Category: Software

General-purpose computers doing something specific

Poughkeepsie ACM Chapter Presentation: Plotting Like It’s 1989!

I’ll be giving an in-depth talk about my adventures restoring that old HP 7475A plotter for the Poughkeepsie ACM Chapter at Marist College this evening:

Superformula Plot - Composite D — Superformula Plot – Composite D

This being the Association for Computing Machinery, I will talk a bit about the Superformula that makes it all possible:

Gielis Superformula - parameters — Gielis Superformula – parameters

The presentation will look a lot like this: ACM – Plotting Like Its 1989. The PDF doesn’t include my patter, but perhaps the linky love on each screen can fill in the details.

If you’re following along, the Python source code running on the plotter as a GitHub Gist:

	from chiplotle import *
	from math import *
	from datetime import *
	from time import *
	from types import *
	import random


	def superformula_polar(a, b, m, n1, n2, n3, phi):
	''' Computes the position of the point on a
	superformula curve.
	Superformula has first been proposed by Johan Gielis
	and is a generalization of superellipse.
	see: http://en.wikipedia.org/wiki/Superformula
	Tweaked to return polar coordinates
	'''

	t1 = cos(m * phi / 4.0) / a
	t1 = abs(t1)
	t1 = pow(t1, n2)

	t2 = sin(m * phi / 4.0) / b
	t2 = abs(t2)
	t2 = pow(t2, n3)

	t3 = -1 / float(n1)
	r = pow(t1 + t2, t3)
	if abs(r) == 0:
	return (0, 0)
	else:
	# return (r * cos(phi), r * sin(phi))
	return (r, phi)


	def supershape(width, height, m, n1, n2, n3,
	point_count=10 * 1000, percentage=1.0, a=1.0, b=1.0, travel=None):
	'''Supershape, generated using the superformula first proposed
	by Johan Gielis.

	– `points_count` is the total number of points to compute.
	– `travel` is the length of the outline drawn in radians.
	3.1416 * 2 is a complete cycle.
	'''
	travel = travel or (10 * 2 * pi)

	# compute points…
	phis = [i * travel / point_count
	for i in range(1 + int(point_count * percentage))]
	points = [superformula_polar(a, b, m, n1, n2, n3, x) for x in phis]

	# scale and transpose…
	path = []
	for r, a in points:
	x = width * r * cos(a)
	y = height * r * sin(a)
	path.append(Coordinate(x, y))

	return Path(path)


	# RUN DEMO CODE

	if __name__ == '__main__':

	override = False

	plt = instantiate_plotters()[0]
	# plt.write('IN;')

	if plt.margins.soft.width < 11000: # A=10365 B=16640
	maxplotx = (plt.margins.soft.width / 2) – 100
	maxploty = (plt.margins.soft.height / 2) – 150
	legendx = maxplotx – 2900
	legendy = -(maxploty – 750)
	tscale = 0.45
	numpens = 4
	# prime/10 = number of spikes
	m_values = [n / 10.0 for n in [11, 13, 17, 19, 23]]
	# ring-ness 0.1 to 2.0, higher is larger
	n1_values = [
	n / 100.0 for n in range(55, 75, 2) + range(80, 120, 5) + range(120, 200, 10)]
	else:
	maxplotx = plt.margins.soft.width / 2
	maxploty = plt.margins.soft.height / 2
	legendx = maxplotx – 3000
	legendy = -(maxploty – 900)
	tscale = 0.45
	numpens = 6
	m_values = [n / 10.0 for n in [11, 13, 17, 19, 23, 29, 31,
	37, 41, 43, 47, 53, 59]] # prime/10 = number of spikes
	# ring-ness 0.1 to 2.0, higher is larger
	n1_values = [
	n / 100.0 for n in range(15, 75, 2) + range(80, 120, 5) + range(120, 200, 10)]

	print " Max: ({},{})".format(maxplotx, maxploty)

	# spiky-ness 0.1 to 2.0, higher is spiky-er (mostly)
	n2_values = [
	n / 100.0 for n in range(10, 60, 2) + range(65, 100, 5) + range(110, 200, 10)]

	plt.write(chr(27) + '.H200:') # set hardware handshake block size
	plt.set_origin_center()
	# scale based on B size characters
	plt.write(hpgl.SI(tscale * 0.285, tscale * 0.375))
	# slow speed for those abrupt spikes
	plt.write(hpgl.VS(10))

	while True:

	# standard loadout has pen 1 = fine black
	plt.write(hpgl.PA([(legendx, legendy)]))
	pen = 1
	plt.select_pen(pen)
	plt.write(hpgl.PA([(legendx, legendy)]))
	plt.write(hpgl.LB("Started " + str(datetime.today())))

	if override:
	m = 4.1
	n1_list = [1.15, 0.90, 0.25, 0.59, 0.51, 0.23]
	n2_list = [0.70, 0.58, 0.32, 0.28, 0.56, 0.26]
	else:
	m = random.choice(m_values)
	n1_list = random.sample(n1_values, numpens)
	n2_list = random.sample(n2_values, numpens)

	pen = 1
	for n1, n2 in zip(n1_list, n2_list):
	n3 = n2
	print "{0} – m: {1:.1f}, n1: {2:.2f}, n2=n3: {3:.2f}".format(pen, m, n1, n2)
	plt.select_pen(pen)
	plt.write(hpgl.PA([(legendx, legendy – 100 * pen)]))
	plt.write(
	hpgl.LB("Pen {0}: m={1:.1f} n1={2:.2f} n2=n3={3:.2f}".format(pen, m, n1, n2)))
	e = supershape(maxplotx, maxploty, m, n1, n2, n3)
	plt.write(e)
	pen = pen + 1 if (pen % numpens) else 1

	pen = 1
	plt.select_pen(pen)
	plt.write(hpgl.PA([(legendx, legendy – 100 * (numpens + 1))]))
	plt.write(hpgl.LB("Ended " + str(datetime.today())))
	plt.write(hpgl.PA([(legendx, legendy – 100 * (numpens + 2))]))
	plt.write(hpgl.LB("More at https://softsolder.com/?s=7475a"))
	plt.select_pen(0)
	plt.write(hpgl.PA([(-maxplotx,maxploty)]))

	print "Waiting for plotter… ignore timeout errors!"
	sleep(40)
	while NoneType is type(plt.status):
	sleep(5)

	print "Load more paper, then …"
	print " … Press ENTER on the plotter to continue"
	plt.clear_digitizer()
	plt.digitize_point()

	plotstatus = plt.status
	while (NoneType is type(plotstatus)) or (0 == int(plotstatus) & 0x04):
	plotstatus = plt.status

	print "Digitized: " + str(plt.digitized_point)

view raw PlotterShapes.py hosted with ❤ by GitHub

2016-01-25

Microscope Stage Positioner

Given the vanishingly small depth of field provided by a cheap USB camera peering through the stereo zoom microscope, I’ve always wanted a better way of moving objects by small increments. The rehabilitated micropositioner didn’t have the right orientation or end effector:

So I rearranged the axis slides and added a small table:

That frees up the magnetic base and husky angle bracket, plus a few odds & ends, for future adventures.

The clear base is a random chunk of acrylic, bandsawed to the proper length, then tediously squared and drilled on the Sherline:

Microscope Stage Positioner - base squaring — Microscope Stage Positioner – base squaring

I briefly thought of printing the base, but came to my senses: there are better ways to make big flat surfaces.

The little aluminum table has a nubbly spray coating that came straight from the heap and looks surprisingly good after squaring & drilling. The X axis block puts it below the platform and one screw head above the desk when the Y axis arm sits flat on the acrylic base.

One solid model view arranges things in more-or-less the proper layout to check the alignment:

Microscope Stage Positioner - solid model - Show layout — Microscope Stage Positioner – solid model – Show layout

The build layout reduces the platform space:

Microscope Stage Positioner - Slic3r preview — Microscope Stage Positioner – Slic3r preview

You’re looking at four hours of PETG print time at 0.2 mm layer thickness with 15% infill and Hilbert Curve surfaces.

All of the screws have UNF fine-pitch threads (4-48, 6-40, 8-36, stuff like that), so the solid model includes the spacing required to reuse the original screws: those big holes in the Y axis arm end in little clearance holes for the tiny screws. Some of the screws bottom out with barely two millimeters of thread engagement in the slides, while others could jam against the racks. I didn’t want to cut that many screws from my Brownell’s gun screw assortment unless I absolutely had to. So far, so good.

I spent quite a while doodling the layout to convince myself that it would actually work:

Microscope Stage Positioner - layout doodle — Microscope Stage Positioner – layout doodle

Memo to self: Next time, use a larger scale!

Although the whole lashup works as intended, those metal hunks are way too heavy for the plastic block that fits between the Z axis drive pillar and the X axis slide: that long Y axis arm drooped toward the front by about 5 mm. A small shim raised the front of the Z axis footprint enough to level the arm, but I think the right answer is a metal upright with a bigger footprint that spreads the load.

All that mass hanging out in mid-air turns the plastic pieces into springs: you can’t keep your fingers on the knobs. Fortunately, everything returns to the same position after you release the knob, so it’s easy to move in precise increments if you close your eyes until the view settles down.

There’s a reason optical equipment uses cast iron, steel, and brass… but I’ll settle for plastic.

The OpenSCAD source code as a GitHub gist:

	// Microscope Stage Positioner
	// Ed Nisley KE4ZNU January 2016

	Layout = "Build"; // Show Build
	// Base ZStand YMount XMount

	Gap = 0.0;

	//- Extrusion parameters must match reality!

	ThreadThick = 0.25;
	ThreadWidth = 0.40;

	HoleWindage = 0.2;

	Protrusion = 0.1; // make holes end cleanly

	inch = 25.4;

	function IntegerMultiple(Size,Unit) = Unit * ceil(Size / Unit);

	//———————-
	// Dimensions

	SlipFit = 0.1;

	ZDrive = [26.0,19.6,75.0]; // stationary part of Z drive
	ZDriveOffset =[0,0,22.0]; // left front corner of stationary Z base
	ZWall = 4.0; // thickness of edge wrapped around Z columns

	YStageBlock = [25.0,61.0,17.0]; // Y stage mount + slide
	YStageOffset = [-6.0,4.0,0.0]; // offset to inner corner of Y stage holder

	YArm = [10.0,93.0,17.0]; // mount to stationary part of Y stage

	ZStage = [24.0,9.7,85.0]; // moving part of Z drive
	ZYArm = [(2*ZWall + ZStage[0]),10.0,YArm[2]]; // attaches to ZStage, same thickness as YArm

	XStageBlock = [25.0,20.0,12.0]; // X stage mount + slide
	XStageOffset = [-95.0,-15.0,-26]; // offset to rear left bottom corner of X stage slide

	XTray = [25,25,5]; // X tray attached to bottom of X mount

	//———————-
	// Useful routines

	module PolyCyl(Dia,Height,ForceSides=0) { // based on nophead's polyholes

	Sides = (ForceSides != 0) ? ForceSides : (ceil(Dia) + 2);

	FixDia = Dia / cos(180/Sides);

	cylinder(r=(FixDia + HoleWindage)/2,
	h=Height,
	$fn=Sides);
	}


	//– Z Stand

	module ZStand() {

	Holes = [12.0,41.5,68.0];
	HoleOD = 3.5;
	HolesOC = 15.0;

	echo(str("Z Stand holes OC: ",HolesOC));

	ZPlate = 6.0; // thickness of Z plate = max screw grab distance
	ZStandWrap = 2.0; // length of edge wrapped around Z column

	MaxY = 9.0;
	MinY = -14.0;

	difference() {
	union() {
	linear_extrude(height=ZDriveOffset[2])
	polygon(points=[
	[-ZWall,MaxY], // limited by Z slide rack
	[ZDrive[0] + ZWall,MaxY],
	[ZDrive[0] + ZWall,MinY], // limited by X slide rack
	[-ZWall,MinY]
	]);
	linear_extrude(height=(ZDrive[2] + ZDriveOffset[2]),convexity=4)
	polygon(points=[
	[-SlipFit,0],
	[ZDrive[0] + SlipFit,0.0],
	[ZDrive[0] + SlipFit,ZStandWrap],
	[ZDrive[0] + ZWall,ZStandWrap],
	[ZDrive[0] + ZWall,-ZPlate],
	[-ZWall,-ZPlate],
	[-ZWall,ZStandWrap],
	[-SlipFit,ZStandWrap]
	]);
	}

	for (i = [0:len(Holes) – 1]) // holes along Z stand
	translate([ZDrive[0]/2,ZDrive[1]/2,(Holes[i] + ZDriveOffset[2])])
	rotate([90,0,0])
	PolyCyl(HoleOD,ZDrive[1]);

	for (i = [-1,1]) // mounting screw holes
	translate([i*HolesOC/2 + ZDrive[0]/2, // center the holes from side to side
	(MaxY + MinY)/2, // moby hack to put holes on midline
	-Protrusion])
	PolyCyl(3.5,0.75*ZDriveOffset[2],6);
	}
	}

	//– Y Mounting arm
	// Polygon origin at inner corner nearest the Z stand column

	module YMount() {

	YHoles = [12.0,48.0,84.0]; // mounting holes along Y stage arm, from outside in
	YScrewLength = 4.0; // screw head to Y stage mount

	ZStageBase = [(ZDrive[0] – ZStage[0])/2,(ZDrive[1] + ZStage[1]),0.0] – YStageOffset; // local coordinates of Z slide left rear corner
	ZHoles = [26.5,55.0,71.0];

	ZStageWrap = 8.0; // length of edge wrapped around Z stage
	Trim = ZStageBase[1] – ZStageWrap;

	union() {
	difference() {
	linear_extrude(height=YArm[2],convexity=5)
	polygon(points=[
	[-Trim,0.0],
	[-YStageBlock[0],0.0],
	[-YStageBlock[0],-(YArm[1] + SlipFit)],
	[-(YStageBlock[0] + YArm[0]),-(YArm[1] + SlipFit)],
	[-(YStageBlock[0] + YArm[0]),Trim],
	[-Trim,(ZStageBase[1] + ZYArm[1])],
	[(ZStageBase[0] + ZStage[0]/2),(ZStageBase[1] + ZYArm[1])],
	[(ZStageBase[0] + ZStage[0] + ZWall),(ZStageBase[1] + 0*ZYArm[1])],
	[(ZStageBase[0] + ZStage[0] + ZWall),(ZStageBase[1] – ZStageWrap)],
	[(ZStageBase[0] + ZStage[0] + SlipFit),(ZStageBase[1] – ZStageWrap)],
	[(ZStageBase[0] + ZStage[0] + SlipFit),ZStageBase[1]],
	[(ZStageBase[0] – SlipFit),ZStageBase[1]],
	[(ZStageBase[0] – SlipFit),(ZStageBase[1] – ZStageWrap)],
	[0.0,(ZStageBase[1] – ZStageWrap)],
	[0.0,Trim]
	]);

	for (j=[0:len(YHoles) – 1]) { // Y stage mounting screws
	translate([-(YStageBlock[0] + YScrewLength),
	(-YArm[1] + YHoles[j] – 2*SlipFit),
	YArm[2]/2])
	rotate([0,-90,0]) rotate(180/6)
	PolyCyl(5.5,YArm[0],6);
	translate([-(YStageBlock[0] – Protrusion),
	(-YArm[1] + YHoles[j] – 2*SlipFit),
	YArm[2]/2])
	rotate([0,-90,0]) rotate(180/6)
	PolyCyl(2.5,2*YArm[0],6);
	}
	}
	if (true)
	difference() {
	linear_extrude(height=ZStage[2],convexity=5)
	polygon(points=[
	[(ZStageBase[0] – ZWall),(ZStageBase[1] + 5.0)],
	[(ZStageBase[0] + ZStage[0] + ZWall),(ZStageBase[1] + 5.0)],
	[(ZStageBase[0] + ZStage[0] + ZWall),(ZStageBase[1] – ZStageWrap)],
	[(ZStageBase[0] + ZStage[0] + SlipFit),(ZStageBase[1] – ZStageWrap)],
	[(ZStageBase[0] + ZStage[0] + SlipFit),ZStageBase[1]],
	[(ZStageBase[0] – SlipFit),ZStageBase[1]],
	[(ZStageBase[0] – SlipFit),(ZStageBase[1] – ZStageWrap)],
	[(ZStageBase[0] – ZWall),(ZStageBase[1] – ZStageWrap)],
	]);
	for (k=[0:len(ZHoles) – 1])
	translate([(ZStageBase[0] + ZStage[0]/2),0.0,ZHoles[k]])
	rotate([-90,0,0])
	PolyCyl(3.5,2*ZStageBase[1],6);
	}
	}
	}

	//– X Slide attachment
	// Origin at left rear bottom of mount

	module XMount() {

	XHoles = [6.0,18.0]; // from end of X slide
	XHolesOffset = 7.0; // from bottom of X slide

	TrayHolesOC = 10.0;
	echo(str("Tray holes OC: ",TrayHolesOC));

	BlockOAH = XStageBlock[2] – XStageOffset[2] – XTray[2]; // overall height of mount

	difference() {
	translate([XStageBlock[0],0,BlockOAH])
	rotate([0,90,180])
	linear_extrude(height=XStageBlock[0],convexity=2)
	polygon(points=[
	[0,0],
	[0.0,7.0],
	[(XStageBlock[2] + SlipFit),7.0],
	[(XStageBlock[2] + SlipFit),XStageBlock[1]],
	[BlockOAH,XStageBlock[1]],
	[BlockOAH,0.0],
	]);

	for (i=[0:len(XHoles) – 1]) // holes for X stage screws
	translate([XHoles[i],Protrusion,BlockOAH – XStageBlock[2] + XHolesOffset])
	rotate([90,0,0])
	PolyCyl(3.5,2*7.0,6);

	for (i=[-1,1]) // holes for tray mount
	translate([i*TrayHolesOC/2 + XStageBlock[0]/2,-XStageBlock[1]/2,-Protrusion])
	PolyCyl(2.5,0.75*(BlockOAH – XStageBlock[2]),6);
	}

	}

	//———————-
	// Build it

	if (Layout == "ZStand")
	ZStand();

	if (Layout == "YMount")
	YMount();

	if (Layout == "XMount")
	XMount();


	if (Layout == "Show") {

	color("lightgreen")
	ZStand();

	color("orange")
	translate(YStageOffset)
	YMount();

	color("lightblue")
	translate(XStageOffset + [0,0,-XStageOffset[2]])
	XMount();
	}

	if (Layout == "Build") {

	translate([20,0,0])
	ZStand();

	translate([YStageBlock[0]/2,0,0])
	YMount();

	translate([20,-30,0])
	XMount();
	}

view raw Microscope Stage Positioner.scad hosted with ❤ by GitHub

2016-01-18

Olfa Rotary Cutter Spacer

At some point along the way, the bright yellow washer (they call it a “spacer”) on Mary’s 60 mm Olfa rotary cutter went missing. A casual search suggests that replacement washers come directly from Olfa after navigating their phone tree, but …

Judging from scuffs on the rear surface, the washer serves two purposes:

Hold the blade close to the handle against slightly misaligned cutting forces
Add more compression to the wave washer under the nut

This model is much more intricate than the stock washer:

Olfa Rotary Cutter - backing washer — Olfa Rotary Cutter – backing washer

The trench across the middle of the thicker part allows a wider compression adjustment range for the wave washer and provides more thread engagement at the lightest setting for my liking. The shape comes from the chord equation based on measurements of the wave washer:

Olfa Rotary Cutter - washer doodles — Olfa Rotary Cutter – washer doodles

The wave washer keys on the bolt flats: the whole affair rotates with the blade and gives the nut no inclination to unscrew. If you remove the trench, the remaining hole has the proper shape to key on the bolt and rotate with it; with the trench in place, the wave washer’s sides haul the plastic washer along with it.

The plain ring, just two threads thick, glues bottom-to-bottom on the thicker part to soak up the air gap and provide more blade stability. It’s not entirely clear that’s a win; it’s easy to omit.

It looks about like you’d expect:

Olfa Rotary Cutter - washer in place — Olfa Rotary Cutter – washer in place

The wave washer must go on the bolt with the smooth curve downward into the trench. That orientation that wasn’t enforced by the Official Olfa spacer washer’s smooth sides.

The nut sits upside-down to show the face that normally sits against the wave washer. I’d lay long odds that the recess around the threads originally held a conical compression spring with a penchant for joining the dust bunnies under the sewing table. You can insert the wave washer the wrong way, but it doesn’t store enough energy to go airborne unless you drop it, which did happen once with the expected result.

The OpenSCAD source code as a GitHub gist:

	// Olfa rotary cutter backing washer
	// Ed Nisley KE4ZNU January 2016

	Layout = "Build";

	//- Extrusion parameters must match reality!
	// Print with +1 shells and 3 solid layers

	ThreadThick = 0.20;
	ThreadWidth = 0.40;

	HoleWindage = 0.2;

	function IntegerMultiple(Size,Unit) = Unit * ceil(Size / Unit);

	Protrusion = 0.1; // make holes end cleanly

	//———————-
	// Dimensions

	WasherOD = 35.0;
	WasherThick = 1.5;

	WaveOD = 14.0; // wave washer flat dia
	WaveM = 1.8; // height of wave washer bend
	BendRad = (pow(WaveM,2) + pow(WaveOD,2)/4) / (2*WaveM); // radius of wave washer bend

	echo(str("Wave washer bend radius: ",BendRad));

	SpacerID = WaveOD + 2.0;
	SpacerThick = 2*ThreadThick;

	NumSides = 12*4;
	$fn = NumSides;
	//———————-
	// Useful routines

	module PolyCyl(Dia,Height,ForceSides=0) { // based on nophead's polyholes

	Sides = (ForceSides != 0) ? ForceSides : (ceil(Dia) + 2);

	FixDia = Dia / cos(180/Sides);

	cylinder(r=(FixDia + HoleWindage)/2,
	h=Height,
	$fn=Sides);
	}

	//———————-
	// Parts

	module Upper() {
	difference() {
	cylinder(d1=WasherOD,d2=(WasherOD – 2.0),h=WasherThick);
	translate([0,0,-Protrusion])
	intersection() {
	PolyCyl(8.2,2.0,8);
	cube([(6.0 + HoleWindage),10,2*WasherThick],center=true);
	}
	translate([-(WaveOD + 1.0)/2,0,BendRad])
	rotate([0,90,0]) rotate(0*180/16)
	PolyCyl(BendRad*2,(WaveOD + 1),16);
	}
	}

	module Spacer() {
	difference() {
	cylinder(d=WasherOD,h=SpacerThick);
	translate([0,0,-Protrusion])
	cylinder(d=SpacerID,h=2*SpacerThick);
	}
	}

	//———————-
	// Build it!

	if (Layout == "Show") {
	translate([0,0,SpacerThick])
	color("Cyan")
	Upper();
	color("LightCyan")
	Spacer();
	}

	if (Layout == "Build") {
	translate([-0.6*WasherOD,0,0])
	Upper();
	translate([0.6*WasherOD,0,0])
	Spacer();
	}

view raw Olfa Rotary Cutter.scad hosted with ❤ by GitHub

2016-01-13

HP 7475A: Superformula Successes

In the course of running off some Superformula plots, I found what must be my original stash of B-size plotter paper. Although it wasn’t archival paper and has yellowed a bit with age, it’s the smoothest and creamiest paper I’ve touched in quite some time: far nicer than the cheap stuff I picked up while reconditioning the HP 7475A plotter & its assorted pens.

Once in a while, all my errors and omissions cancel out enough to produce interesting results on that historic paper, hereby documented for future reference…

A triangle starburst:

Superformula - triangle burst — Superformula – triangle burst

Superformula - triangle burst - detail — Superformula – triangle burst – detail

A symmetric starburst:

Superformula - starburst — Superformula – starburst

Superformula - starburst - detail — Superformula – starburst – detail

Complex meshed ovals:

Superformula - meshed ovals — Superformula – meshed ovals

Superformula - meshed ovals - details — Superformula – meshed ovals – details

They look better in person, of course. Although inkjet printers produce more accurate results in less time, those old pen plots definitely look better in some sense.

The demo program lets you jam a fixed set of parameters into the plot, so (at least in principle) one could reproduce a plot from the parameters in the lower right corner. Here you go:

The triangle starburst:

Superformula - triangle burst - parameters — Superformula – triangle burst – parameters

The symmetric starburst:

Superformula - starburst - parameters — Superformula – starburst – parameters

The meshed ovals:

Superformula - meshed ovals - parameters — Superformula – meshed ovals – parameters

The current Python / Chiplotle source code as a GitHub gist:

	from chiplotle import *
	from math import *
	from datetime import *
	from time import *
	from types import *
	import random


	def superformula_polar(a, b, m, n1, n2, n3, phi):
	''' Computes the position of the point on a
	superformula curve.
	Superformula has first been proposed by Johan Gielis
	and is a generalization of superellipse.
	see: http://en.wikipedia.org/wiki/Superformula
	Tweaked to return polar coordinates
	'''

	t1 = cos(m * phi / 4.0) / a
	t1 = abs(t1)
	t1 = pow(t1, n2)

	t2 = sin(m * phi / 4.0) / b
	t2 = abs(t2)
	t2 = pow(t2, n3)

	t3 = -1 / float(n1)
	r = pow(t1 + t2, t3)
	if abs(r) == 0:
	return (0, 0)
	else:
	# return (r * cos(phi), r * sin(phi))
	return (r, phi)


	def supershape(width, height, m, n1, n2, n3,
	point_count=10 * 1000, percentage=1.0, a=1.0, b=1.0, travel=None):
	'''Supershape, generated using the superformula first proposed
	by Johan Gielis.

	– `points_count` is the total number of points to compute.
	– `travel` is the length of the outline drawn in radians.
	3.1416 * 2 is a complete cycle.
	'''
	travel = travel or (10 * 2 * pi)

	# compute points…
	phis = [i * travel / point_count
	for i in range(1 + int(point_count * percentage))]
	points = [superformula_polar(a, b, m, n1, n2, n3, x) for x in phis]

	# scale and transpose…
	path = []
	for r, a in points:
	x = width * r * cos(a)
	y = height * r * sin(a)
	path.append(Coordinate(x, y))

	return Path(path)


	# RUN DEMO CODE

	if __name__ == '__main__':

	override = False

	plt = instantiate_plotters()[0]
	# plt.write('IN;')

	if plt.margins.soft.width < 11000: # A=10365 B=16640
	maxplotx = (plt.margins.soft.width / 2) – 100
	maxploty = (plt.margins.soft.height / 2) – 150
	legendx = maxplotx – 2900
	legendy = -(maxploty – 750)
	tscale = 0.45
	numpens = 4
	# prime/10 = number of spikes
	m_values = [n / 10.0 for n in [11, 13, 17, 19, 23]]
	# ring-ness 0.1 to 2.0, higher is larger
	n1_values = [
	n / 100.0 for n in range(55, 75, 2) + range(80, 120, 5) + range(120, 200, 10)]
	else:
	maxplotx = plt.margins.soft.width / 2
	maxploty = plt.margins.soft.height / 2
	legendx = maxplotx – 3000
	legendy = -(maxploty – 900)
	tscale = 0.45
	numpens = 6
	m_values = [n / 10.0 for n in [11, 13, 17, 19, 23, 29, 31,
	37, 41, 43, 47, 53, 59]] # prime/10 = number of spikes
	# ring-ness 0.1 to 2.0, higher is larger
	n1_values = [
	n / 100.0 for n in range(15, 75, 2) + range(80, 120, 5) + range(120, 200, 10)]

	print " Max: ({},{})".format(maxplotx, maxploty)

	# spiky-ness 0.1 to 2.0, higher is spiky-er (mostly)
	n2_values = [
	n / 100.0 for n in range(10, 60, 2) + range(65, 100, 5) + range(110, 200, 10)]

	plt.write(chr(27) + '.H200:') # set hardware handshake block size
	plt.set_origin_center()
	# scale based on B size characters
	plt.write(hpgl.SI(tscale * 0.285, tscale * 0.375))
	# slow speed for those abrupt spikes
	plt.write(hpgl.VS(10))

	while True:

	# standard loadout has pen 1 = fine black
	plt.write(hpgl.PA([(legendx, legendy)]))
	pen = 1
	plt.select_pen(pen)
	plt.write(hpgl.PA([(legendx, legendy)]))
	plt.write(hpgl.LB("Started " + str(datetime.today())))

	if override:
	m = 4.1
	n1_list = [1.15, 0.90, 0.25, 0.59, 0.51, 0.23]
	n2_list = [0.70, 0.58, 0.32, 0.28, 0.56, 0.26]
	else:
	m = random.choice(m_values)
	n1_list = random.sample(n1_values, numpens)
	n2_list = random.sample(n2_values, numpens)

	pen = 1
	for n1, n2 in zip(n1_list, n2_list):
	n3 = n2
	print "{0} – m: {1:.1f}, n1: {2:.2f}, n2=n3: {3:.2f}".format(pen, m, n1, n2)
	plt.select_pen(pen)
	plt.write(hpgl.PA([(legendx, legendy – 100 * pen)]))
	plt.write(
	hpgl.LB("Pen {0}: m={1:.1f} n1={2:.2f} n2=n3={3:.2f}".format(pen, m, n1, n2)))
	e = supershape(maxplotx, maxploty, m, n1, n2, n3)
	plt.write(e)
	pen = pen + 1 if (pen % numpens) else 1

	pen = 1
	plt.select_pen(pen)
	plt.write(hpgl.PA([(legendx, legendy – 100 * (numpens + 1))]))
	plt.write(hpgl.LB("Ended " + str(datetime.today())))
	plt.write(hpgl.PA([(legendx, legendy – 100 * (numpens + 2))]))
	plt.write(hpgl.LB("More at https://softsolder.com/?s=7475a"))
	plt.select_pen(0)
	plt.write(hpgl.PA([(-maxplotx,maxploty)]))

	print "Waiting for plotter… ignore timeout errors!"
	sleep(40)
	while NoneType is type(plt.status):
	sleep(5)

	print "Load more paper, then …"
	print " … Press ENTER on the plotter to continue"
	plt.clear_digitizer()
	plt.digitize_point()

	plotstatus = plt.status
	while (NoneType is type(plotstatus)) or (0 == int(plotstatus) & 0x04):
	plotstatus = plt.status

	print "Digitized: " + str(plt.digitized_point)

view raw PlotterShapes.py hosted with ❤ by GitHub

2016-01-12

Miniature Chain Mail: Handouts

I ran off a few patches of miniature chain mail for holiday handouts to a few folks who’d appreciate them:

Chain Mail Armor - 6x6 9.6 mm - top view — Chain Mail Armor – 6×6 9.6 mm – top view

A little patch like that makes a fondletoy that’s easier to pocket than, say, a planetary gear bearing and should be robust enough to withstand quite a bit of abuse.

Alas, it turned out that recent Slic3r development versions suffered a bridging regression. The stable 1.2.9 version does the right thing:

Slic3r 1.2.9 - good bridging — Slic3r 1.2.9 – good bridging

The hot-from-Github version goes diagonally, producing a pattern like an internal layer that normally sits atop the (omitted) bridge layer:

Slic3r 7c8b710 - diagonal bridging — Slic3r 7c8b710 – diagonal bridging

While that might barely work, the little bitty link bars will certainly fall into the abyss:

Slic3r 7c8b710 - diagonal bridging on links — Slic3r 7c8b710 – diagonal bridging on links

Given the complexity of slicing algorithms, I definitely can’t track down the problem; using the stable version for a while should suffice.

The OpenSCAD source code as a GitHub gist:

	// Chain Mail Armor Buttons
	// Ed Nisley KE4ZNU – December 2014

	Layout = "Build"; // Link Button LB Joiner Joiners Build PillarMod

	//——-
	//- Extrusion parameters must match reality!
	// Print with 1 shell and 2+2 solid layers

	ThreadThick = 0.25;
	ThreadWidth = 0.40;

	HoleWindage = 0.2;

	Protrusion = 0.1; // make holes end cleanly

	function IntegerMultiple(Size,Unit) = Unit * ceil(Size / Unit);

	//——-
	// Dimensions

	//- Set maximum sheet size

	SheetSizeX = 125; // 170 for full sheet on M2
	SheetSizeY = 125; // 230 …

	//- Diamond or rectangular sheet?

	Diamond = false; // true = rotate 45 degrees, false = 0 degrees for square

	BendAround = "X"; // X or Y = maximum flexibility around designated axis

	Cap = true; // true = build bridge layers over links
	CapThick = 4 * ThreadThick; // flat cap on link: >= 3 layers for solid bridging

	Armor = true && Cap; // true = build armor button atop (required) cap
	ArmorThick = IntegerMultiple(2.0,ThreadThick); // height above cap surface

	ArmorSides = 4;
	ArmorAngle = true ? 180/ArmorSides : 0; // true -> rotate half a side for best alignment

	//- Link bar sizes

	BarThick = 3 * ThreadThick;
	BarWidth = 3.3 * ThreadWidth;

	BarClearance = 3 * ThreadThick; // vertical clearance above & below bars

	VertexHack = false; // true to slightly reduce openings to avoid coincident vertices

	//- Compute link sizes from those values

	//- Absolute minimum base link: bar width + corner angle + build clearance around bars
	// rounded up to multiple of thread width to ensure clean filling
	BaseSide = IntegerMultiple((4BarWidth + 2BarWidth/sqrt(2) + 3(2ThreadWidth)),ThreadWidth);

	BaseHeight = 2*BarThick + BarClearance; // both bars + clearance

	echo(str("BaseSide: ",BaseSide," BaseHeight: ",BaseHeight));
	//echo(str(" Base elements: ",4BarWidth,", ",2BarWidth/sqrt(2),", ",3(2ThreadWidth)));
	//echo(str(" total: ",(4BarWidth + 2BarWidth/sqrt(2) + 3(2ThreadWidth))));

	BaseOutDiagonal = BaseSide*sqrt(2) – BarWidth;
	BaseInDiagonal = BaseSidesqrt(2) – 2(BarWidth/2 + BarWidth*sqrt(2));

	echo(str("Outside diagonal: ",BaseOutDiagonal));

	//- On-center distance measured along coordinate axis
	// the links are interlaced, so this is half of what you think it should be…

	LinkOC = BaseSide/2 + ThreadWidth;

	LinkSpacing = Diamond ? (sqrt(2)*LinkOC) : LinkOC;
	echo(str("Base spacing: ",LinkSpacing));

	//- Compute how many links fit in sheet

	MinLinksX = ceil((SheetSizeX – (Diamond ? BaseOutDiagonal : BaseSide)) / LinkSpacing);
	MinLinksY = ceil((SheetSizeY – (Diamond ? BaseOutDiagonal : BaseSide)) / LinkSpacing);
	echo(str("MinLinks X: ",MinLinksX," Y: ",MinLinksY));

	NumLinksX = ((0 == (MinLinksX % 2)) && !Diamond) ? MinLinksX + 1 : MinLinksX;
	NumLinksY = ((0 == (MinLinksY % 2) && !Diamond)) ? MinLinksY + 1 : MinLinksY;
	echo(str("Links X: ",NumLinksX," Y: ",NumLinksY));

	//- Armor button base

	ButtonHeight = BaseHeight + BarClearance + CapThick;
	echo(str("ButtonHeight: ",ButtonHeight));

	//- Armor ornament size & shape
	// Fine-tune OD & ID to suit the number of sides…

	TotalHeight = ButtonHeight + ArmorThick;
	echo(str("Overall Armor Height: ",TotalHeight));

	ArmorOD = 1.0 * BaseSide; // tune for best base fit
	ArmorID = 10 * ThreadWidth; // make the tip blunt & strong

	//——-

	module ShowPegGrid(Space = 10.0,Size = 1.0) {

	RangeX = floor(95 / Space);
	RangeY = floor(125 / Space);

	for (x=[-RangeX:RangeX])
	for (y=[-RangeY:RangeY])
	translate([xSpace,ySpace,Size/2])
	%cube(Size,center=true);

	}


	//——-
	// Create link with armor button as needed

	module Link(Topping = false) {

	LinkHeight = (Topping && Cap) ? ButtonHeight : BaseHeight;

	render(convexity=3)
	rotate((BendAround == "X") ? 90 : 0)
	rotate(Diamond ? 45 : 0)
	union() {
	difference() {
	translate([0,0,LinkHeight/2]) // outside shape
	intersection() {
	cube([BaseSide,BaseSide,LinkHeight],center=true);
	rotate(45)
	cube([BaseOutDiagonal,BaseOutDiagonal,(LinkHeight + 2*Protrusion)],center=true);
	}

	translate([0,0,(BaseHeight + BarClearance + 0*ThreadThick – Protrusion)/2])
	intersection() { // inside shape
	cube([(BaseSide – 2*BarWidth),
	(BaseSide – 2*BarWidth),
	(BaseHeight + BarClearance + 0*ThreadThick + (VertexHack ? Protrusion/2 : 0))],
	center=true);
	rotate(45)
	cube([BaseInDiagonal,
	BaseInDiagonal,
	(BaseHeight + BarClearance + 0*ThreadThick + (VertexHack ? Protrusion/2 : 0))],
	center=true);
	}

	translate([0,0,((BarThick + 2*BarClearance)/2 + BarThick)]) // openings for bars
	cube([(BaseSide – 2BarWidth – 2BarWidth/sqrt(2) – (VertexHack ? Protrusion/2 : 0)),
	(2*BaseSide),
	BarThick + 2*BarClearance – Protrusion],
	center=true);

	translate([0,0,(BaseHeight/2 – BarThick)])
	cube([(2*BaseSide),
	(BaseSide – 2BarWidth – 2BarWidth/sqrt(2) – (VertexHack ? Protrusion/2 : 0)),
	BaseHeight],
	center=true);

	}

	if (Topping && Armor)
	translate([0,0,(ButtonHeight – Protrusion)]) // sink slightly into the cap
	rotate(ArmorAngle)
	cylinder(d1=ArmorOD,d2=ArmorID,h=(ArmorThick + Protrusion), $fn=ArmorSides);
	}

	}


	//——-
	// Create split buttons to join sheets

	module Joiner() {

	translate([-LinkSpacing,0,0])
	difference() {
	Link(false);
	translate([0,0,BarThick + BarClearance + TotalHeight/2 – Protrusion])
	cube([2LinkSpacing,2LinkSpacing,TotalHeight],center=true);
	}

	translate([LinkSpacing,0,0])
	intersection() {
	translate([0,0,-(BarThick + BarClearance)])
	Link(true);
	translate([0,0,TotalHeight/2])
	cube([2LinkSpacing,2LinkSpacing,TotalHeight],center=true);
	}

	}


	//——-
	// Build it!

	//ShowPegGrid();

	if (Layout == "Link") {
	Link(false);
	}

	if (Layout == "Button") {
	Link(true);
	}

	if (Layout == "LB") {
	color("Brown") Link(true);
	translate([LinkSpacing,LinkSpacing,0])
	color("Orange") Link(false);
	}

	if (Layout == "Build")
	for (ix = [0:(NumLinksX – 1)],
	iy = [0:(NumLinksY – 1)]) {
	x = (ix – (NumLinksX – 1)/2)*LinkSpacing;
	y = (iy – (NumLinksY – 1)/2)*LinkSpacing;
	translate([x,y,0])
	color([(ix/(NumLinksX – 1)),(iy/(NumLinksY – 1)),1.0])
	if (Diamond)
	Link((ix + iy) % 2); // armor at odd,odd & even,even points
	else
	if ((iy % 2) && (ix % 2)) // armor at odd,odd points
	Link(true);
	else if (!(iy % 2) && !(ix % 2)) // connectors at even,even points
	Link(false);
	}

	if (Layout == "Joiner")
	Joiner();

	if (Layout == "Joiners") {
	NumJoiners = max(MinLinksX,MinLinksY)/2;
	for (iy = [0:(NumJoiners – 1)]) {
	y = (iy – (NumJoiners – 1)/2)2LinkSpacing + LinkSpacing/2;
	translate([0,y,0])
	color([0.5,(iy/(NumJoiners – 1)),1.0])
	Joiner();
	}
	}

	if (Layout == "PillarMod") // Slic3r modification volume to eliminate pillar infill
	translate([0,0,(BaseHeight + BarClearance)/2])
	cube([1.5SheetSizeX,1.5SheetSizeY,BaseHeight + BarClearance],center=true);

view raw Chain Mail Square Armor.scad hosted with ❤ by GitHub

2016-01-11

Lenovo Q150: Setup for HP 7475A Plotter Demo
Starting with a blank 120 GB SSD, I had to disable the “Plug-n-Play OS” BIOS option to get the Lenovo Q150 to boot from a System Rescue CD USB stick. While the hood was up, I told the BIOS to ignore keyboard errors so it can boot headless.

Partitioning:
- 50 GB ext4 partition for Mint
- 8 GB swap
- The remainder unallocated
Booting & installing Mint Linux 17.2 XFCE from another USB stick went smoothly, after which it inhaled the usual gazillion updates. Rather than wait for the auto-updater to wake up and smell the repositories, I generally get it done thusly:
```
sudo apt-get update
sudo apt-get upgrade
apt-get dist-upgrade
apt-get autoremove
```
Add my user to the dialout group, so I have access to the USB serial converter on /dev/ttyUSB0 that will drive the plotter.

Configure a static IP address that appears in the appropriate /etc/hosts files.

Install some useful packages:
- nfs-common
- openssh-server
- htop and iotop
Set up ssh for public key authentication, rather than passwords, on an unusual port, so everything else can happen from the Comfy Chair upstairs.

Install packages that Chiplotle will need:
- build-essential
- python-setuptools
- python-dev
- python-numpy
- python-serial
- hp2xx
I think some of those would be auto-installed as dependencies by the next step, but now I can remember what they are for the next time around this action loop:
```
sudo easy_install -U chiplotle
... blank line to show underscore above ...
```
Plug the old hard drive into a USB-SATA adapter to copy:
- ~/.bashrc — my familiar colorful prompt
- baseplotter.py — works properly with hardwired handshaking
- ~/.chiplotle/config.py — set up to use rtscts handshaking
- PlotterShapes.py — the demo program
Then chuck up some paper and pens to let it grind out art:

HP 7475A – demo plot

It’s good clean fun…
2016-01-08

Chip-on-board LED Desk Lamp Retrofit

After the 5 mm white LEDs failed on the original desk lamp rebuild, I picked up some chip-on-board LED lamps from the usual eBay supplier:

COB LED Desk Lamp - bottom — COB LED Desk Lamp – bottom

The LED’s aluminum baseplate (perhaps there’s an actual “board” inside the yellow silicone fill) is firmly epoxied to a small heatsink from the Big Box o’ Heatsinks, chosen on the basis of being the right size and not being too battered.

The rather limited specs say the LED supply voltage can range from 9 to 12 V, suggesting a bit of slack, with a maximum dissipation of 3 W, which definitely requires a heatsink.

The First Light test looked promising:

COB LED Desk Lamp - first light — COB LED Desk Lamp – first light

That’s driven from the same 12 VDC 200 mA wall wart that I used for the failed ring light version. Measuring the results shows that the supply now runs at the ragged edge of its current rating, with the output voltage around 10.5 V with plenty of ripple:

The 260 mA current (bottom, trace 1 at 100 mA/div) varies from 200 to 300 mA as the voltage (top, trace 2 at 2 V/div) varies between 10 V and a bit under 11 V. If you believe the RMS values, it’s dissipating 2.7 W and the heatsink runs at a pleasant 105 °F in an ordinary room. The wall wart gets about as warm as you’d expect; it contains an old heavy-iron transformer and rectifier, not a trendy switcher.

The heatsink mount looks nice, in a geeky way:

COB LED Desk Lamp - side detail — COB LED Desk Lamp – side detail

The left side must be that long to anchor the gooseneck; I thought about tapering the slab a bit, but, really, it’s OK the way it is. Dabs of epoxy hold the gooseneck and heatsink in place.

The heatsink rests on a small ledge at the bottom of the slab that’s as tall as the COB LED is thick, with a wire channel from the gooseneck socket:

COB LED Heatsink mount - Slic3r — COB LED Heatsink mount – Slic3r

The Hilbert Curve infill on the top produces a textured finish; I’m a sucker for that pattern.

The old lamp base isn’t particularly stylin’, but the new head lights up my desk below the big monitors without any glare:

COB LED Desk Lamp - overview — COB LED Desk Lamp – overview

Now, let’s see how long this one lasts…

The OpenSCAD source code as a Github gist:

	// Chip-on-board LED light heatsink mount for desk lamp
	// Ed Nisley KE4ZNU December 2015

	Layout = "Show"; // Show Build

	//- Extrusion parameters must match reality!

	ThreadThick = 0.25;
	ThreadWidth = 0.40;

	HoleWindage = 0.2;

	Protrusion = 0.1; // make holes end cleanly

	inch = 25.4;

	function IntegerMultiple(Size,Unit) = Unit * ceil(Size / Unit);

	//———————-
	// Dimensions

	ID = 0; // for round things
	OD = 1;
	LENGTH = 2;

	Gooseneck = [3.0,5.0,15.0]; // anchor for end of gooseneck

	COB = [25.0,23.0,2.5]; // Chip-on-board LED module

	Heatsink = [35.5,31.5,4.0]; // height is solid base bottom
	HSWire = [23.0,28.0,53.3]; // anchor width OC, width OAL, length OC
	HSWireDia = 1.4;

	HSLip = 1.0; // width of lip under heatsink

	BaseMargin = 22ThreadWidth;
	BaseRadius = Gooseneck[OD]; // 2 x gooseneck = enough anchor, sets slab thickness
	BaseSides = 2*4;
	Base = [(Gooseneck[LENGTH] + Gooseneck[OD] + Heatsink[0] + 2*BaseRadius + BaseMargin),
	(Heatsink[1] + 2BaseRadius + 2BaseMargin),
	2*BaseRadius];


	//———————-
	// Useful routines

	module PolyCyl(Dia,Height,ForceSides=0) { // based on nophead's polyholes

	Sides = (ForceSides != 0) ? ForceSides : (ceil(Dia) + 2);

	FixDia = Dia / cos(180/Sides);

	cylinder(r=(FixDia + HoleWindage)/2,
	h=Height,
	$fn=Sides);
	}

	//– Lamp heatsink mount

	module Lamp() {

	difference() {
	translate([(Base[0]/2 – BaseRadius – Gooseneck[LENGTH]),0,0])
	hull()
	for (i=[-1,1], j=[-1,1])
	translate([i(Base[0]/2 – BaseRadius),j(Base[1]/2 – BaseRadius),Base[2]/2])
	sphere(r=BaseRadius/cos(180/BaseSides),$fn=BaseSides);

	translate([(Heatsink[0]/2 + Gooseneck[OD]),0,Heatsink[2] + COB[2]]) // main heatsink recess
	scale([1,1,2])
	cube((Heatsink + [HoleWindage,HoleWindage,0.0]),center=true);

	translate([(Heatsink[0]/2 + Gooseneck[OD]),0,Heatsink[2] – Protrusion]) // lower lip to shade lamp module
	scale([1,1,2])
	cube(Heatsink – [2HSLip,2HSLip,0],center=true);

	translate([0,0,Base[2]/2]) // goooseneck insertion
	rotate([0,-90,0]) rotate(180/8)
	PolyCyl(Gooseneck[OD],Base[0],8);

	translate([0,0,Base[2]/2 + Gooseneck[ID]/2]) // wire exit
	rotate([180,0,0])
	PolyCyl(Gooseneck[ID],Base[2],6);

	translate([Gooseneck[OD],0,(COB[2] – Protrusion)/2]) // wire slot
	rotate([180,0,0])
	cube([2*Gooseneck[OD],Gooseneck[ID],(COB[2] + Protrusion)],center=true);

	}

	}

	//———————-
	// Build it

	if (Layout == "Show") {
	Lamp();
	}

	if (Layout == "Build") {

	}

view raw Chip On Board Heatsink Mount.scad hosted with ❤ by GitHub

2016-01-06

Category: Software

Poughkeepsie ACM Chapter Presentation: Plotting Like It’s 1989!

Microscope Stage Positioner

Olfa Rotary Cutter Spacer

HP 7475A: Superformula Successes

Miniature Chain Mail: Handouts

Lenovo Q150: Setup for HP 7475A Plotter Demo

Chip-on-board LED Desk Lamp Retrofit