Astrolabe cases

Two sets of friends are getting married, and as both couples are intellectually curious, I thought an astrolabe would be a nice gift.  But astrolabes alone require some kind of protection... so I decided to make cases for them.

I started from a block of black walnut cut from a tree we had taken down earlier this year.  Since I had previously split it, the wood had been drying all summer in the back yard.

Mostly, the woodworking needed for the boxes was nothing particularly special.  The steps I did were:

1. Rough cut the block of wood into blocks, each about 2 inches larger than my intended final size.  I used a chainsaw for this, and did the work outside.
2. Power planed the blocks so that the edges were square and partially smooth.  Since my power planer makes an enormous mess, I also did this outside.  (The chips from the chainsaw and power planer go in my compost...)
3. Using a large hand crosscut saw, I sliced off the lids of the boxes.  This is a somewhat delicate operation -- even though it requires lots of force -- as you must ensure that the cut is perfectly planar and parallel to (at least one of) the faces of the block.  I don't have a large enough power saw blade, so this is also a manual step!  In all honesty, this is a ripping operation, so I should have used a rip saw... but I don't have one.  My crosscut saw works well enough.
4. I did an initial sanding of the cut surfaces and did a little bit of squaring up of the other faces.
5. I recessed the parts of the box that receive the astrolabe.  This involved tracing the outline of a (disassembled) astrolabe to where the recess needed to go on both the base and the lid of the box.  I then used a router in 1/16" depth increments to cut the recess.  For the base, the recess is stepped since the thumb ring is supported in a more shallow recess than the rest of the astrolabe.  This also gives room for the pointers.  I also recessed the lid.
6. Power belt sanding.  Lots of it!  Starting with 60 grit, I got all faces parallel and square and cleaned off all the cut marks from the saws and planes.  I also rounded the edges where I wanted them round.  Then I repeated the whole process  with 80, 100, 150, and 180 grit.
7. Since I wanted a very fine finish, I then hand sanded the entire box with 220, 320, and 400 grit sandpaper.  Walnut will polish nicely with finer sandpaper if you're planning for an oil finish, but that wasn't necessary for this project.
8. Five coats of polyurethane with plenty of time for drying, and 400 grit hand sanding between each coat.  I made sure that the recesses were left unfinished, since I wanted to adhere a velvet lining.

I wanted to line the inside of the boxes with velvet to protect the astrolabe.  Since the cast acrylic I have been using recently for astrolabes is actually fairly sturdy, a velvet-lined box is surely overkill.  (I did accidentally drop my larger astrolabe, and that shattered the thumb ring.  Since super glue is actually an acrylic, it was a simple matter to fix the crack.  Super glue leaves a mostly invisible joint on acrylic and bonds almost instantly.)

Velvet is a fairly troublesome material for lining.  To make it adhere to a flat surface inside the box, you must support it.  The usual way this is done is to glue the velvet to a sheet of cardboard first, and then glue the cardboard to the box.  Since velvet frays badly, you need to roll the velvet around the back of the cardboard (a second gluing) so that no cut edges show.  Finally, since the boxes have a circular cutout to fit the astrolabe, I had to figure out how to manage that joint.

In the end, I glued the cardboard to the velvet, rolled and glued the edges, but left the circular bottom edge alone.  After the glue dried, I hand stitched the circular bottom edges together.  The result was a stiff velvet "cup" that fits tightly inside the box.

Once the velvet was glued in place, I added hinges and a front clasp.  While hinges and clasps aren't difficult to install, they require precision.  You must be especially careful since you don't want to harm the finish.  I held the box in the vice, but lined it with soft paper towel so that the finish wasn't marred by the vice.  I sharpened (under a microscope) my 1/16" drill bit before starting.  To install the tacks for the clasp, I didn't strike the tacks with the hammer directly, but rather used a recessed punch to ensure that I didn't slip and damage the finish.  When setting the tacks, I also held them in brass tweezers. 

Wooden equatorial sundial

I had a laser cut sundial in our garden, but it was destroyed.  No matter, it didn't work well in autumn.  I made a wooden replacement sundial.  Equatorial sundials are easy to lay out, since all of the hour lines are separated by 15 degrees.  You can quickly draw the plans directly on a piece of wood, as I did, with a compass and protractor.

One small point is that the dial itself will be semicircular.  To ensure that I got everything aligned first, I drilled the center of the circular arc. Even though the center will be cut out later, this way I can sight through the gnomon to ensure that everything is in alignment first.

Then I cut out the pieces,

and traced the hour lines.
 

To ensure that the hour lines are visible, I filed them into the dial.

I also woodburned them so that they are clearly visible. I also traced a vertical line so that I can install it on its mounting pole correctly.

Here is a test fit.

Once I was happy with a tight fit, I installed the gnomon, which is a 1/16" brass wire.

Finally, I put a single nail to join the two pieces.

And installed the completed sundial in the garden!

More power calculations with Woodward's intermittent grasshopper

By joining the count wheel pusher lever of the the Woodward escapement to the escapement trigger, you can make the escapement trigger once per period.  This is the most frequent that the intermittent grasshopper can be triggered.  Triggering every period already happened by accident, but I decided to force it to occur by linking the mechanisms together without using the count wheel.  This way, I could debug the escapement mechanism... and there were indeed problems there.  I think I've resolved them, and this modified mechanism reliably runs until the weight hits the floor.

Currently, the mechanism runs on 1 lb 14 oz, falling 3.9 inches every 10 minutes.  Converting to standard units, this means that the weight falls

3.9 inches * 25.4 mm/inch / (10 min * 60 s/min) = 0.17 mm/s
1 lb 14 oz = 0.85 kg = 8.3 N

Thus the power consumption is 0.17 mm/s * 8.3 N = 1.37 mW.

This is substantially more pessimistic than my previous figure of 0.325 mW averaged over one minute for the count wheel assembly.  This is even with an improvement resulting from a few changes I made.  The pendulum is now hung from two sharp brass points resting in brass cups.

This new hanger ensures a positive positional lock and a definite axis of rotation for the pendulum with substantially less friction than before.

I also made a number of small improvements including reshaping one of the pin wheel pinion teeth, aligning the impulse hook, and stopping the detent's fall a bit earlier.  Finally, I removed every other pin in the pin wheel, which means that the period of the pin wheel is one minute.

Update: 5/13/2019.
By clipping off the tail of the locking detent to make it somewhat more delicately balanced, I can reduce the drive weight by 6.5 oz.  Thus, the power consumption is

3.9 inches * 25.4 mm/inch / (10 min * 60 s/min) * (1.47 lb * 4.43 N/lb) = 1.08 mW.

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.

Two easy projects

Sometimes it's fun just to make simple projects.  Here are two I built this weekend.  A wooden yo-yo

and a sundial for my office.

The sundial is intended to be mounted on the wall, which does not lie in a cardinal direction.  It's therefore what is called "vertical declining" sundial.  My office wall is parallel to 130 degrees, so the gnomon lies off center and the spacing of the hour lines isn't uniform.  I built it according to the description given in

A. Waugh, Sundials: Their Theory and Construction, Dover, 1973.

Hopefully it'll work!

Clock 4 escapement triggers

The next step of constructing Clock 4 is the intermittent triggering mechanism.  Once per minute (one rotation of the count wheel), it triggers the impulse hook to grab one pin of the pin escape wheel.

The impulse hook was cut from the pendulum rod (mostly for aesthetics).  This version has a brass hook rooted in the block and anchored with super glue.  I later replaced this with a stiffer steel one.

The hook is counterweighted by filling the wooden block with lead.  This was sufficient for the brass hook, but not for the steel hook.  I added a screw and nut outrigger counterweight for that.  The steel hook turned out to be a good idea because the brass one was really very pliant, and was getting distorted by each impulse. 

The hook assembly rides on a brass pin on the pendulum.

The impulse hook is triggered by an assembly that sits behind the count wheel.  The straight segment gets grabbed by the count wheel driving pallet (hook) once a minute, and pushes the flat segment against the impulse hook to engage it.

I also made a wood and brass key to wind the clock.

Here is a video the escapement being triggered successfully from the count wheel.  (Hemostats are useful to keep parts in place...)

This has taken the past two days to get it adjusted.  Here is a video of an amusing -- and vexing -- fail mechanism.  Watch to the end... it gets worse!

Next up: the pendulum is indeed not running long enough (as the previous post probably suggests...).  I suspect I do need to increase the weight of the pendulum bob, regardless of the power needs, and figure out how to reduce the friction.  That first requires finding where the friction is...

Clock 4 detent works!

Remaking the detent a few times did the trick.  Each time it worked a little better than the one before, as I flushed out the bugs.  I had a scare where I damaged the gate, but a little super glue seems to be holding it together.  Here is the detent that finally does the job.

The detent properly releases one pin at a time when recoiled by hand with a weight of just about 2.2 lb on the great wheel.

I did not have to modify the pin wheel. It is helpful to have a banking so the detent is held in a convenient position if all the weight is removed.  This also gave a good opportunity for testing the winding mechanism, which does indeed work.

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 pin escape wheel

One of the defining features of Woodward's intermittent grasshopper escapement is the large pin escape wheel.  It is intended to be let off once every minute, so there are sixty pins.  After considering the possibilities for how to index, drill, and make the pins... here is how I proceeded.

Since I print the pattern and glue it to the wood, indexing is "sort of" not a problem.  I started by center punching each pin location.

Since I don't have a drill press, I set up the lathe to index each of the punch locations and drill as well.  The spacing between pins may be accurate enough, because when the drilled holes make their way around to the indexing pin, they're slightly off from the center punch dents.  But it at least this setup ensures that the pins are all the same distance from the center of the wheel.

After initially thinking of steel, then brass pins, I decided that metal pins might be rather loud.  So instead, the pins are made from toothpicks.  They are roughly cut to the right size.

Then they're staked into position...

... the end sticking out the bottom clipped off ...

... and then carefully planed flush with a chisel. 

After all this, I went through and cut off any pins that were longer than the rest, probably to within a 0.5 millimeter or so. 

Here is the escape wheel trial fit in the frame.

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.