Thursday, May 30, 2019

Astrolabe upgrade

American University's Design and Build Lab got a new laser cutter.  Since the astrolabe I made before was drawn as a set of SVG files, I figured that it might be nice to make another astrolabe on the laser cutter.  Indeed, the result is beautiful!

This astrolabe is cut from 1/4" black acrylic with a 1/8" clear acrylic rete (star chart).  I etched the rete on the back of the clear acrylic, so there is no visible parallax error.  The pointer is 3d printed PLA. The brass hardware was hand turned on my lathe.  All of the hardware is friction fit with no adhesive used.  This astrolabe is for a fixed latitude (39 degrees North), so the center pin is (essentially) permanent.  The movement is smooth, but tight.  This is a nice improvement over my previous astrolabe, in which the hole in the rete has enlarged over time.

Unfortunately, we had trouble aligning the back.  The horizontal alignment is perfect, but it's vertically shifted by about 2 mm.  This means that the elevation scale runs off the top of the astrolabe. None of the back scales are very useful as a result, even though it is still attractive.  I think the cause of the vertical shift was an alignment key (which doubles as the ring attachment point) that we added to the front layer, but not the back layer.  We attempted to compensate for this difference, but evidently failed.  However, the compass scale on the front can still be used for elevation sighting, although this requires subtracting 90 degrees from the reading to obtain elevation.

Monday, May 13, 2019

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.