, a pivot, which attaches to the cock, and the detent itself.  The detent has a counterweight instead of a return spring. Here are the parts, with no springs...

... and here is the pivoted detent assembled. 

It wasn't hard, but required a little thought.  The pivoted detent is much easier to adjust, but even a bit too light.  A few tenths of an ounce on the counterweight seemed to help.  But I broke the pivot hole, so I'll need remake it.

As for the rest of the clock, the idea of a 4-second period for a compound pendulum with a small radius is not going to work.  The longest I can get is about 1.5-2 second period with no escapement in place.  So this means the gearing will be all wrong...  Perhaps this clock too will be a timer.

Clock 3 frame and arbors

The frame for clock 3 is intended to be unobtrusive.  It supports the arbors on which most of the wheels spin, except for the center wheel which is supported between two pivots.  I depthed the wheels with the depthing tool and marked their centers directly on the piece of oak that is to become the frame.

I decided to recess the frame like a watch, so that the different wheels are set into the frame to result in a thinner movement.  This ought to keep the center of gravity closer to the wall.  I cut the recesses freehand using a router before cutting the frame.  Although this worked, it wasn't as precise as if I milled it.

After cutting the recesses, I cut the frame out. 

Once cut, I tried the wheels in (no arbors) to fit.  Here are two views.

The detent and the center wheel are supported on two separated cocks attached onto a shelf that mates with the back frame.

The detent cock is set on a threaded rod with a knurled knob that should allow some measure of adjustment once it's installed.

The shelf is supported both by the back frame and two shelf brackets.

Here is the shelf and the wheels, testing for clearance.

The chapter ring is for the minutes only, while the hours are read from a flag attached to the center cock.  Here they are both planned out. 

Both are marked by holes: small holes for the minutes, larger five minute holes.

The hours are marked in binary.

Here are the frame and non-moving parts of the clock being polyurethaned...

The center cock has a steady pin to aid in proper alignment.

The driver arbor consists of two pieces: an inner rod and an outer sleeve with a hole cross-drilled to engage the winding key.

The other arbors are threaded rods, backed with washers to give wheels clearance from the frame.

Scroll saw throat plate

Part of my scroll saw workflow has been to cut wide of the lines and then spend time sanding or filing, because of tearout.  Also, small pinions and the like tended to fall through the throat plate, necessitating hand tools...

I read that a simple solution to this problem is to make a new throat plate for the saw, so that there is only a little hole for the blade.  Once done, it's almost like a new saw!  I could cut much more precisely -- the blade doesn't tend to drift and the tearout is much reduced.  I cut a whole bunch of parts for the chronometer clock...

Clock #3, with a chronometer escapement

The next clock design is progressing!

I wanted this clock to have a chronometer escapement, but I also wanted to rework my design workflow a bit.  Previously, I drew plans in Inkscape, which is straightforward, but doesn't easily manage complex designs.  Additionally, the only gears Inkscape comes with are involute, which I didn't want.  So for the timer, I used an online tool to make epicycloid gears, save them as a DXF and import that into Inkscape.  I thought about scripting something in Inkscape to do this better, but found that awkward.

So instead, I turned to OpenSCAD, which claims to be a "programmer's solid modeler".  This is pretty handy as I can develop libraries for later use and re-use, parameterize everything so that changes are easier (and mostly automated), and I can cut/explode/examine every part of my model without too much effort.

So to start, I wrote a library that builds gears according the British Standard 978 Part 2, taken from tables from the back of "Wheel and Pinion Cutting in Horology".  Note: I had to make use of some additional calculations from Swiss standard NIHS 20-10 in order to get some of the curves to match up properly, the description in BS 978 is slightly underspecified!  Now, I can have consistent gear profiles throughout the design.

I then spent the next few months (starting in May 2016) designing a clock movement, working sporadically.  After getting the chronometer detent and escape wheel pitched correctly -- animations were very helpful -- I got the rest of the movement in order.  I'll design the frame later, probably using the new depthing tool I made for the purpose to pitch the wheels.

The train is intended to be mounted on the wall or in standing case, and is weight driven.  It is built as follows:

• Balance wheel period: 4 s (yes, slow, but that would be kind of mesmerizing...)
• Escape wheel: 15 teeth and advances one tooth each period
• Escape pinion: 8 teeth
• Fourth wheel: 48 teeth
• Fourth pinion: 7 teeth
• Center wheel: 70 teeth
• Center pinion: 8 teeth
• Drive wheel: 80 teeth
• Drive pulley: 2 in diameter

Based on this, the clock should run about 4 days with 60 inches of cable.

As you probably can see in the diagram, I decided to try for a non-standard motion work.  It appears in Daniels' "Watchmaking" on page 173 (not an obvious location, at least for me), and also here, where the author notes that Daniels is a but uncharacteristically thin on details.  Indeed, I agree!  I had to do some side calculations to figure out how to pitch each of the components.  Fortunately, those calculations are now enshrined in my OpenSCAD model, so I don't have to worry about them again, even if I change something!

Now, on to building. The first task was to convince OpenSCAD that I wanted flat plans, not a solid model.  I guess a solid model would be better for 3d printing, which seems like a good idea for later, but I want this clock made from wood!  Fortunately, it was an easy matter to explode the parts all onto the xy-plane and cut them all through.  OpenSCAD exports to DXF, which I did, and then imported that into LibreCAD.  From there, I separated out the different parts into named blocks, and printed them all out onto paper.

My previous clocks have been built from 1/2" birch plywood, which is nice and solid.  However, it feels too heavy, especially for something so dignified as a chronometer, so I am trying 1/8" birch plywood.  Surely this cuts much more quickly, but it is also much more delicate.

I'm also trying a different workflow on the saw.  I am rough cutting the wheels with a 34 tpi spiral blade, and then using a scroll sander to do close-in sanding.   It's not fast by any means (the 80 tooth drive wheel above is only partly finished!), but it seems to give accurate work.  At least, it seems to be much more accurate than my previous work, which required many hours afterward with a file.  This clock will probably get its share of filing as well...  Lots of people have mentioned scroll sanders as existing, but since I don't have a fine belt sander it's quite nice.  I also am doing the work under a 2.5x magnifier and a bright light, so that helps too.

For later reference, it looks like I can cut wheels whose teeth have module 2.0 on the scroll saw.  Anything smaller is too fine!  Fortunately my OpenSCAD model is parametric in the module...

Timer is finished!

I made a number of finishing touches to the gravity escapement timer.  It now runs reliably!
First, I turned a thicker barrel on the lathe

Using a square file, I cut a keyway to engage with the metal teeth on the existing barrel.

Here's the finished barrel, ready for installation...

...and here it is installed.

Many of the wheels weren't running smoothly.  To find where to file, I used a pencil to mark the pinion teeth...

... which transfered to the driving wheel.  This could be filed down as needed.

Quite accidentally, I made the pinion teeth an integer multiple of their driving wheel teeth.  This made debugging easier!  Because I found certain pairs of teeth consistently binding.  I marked them like so

which allowed me to track down the problems! 
 I made a 4 oz pendulum bob from two halves that friction fit to the pendulum. 

The excess screws are for weight!

 
It's worth noting setting that a gravity escapement in beat is quite a bit more delicate than I expected.  Here's a picture of the timer in action...

And a link to a video!