Saturday, January 20, 2018

I've got the government shutdown blues...

I've got the government shutdown blues...  No, not really. :)  If I don't look too hard at the details, I kind of like the idea of the government being shut down – because it means they're spending less money.  Not no money, because the government's idea of “shutdown” is more like “slow down by 3%” than anything a normal person would call shutdown.  But hey, wasting 3% less of my money is better than not doing so!

Anyone under 40 years old or so may not realize that there was a day when the U.S. government never did shut down.  The first one happened in 1980.  They've been coming with increasing frequency in the past few years, as the two political parties play their brinkmanship games.  They're one of the more obvious symptoms of our broken polity, and every time I'm reminded of that (as this morning), I get to pondering about the tiny role that the ideals this country was founded on play in our current federal government.  You'd need a powerful microscope to find an ideal anywhere within a mile of most senators or representatives.  That's very sad, for me, at least, and that's from whence arise my blues this morning...

The past few days I've been hugely enjoying the fruits of Debbie's last baking spree: the most wonderful lemon ricotta cookies (at right).  This batch we're actually keeping, instead of giving them away.  There are a dozen or so left in our freezer.  I'm having two each morning with my tea, so they'll last for a while.  The ricotta makes the cookies moist and soft, while still having a pleasing body.  They are lemony throughout, but there's a dollop of lemon frosting (the off-white stuff) on top of each cookie, and a sprinkle of yellow sugar crystals.  The sweetness is perfect for me: just enough to offset the tang of the lemon, without overpowering it.  They are so good!

We woke up this morning to about 3" of wet, gloppy snow – and we've had another inch since.  The snowfall appears to be petering out, so I'll likely be out plowing and shoveling shortly.  Oh, joy.  :)

Meanwhile, I've been working away on my Sisyphus table software, and I've made some nice progress.  I've got the code in good enough shape now that I've published the GitHub repository for anyone who would like to use it.  I've licensed it under the very permissive MIT license, so should any nut like to incorporate it in another project, they can.  I've still got a lot more that I want to do with it, and no doubt many bugs remain, so that code will be changing.  But anyone who can program and who wants to play with their Sisyphus table is welcome to take it out for a spin.

The photo at right shows my table after an “erase” is almost complete.  If you look very closely at the track visible there, you'll see that it's actually a giant spiral, not a series of concentric circles as you might expect.  The command to make that spiral is very simple:

      0.0 0.0
      -628.3185307179587 1.0

That simple command tells the table to start at 0 radians, 0 distance from the middle, and draw a line to radians, 1.0 distance from the center.  If you're not familiar with radians, I'll make it easy: that many radians is 100 complete circles (one circle equals 2 times pi radians).  The "-" tells it to move the ball counter-clockwise.  A distance of 1.0 from the center just means all the way to the outside edge.  So, in English, that command tells the Sisyphus table to draw a spiral from the center to the outside edge, taking exactly 200 revolutions to do it.

Why did it trace a spiral, and not just a straight line?  Because the Sisyphus table moves the ball using a polar mechanism, not a Cartesian mechanism that most people are familiar with (sometimes called an XY table).  The Sisyphus table has an arm underneath it that can move a magnet (that moves the ball) closer to or further from the table's center, and that arm can be rotated all the way around the center.  That lets the table put the ball anywhere it wants to, but moving the ball in a straight line is an unnatural act for it.  It turns out that the “natural” movement for a polar mechanism is ... a spiral.  More specifically, an arithmetic (or Archimedian) spiral – which is exactly the shape of the spiral on that erase.

I just added the ability for my software to draw circular arcs on the Sisyphus table.  That motion is also an unnatural act for the table, so what I'm really doing is drawing a series of short spirals that differ infinitesimally from an actual circular arc.  The photo at left, below, is the actual result of my first effort on the physical Sisyphus table.  The image at right was generated by my software, emulating the physical table.  This lets me troubleshoot the track generation before I go to the time and trouble of actually drawing it on the table.  To make the trace at left took 9 minutes, 33 seconds.  To make the image at right took 4 seconds.  That's a considerable time savings when iterating during track development!

No comments:

Post a Comment