The Smell of Molten Projects in the Morning

Ed Nisley's Blog: Shop notes, electronics, firmware, machinery, 3D printing, laser cuttery, and curiosities. Contents: 100% human thinking, 0% AI slop.

Category: Software

General-purpose computers doing something specific

  • MPCNC: Z Height Probe

    A little support pillar makes a printable holder for a small tactile pushbutton:

    Z Axis Height Probe - solid model
    Z Axis Height Probe – solid model

    A(n) 0-80 brass washer epoxied atop the butt end of a P100-B1 pogo pin keeps the pin from falling out and provides a flat button pusher:

    MPCNC - Simple Z probe - push plate
    MPCNC – Simple Z probe – push plate

    With the epoxy mostly cured, ease the pin off the tape, flip the whole affair over, shove the switch into position, realign vertically with point down, then let the epoxy finish curing with the washer held in place against the switch to ensure good alignment:

    MPCNC - Simple Z probe - epoxy curing
    MPCNC – Simple Z probe – epoxy curing

    The brass tube ID is a sloppy fit around the pogo pin, but it’s also many pin diameters long and the position error isn’t worth worrying about.

    Solder a cable, clamp it in the pen holder, attach to tool holder:

    MPCNC - Simple Z probe - installed
    MPCNC – Simple Z probe – installed

    The pogo pin provides half a dozen millimeters of compliance,  letting the initial probe speed be much higher than the tactile pushbutton’s overshoot could survive, after which a low-speed probe produces a consistent result.

    Unleashing bCNC’s Autolevel probe cycle:

    MPCNC - Z-probing glass plate
    MPCNC – Z-probing glass plate

    Although the picture shows the MPCNC probing a glass plate, here’s the first height map taken from the bare workbench top with 100 mm grid spacing:

    ProbeArray-100-2018-01-04
    ProbeArray-100-2018-01-04

    The ridge along the right side comes from a visible irregularity in the wood grain, so the numbers actually represent a physical reality.

    Doing it with a 50 mm grid after re-probing the Z=0 level:

    ProbeArray-50-2018-01-04
    ProbeArray-50-2018-01-04

    Eyeballometrically, the second plot is 0.2 mm higher than the first, but this requires a bit more study.

    All in all, not bad for a first pass.

     

     

  • MPCNC: Pen Holder Crunch

    A few tweaks to the Customizable MPCNC Mount for Round Tools produces a Sakura Micron pen holder:

    MPCNC - Sakura Pen Holder - Slic3r preview
    MPCNC – Sakura Pen Holder – Slic3r preview

    The pen body seats atop the holder, with its narrower snout inside the clamp, giving positive control of the point position:

    MPCNC - Sakura in pen adapter
    MPCNC – Sakura in pen adapter

    Unfortunately, should one forget to zero the pen tip to the paper surface before starting a plot, Bad Things happen to good tips:

    MPCNC - Sakura pen - crushed tip
    MPCNC – Sakura pen – crushed tip

    The holder really needs at least a few millimeters of compliance, as a fiber-tip pen makes a fairly delicate tool not intended for applying much force at all to anything.

    But the holder might make a Z axis probe …

  • MPCNC: Rail Height Measurements and Plot Effects

    After once again figuring out how to read a vernier height gage, I measured the height of each end of the MPCNC rails:

    Brown and Sharpe 585 Height Gage
    Brown and Sharpe 585 Height Gage

    The process:

    • Position the gage near the end of the gantry’s travel
    • Twiddle the knurled ring to lower the probe (a.k.a. lathe bit) until …
    • It firmly captures the paper slip, then …
    • Twiddle the ring the other way until …
    • The paper barely moves
    • Read the vernier and take a picture

    So the numbers come out one paper thickness higher than the actual rail height; subtract 0.1 mm = 4 mil to get the true height:

    MPCNC Rail Height - 2017-12-23
    MPCNC Rail Height – 2017-12-23

    In round numbers, the difference is under 0.3 mm along each rail.

    The outer numbers on the lower sketch show the difference between each reading and the lowest value along that axis: the left rear corner is (roughly) 0.5 mm higher than the right front. The numbers inside the square give the additional height, rounded to sensible values, required to raise the low corners.

    Which means you can’t plot at, say, Z=-0.2 mm to reduce the pen loading, because the pen doesn’t uniformly touch the paper across the entire plot:

    MPCNC - Unlevel Z -0.2 plot
    MPCNC – Unlevel Z -0.2 plot

    These images have been perspective & aspect ratio corrected, then ruthlessly contrast-stretched to make the traces visible; the lighting isn’t that awful in person!

    With the plot at Z=-0.2, the legends toward the front came out OK, but they’re missing along the far edge. The Spirograph traces go completely missing toward the left rear as the pen rises away from the paper, although I think we’re also seeing some ripples in the paper sheet.

    Although such a small error probably makes no difference to a wood router, let’s see what we can do.

    Manually editing the G-Code to put successive traces at 0.1 mm increments from Z=-0.3 to Z=-0.6 mm, then replotting on the same piece of paper, shows the problem a bit better:

    MPCNC - Unlevel plot - multiple Z
    MPCNC – Unlevel plot – multiple Z

    All of the legends remain at Z=-0.2, because I wasn’t up for editing every pen-down command.

    Even at Z=-0.6 mm, the pen doesn’t quite touch in the left rear corner. Previously, I’d been plotting at a nice, round Z=-1.0 mm, which worked fine. I didn’t run any tests below Z=-0.6, but I think Z=-0.8 would draw a complete plot.

    That agrees reasonably well with the height gage measurements.

    It’s obviously impossible to re-level the rails by dinking around with the corner post lengths, because I can’t move the EMT in precise increments and it’d never stay in that position anyway. Instead, I should slide shims under the three lowest corner feet to raise them enough to match the left rear corner.

  • MPCNC: Plotter Pen Holder Spring Constant

    Watching the MPCNC plot Spirograph patterns led me to wonder about how much force the printed drag knife holder applies to the pen:

    Spirograph - liquid ink pen - detail
    Spirograph – liquid ink pen – detail

    The HP 7475A plotter spec calls for 19 g = 0.67 oz of downward force on the pen, so, in an ideal world, one might want to use one’s collection of aging plotter pens in a similar manner.

    Plotter pen, meet digital scale:

    MPCNC - Plotter pen force test
    MPCNC – Plotter pen force test

    Stepping the pen downward in 0.1 mm increments produced a set of numbers and a tidy linear fit graph:

    MPCNC Plotter Pen Holder - Spring Constant
    MPCNC Plotter Pen Holder – Spring Constant

    I hereby swear I’m not making things up: the spring constant really is a nice, round 100 g/mm!

    I set plot_z = -1.0 in the GCMC program, with Z=0.5 touched off atop a defunct ID card on the paper surface to compensate for any tabletop warp / bow / misalignment, plus any errors from the tool length probe. An eyeballometric scan against a straightedge shows pretty nearly no misalignment, which means the holder mashes the pen against the paper with about 100 g of force, five times the HP spec.

    A distinct case of pen abuse rears its ugly head.

    It’s time to conjure a height probe for the tool holder.

  • Spirograph Random Numbers: What Are The Odds?

    The GCMC Spirograph Generator program chooses parameters using pseudo-random numbers based on a seed fed in from the Bash script, so I was surprised to see two plots overlap exactly:

    Overlaid pattern - G-Code simulator
    Overlaid pattern – G-Code simulator

    The two overlapping traces are the 15 inward-pointing wedges around the central rosette.

    The first one:

    (PRNG seed: 38140045)
    (Paper size: [16.50in,14in])
    (PlotSize: [15.50in,13.00in])
    (Stator 3: 150)
    (Rotor  4: 40)
    (GCD: 10)
    (Offset: -0.94)
    (Dia ratio: -0.27)
    (Lobes: 15)
    (Turns: 4)
    (Plot scale: [5.11in,4.29in])
    (Tool change: 1)
    T1
    M6
    

    The second one:

    (PRNG seed: 74359295)
    (Paper size: [16.50in,14in])
    (PlotSize: [15.50in,13.00in])
    (Stator 3: 150)
    (Rotor  4: 40)
    (GCD: 10)
    (Offset: -0.93)
    (Dia ratio: -0.27)
    (Lobes: 15)
    (Turns: 4)
    (Plot scale: [5.12in,4.30in])
    (Tool change: 3)
    T3
    M6
    

    The Offset isn’t quite the same, but the pen width covers up the difference.

    With only four Stators and 17 Rotors, the probability of picking the same pair works out to 0.25 × 0.059 = 1.4%. You can sometimes get the same number of Lobes and Turns from several different Stator + Rotor combinations, but these were exact matchs with the same indices.

    The Pen Offset within the Rotor comes from a fraction computed with ten bit resolution, so each Offset value represents slightly under 0.1% of the choices. If any four adjacent values look about the same, then it’s only eight bits of resolution and each represents 0.4%.

    The Rotor and Stator set the Diameter ratio, but the sign comes from what’s basically a coin flip based on the sign of a fraction drawn from 256 possibilities; call it 50%.

    Overall, you’re looking at a probability of 28 ppm = 0.0028%, so I (uh, probably) won’t see another overlay for a while …

    I don’t know how to factor the PRNG sequence into those numbers, although it surely affects the probability. In this case, two different seeds produced nearly the same sequence of output values, within the resolution of my hack-job calculations.

    Whatever. It’s good enough for my simple purposes!

  • MPCNC: Spirograph Generator with Tool Changes

    An improved version of my GCMC Spirograph pattern generator, now with better annotation and tool changes:

    Spirograph pattern - overview
    Spirograph pattern – overview

    The GCMC code sets the stator and rotor gear tooth counts, the rotor diameter, and the pen offset using a pseudo-random number generator. This requires randomizing the PRNG seed, which I do in the calling script with the nanosecond of the current second: rnd=$(date +%N).

    The G-Code file name also comes from the timestamp:

    ts=$(date +%Y%m%d-%H%M%S)
    fn='Spiro_'${ts}'.ngc'
    # blank line to make the underscore visible
    

    Which means you must call the Bash script slowly to generate a pile o’ plots:

    for i in {1..60} ; do sh /mnt/bulkdata/Project\ Files/Mostly\ Printed\ CNC/Patterns/spiro.sh ; sleep 1 ; done
    

    Sift through the heap with drag-n-drop action using an online G-Code previewer. There seems no clean way to convert G-Code to a bitmap on the command line, although you can do it manually, of course.

    The GCMC program spits out the G-code for one plot at a time, so the Bash script calls it four times to fill a sheet of paper with random patterns:

    for p in $(seq 4)
    do
      rnd=$(date +%N)
      gcmc -D Pen=$p -D $Paper -D PRNG_Seed=$rnd $Flags $LibPath -q "$Spirograph" >> $fn
    done
    

    The -q parameter tells GCMC to not include the prolog and epilog files, because the calling script glues those onto the lump of G-Code for all four plots.

    The -D Pen=$p parameter tells the GCMC program which “tool” to select with a Tn M6 tool change command before starting the plot. Although plotter pens have a well-defined position in the holder and a pretty nearly constant length, you must have a tool length probe installed and configured:

    MPCNC Tool Length Probe - Plotter Pen
    MPCNC Tool Length Probe – Plotter Pen

    Set the overall sheet size in inches or millimeters to get a plot centered in the middle of the page with half-inch margins all around:

    Paper='PaperSize=[16.5in,14in]
    

    With all that in hand, those good old black ceramic-tip pens give impeccable results:

    Spirograph pattern - black ceramic pen - detail
    Spirograph pattern – black ceramic pen – detail

    The surviving ones, anyhow. I must apply my collection of Sakura Micron pens to this task.

    The other three colors come from fiber pens with reasonably good tips:

    Spirograph pattern - central details
    Spirograph pattern – central details

    They’re a lot like diatoms: all different and all alike.

    The GCMC and Bash source code as a GitHub Gist:

    # Spirograph G-Code Generator
    # Ed Nisley KE4ZNU – December 2017
    Paper='PaperSize=[16.5in,14in]'
    Flags="-P 2"
    LibPath="-I /opt/gcmc/library"
    Spirograph='/mnt/bulkdata/Project Files/Mostly Printed CNC/Patterns/Spirograph.gcmc'
    Prolog="/home/ed/.config/gcmc/prolog.gcmc"
    Epilog="/home/ed/.config/gcmc/epilog.gcmc"
    ts=$(date +%Y%m%d-%H%M%S)
    fn='Spiro_'${ts}'.ngc'
    echo Output: $fn
    rm -f $fn
    echo "(File: "$fn")" > $fn
    cat $Prolog >> $fn
    for p in $(seq 4)
    do
    rnd=$(date +%N)
    gcmc -D Pen=$p -D $Paper -D PRNG_Seed=$rnd $Flags $LibPath -q "$Spirograph" >> $fn
    done
    cat $Epilog >> $fn
    view raw spiro.sh hosted with ❤ by GitHub
    // Spirograph simulator for MPCNC used as plotter
    // Ed Nisley KE4ZNU – 2017-12-23
    // Spirograph equations:
    // https://en.wikipedia.org/wiki/Spirograph
    // Loosely based on GCMC cycloids.gcmc demo:
    // https://gitlab.com/gcmc/gcmc/tree/master/example/cycloids.gcmc
    // Required command line parameters:
    // -D Pen=n pen selection for tool change and legend position
    // -D PaperSize=[x,y] overall sheet size: [17in,11in]
    // -D PRNG_Seed=i non-zero random number seed
    include("tracepath.inc.gcmc");
    include("engrave.inc.gcmc");
    //—–
    // Greatest Common Divisor
    // https://en.wikipedia.org/wiki/Greatest_common_divisor#Using_Euclid's_algorithm
    // Inputs = integers without units
    function gcd(a,b) {
    local d=0;
    if (!isnone(a) || isfloat(a) || !isnone(b) || isfloat(b)) {
    warning("Values must be dimensionless integers");
    }
    while (!((a | b) & 1)) { // remove and tally common factors of two
    a >>= 1;
    b >>= 1;
    d++;
    }
    while (a != b) {
    if (!(a & 1)) {a >>= 1;} // discard non-common factor of 2
    elif (!(b & 1)) {b >>= 1;} // … likewise
    elif (a > b) {a = (a – b) >> 1;} // gcd(a,b) also divides a-b
    else {b = (b – a) >> 1;} // … likewise
    }
    local GCD = a*(1 << d); // form gcd
    // message("GCD: ",GCD);
    return GCD;
    }
    //—–
    // Max and min functions
    function max(x,y) {
    return (x > y) ? x : y;
    }
    function min(x,y) {
    return (x < y) ? x : y;
    }
    //—–
    // Pseudo-random number generator
    // Based on xorshift:
    // https://en.wikipedia.org/wiki/Xorshift
    // http://www.jstatsoft.org/v08/i14/paper
    // Requires initial state from calling script
    // -D "PRNG_Seed=$(date +%N)"
    function XORshift() {
    local x = PRNG_State;
    x ^= x << 13;
    x ^= x >> 17;
    x ^= x << 5;
    PRNG_State = x;
    return x;
    }
    //—–
    // Spirograph tooth counts mooched from:
    // http://nathanfriend.io/inspirograph/
    // Stators has both inside and outside counts, because we're not fussy
    Stators = [96, 105, 144, 150];
    Rotors = [24, 30, 32, 36, 40, 45, 48, 50, 52, 56, 60, 63, 64, 72, 75, 80, 84];
    //—–
    // Start drawing things
    // Set these variables from command line
    comment("PRNG seed: ",PRNG_Seed);
    PRNG_State = PRNG_Seed;
    // Define some useful constants
    AngleStep = 2.0deg;
    Margins = [0.5in,0.5in] * 2;
    comment("Paper size: ",PaperSize);
    PlotSize = PaperSize – Margins;
    comment("PlotSize: ",PlotSize);
    //—–
    // Set up gearing
    s = (XORshift() & 0xffff) % count(Stators);
    StatorTeeth = Stators[s];
    comment("Stator ",s,": ",StatorTeeth);
    r = (XORshift() & 0xffff) % count(Rotors);
    RotorTeeth = Rotors[r];
    comment("Rotor ",r,": ",RotorTeeth);
    GCD = gcd(StatorTeeth,RotorTeeth); // reduce teeth to ratio of least integers
    comment("GCD: ",GCD);
    StatorN = StatorTeeth / GCD;
    RotorM = RotorTeeth / GCD;
    L = to_float((XORshift() & 0x3ff) – 512) / 100.0; // normalized pen offset in rotor
    comment("Offset: ", L);
    sgn = sign((XORshift() & 0xff) – 128);
    K = sgn*to_float(RotorM) / to_float(StatorN); // normalized rotor dia
    comment("Dia ratio: ",K);
    Lobes = StatorN; // having removed all common factors
    Turns = RotorM;
    comment("Lobes: ", Lobes);
    comment("Turns: ", Turns);
    //—–
    // Crank out a list of points in normalized coordinates
    Path = {};
    Xmax = 0.0;
    Xmin = 0.0;
    Ymax = 0.0;
    Ymin = 0.0;
    for (a=0.0deg ; a <= Turns*360deg ; a += AngleStep) {
    x = (1 – K)*cos(a) + L*K*cos(a*(1 – K)/K);
    if (x > Xmax) {Xmax = x;}
    elif (x < Xmin) {Xmin = x;}
    y = (1 – K)*sin(a) – L*K*sin(a*(1 – K)/K);
    if (y > Ymax) {Ymax = y;}
    elif (y < Ymin) {Ymin = y;}
    Path += {[x,y]};
    }
    //message("Max X: ", Xmax, " Y: ", Ymax);
    //message("Min X: ", Xmin, " Y: ", Ymin); // min will always be negative
    Xmax = max(Xmax,-Xmin); // odd lobes can cause min != max
    Ymax = max(Ymax,-Ymin); // … need really truly absolute maximum
    //—–
    // Scale points to actual plot size
    PlotScale = [PlotSize.x / (2*Xmax), PlotSize.y / (2*Ymax)];
    comment("Plot scale: ", PlotScale);
    Points = scale(Path,PlotScale); // fill page, origin at center
    //—–
    // Set up pen
    if (Pen > 0) {
    comment("Tool change: ",Pen);
    toolchange(Pen);
    }
    //—–
    // Plot the curve
    feedrate(3000.0mm);
    safe_z = 1.0mm;
    plot_z = -1.0mm;
    tracepath(Points, plot_z);
    //—–
    // Put legend in proper location
    feedrate(500mm);
    TextSize = [3.0mm,3.0mm];
    TextLeading = 1.5; // line spacing as multiple of nominal text height
    MaxPen = 4;
    line1 = typeset("Seed: " + PRNG_Seed + " Stator: " + StatorTeeth + " Rotor: " + RotorTeeth,FONT_HSANS_1);
    line2 = typeset("Offset: " + L + " GCD: " + GCD + " Lobes: " + Lobes + " Turns: " + Turns,FONT_HSANS_1);
    maxlength = TextSize.x * max(line1[-1].x,line2[-1].x);
    textpath = line1 + (line2 – [-, TextLeading, -]); // undef – n -> undef to preserve coordinates
    if (Pen == 1 || Pen > MaxPen ) { // catch and fix obviously bogus pen selections
    textorg = [PlotSize.x/2 – maxlength,-(PlotSize.y/2 – TextLeading*TextSize.y)];
    }
    elif (Pen == 2) {
    textorg = [-PlotSize.x/2,-(PlotSize.y/2 – TextLeading*TextSize.y)];
    }
    elif (Pen == 3) {
    textorg = [PlotSize.x/2 – maxlength, PlotSize.y/2 – TextSize.y];
    }
    elif (Pen == 4) {
    textorg = [-PlotSize.x/2, PlotSize.y/2 – TextSize.y];
    }
    else {
    Pen = 0; // squelch truly bogus pens
    textorg = [0mm,0mm]; // just to define it
    }
    if (Pen) { // Pen = 0 suppresses legend
    placepath = scale(textpath,TextSize) + textorg;
    comment("Legend begins");
    engrave(placepath,safe_z,plot_z);
    }
    if (Pen == 1) { // add attribution along right margin
    attrpath = typeset("Ed Nisley – KE4ZNU – softsolder.com",FONT_HSANS_1);
    attrpath = rotate_xy(attrpath,90deg);
    attrorg = [PlotSize.x/2,5*TextLeading*TextSize.y – PlotSize.y/2];
    placepath = scale(attrpath,TextSize) + attrorg;
    comment("Attribution begins");
    engrave(placepath,safe_z,plot_z);
    }
    goto([-,-,25.0mm]);
    view raw Spirograph.gcmc hosted with ❤ by GitHub
  • MPCNC: GCMC Text vs. Speed

    GCMC includes single-stroke fonts derived from Hershey fonts, so I added a legend to the Spirograph Shakedown generator:

    MPCNC - GCMC Text - 3000 mm-min
    MPCNC – GCMC Text – 3000 mm-min

    Obviously, plotting 2.5 mm tall characters at 3000 mm/min = 50 mm/s isn’t a Good Idea on a less-than-absolutely-rigid CNC machine.

    Slowing down to 250 mm/min = 4.2 mm/s produces much better results:

    MPCNC - GCMC Text - 250 mm-min
    MPCNC – GCMC Text – 250 mm-min

    A closer look, albeit with less-than-crisp focus:

    MPCNC - GCMC Text - 250 mm-min - detail
    MPCNC – GCMC Text – 250 mm-min – detail

    This isn’t a conclusive test, but it reminds me that Speed Kills.

    The green plotter pen started life with a standard 0.3 mm felt nib, but it’s worn somewhat wider over the intervening years decades. Those 2.5 mm characters would look better coming from a narrow ceramic pen, which would require a pen change before doing the legend; using 4 mm characters would produce better results.

    The line spacing is 110% of the font X height, which obviously isn’t quite enough. Something on the order of 150% should look better.

    This GCMC code (including those mods) produces the legend:

    feedrate(250mm);
    
    textsize = [4.0mm,4.0mm];
    textat = [0.5*PlotSize.x/2,-PlotSize.y/2 + 2*textsize.y];
    
    textpath = typeset("Seed: " + PRNG_Seed + "  Stator: " + StatorTeeth + "  Rotor: " + RotorTeeth,FONT_HSANS_1);
    scalepath = scale(textpath,textsize);
    placepath = scalepath + textat;
    engrave(placepath,1.0mm,-1.0mm);
    
    textpath = typeset("Offset: " + L + "  Lobes: " + Lobes + "  Turns: " + Turns,FONT_HSANS_1);
    scalepath = scale(textpath,textsize);
    placepath = scalepath + textat + [-,-1.5*textsize.y];
    engrave(placepath,1.0mm,-1.0mm);