Given those, along with the deck radius and notch height (equals the underlying scale height), calculate four points defining the start and end of the ramps and connect the dots:
local a0 = FLNotchOffset;
local p0 = DeckRad * [cos(a0),sin(a0),-];
local a1 = a0 + FLNotchArc;
local p1 = DeckRad * [cos(a1),sin(a1),-];
arc_cw(p1,-DeckRad); // largest arc
local r = DeckRad - ScaleHeight;
local a3 = a1 - FLRampArc;
local p3 = r * [cos(a3),sin(a3),-];
local a4 = a0 + FLRampArc;
local p4 = r * [cos(a4),sin(a4),-];
arc_cw(p4,r); // smallest arc
move(p0); // end of notch
arc_cw([DeckRad,0,-],DeckRad); // round off corner
The arc_cw() functions draw arcs, as you’d expect, with a positive radius tracing the shortest arc and a negative radius for the longest arc. Although I know how that works, I must still preview the result to verify the G-Code does what I want, not what I said.
Following a linkie I can no longer find led me to retrieve the Tektronix Circuit Computer in my Box o’ Slide Rules:
I’m pretty sure it came from Mad Phil’s collection. One can line up the discolored parts of the decks under their cutout windows to restore it to its previous alignment; most likely it sat at the end of a row of books (remember books?) on his reference shelf.
The reverse side lists the equations it can solve, plus pictorial help for the puzzled:
Some searching reveals the original version had three aluminum disks, shaped and milled and photo-printed, with a honkin’ hex nut holding the cursor in place. The one I have seems like laser-printed card stock between plastic laminating film; they don’t make ’em like that any more, either.
TEK PN 003-023 (the paper edition) runs about thirty bucks (modulo the occasional outlier) on eBay, so we’re not dealing in priceless antiquity here. The manual is readily available as a PDF, with photos in the back.
Some doodling produced key measurements:
All the dimensions are hard inches, of course.
Each log decade spans 18°, with the Inductive Frequency scale at 36° for the square root required to calculate circuit resonance.
Generating the log scales requires handling all possible combinations of:
Scales increase clockwise
Scales increase counterclockwise
Ticks point outward
Ticks point inward
Text reads from center
Text reads from rim
I used the 1×100 tick on the outer scale of each deck as the 0° reference for the other scales on that deck. The 0° tick appears at the far right of plots & engravings & suchlike.
The L/R Time Constant (tau = τ) pointer on the top deck and the corresponding τL scale on the bottom deck has (what seems like) an arbitrary -150° offset from the 0° reference.
The Inductive Frequency scale has an offset of 2π, the log of which is 0.79818 = 14.37°.
The risetime calculations have a factor of 2.197, offsetting those pointers from their corresponding τ pointer by 0.342 = log(2.197) = 6.15°.
A fair bit of effort produced a GCMC program creating a full-size check plot of the bottom deck on the MPCNC:
By the conservation of perversity, the image is rotated 90° to put the 1 H tick straight up.
The 3018 can’t handle a 7.75 inch = 196 mm disk, but a CD-size (120 mm OD) engraving came out OK on white plastic filled with black crayon:
The millimeter scale over on the right shows the letters stand a bit under 1 mm tall. And, yes, the middle scale should read upside-down.
Properly filling the engraved lines remains an ongoing experiment. More downforce on the diamond or more passes through the G-Code should produce deeper trenches, perhaps with correspondingly higher ridges along the sides. Sanding & polishing the plastic without removing the ink seems tedious.
The Great Dragorn of Kismet observes I have a gift for picking projects at the cutting edge of consumer demand.
More doodles while figuring the GCMC code produced a summary of the scale offsets:
Musings on the parameters of each scale:
How to draw decades of tick marks:
It turned out easier to build vectors of tick mark values and their corresponding lengths, with another list of ticks to be labeled, than to figure out how to automate those values.
In principle, the grid keeps the object aligned with the machine axes and the blocks put the upper surface more-or-less parallel with the platform. The XY origin, at the G28 location I’ve been using for tool changes, is on the midline of the sole, with Z touched off by probing the platform beside the sole.
The only interesting part of the orthotic is the rigid white plastic plate, which extends about 20 mm into a pocket in the black foam, so the probe area excludes the bendy part.
I’m abusing the bCNC Auto-level probe routine to get the height map, because it produces a tidy file of XYZ coordinates with three header lines describing the overall probe area:
The first two lines give the X and Y coordinate ranges and number of samples. The third line is the Z axis range and probe speed (?). After that, it’s just probed XYZ coordinates, all the way down.
Meshlab can import ASC files consisting of XYZ coordinates, with the ability to skip a specific number of header lines:
If you don’t skip those three lines, then you get three additional points, far off in XYZ space, that will confuse the next step.
Checking the Grid Triangulation box (the default) produces a nicely lofted sheet:
It is, however, a single-sided sheet, not a manifold 3D object. After a few days of screwing around, I’m unable to find any (automatic, reliable, non-manual) way to solidify the thing in Meshlab, so just save it as a PLY file in ASCII format:
Import it into Meshmixer, Ctrl-A to select the whole thing, click (Select →) Edit → Extrude, pick Y-Axis and Flat EndType, then extrude a convenient base in the negative direction:
For whatever reason, some 3D programs show machine-tool coordinates with Z pointing upward and others aim the Z axis at your face. Both must have made sense at the time, because Meshmixer defaults to swapping the Y and Z coordinates on import / export.
The Density slider controls the number of generated faces in the extruded section, so tune for best results.
I have no idea what Harden does.
Accept the result and you have a solid object suitable for further modeling.
The brass probe rod sports a 3/32 inch ball epoxied on its tip, although for my simple needs I could probably use the bare rod:
I clamped the rod to extend a bit beyond the plate, where it can soak up most of the switch release travel, leaving just enough to reset the clickiness after each probe:
The probe responds only to Z motion, not tip deflection in XY, so it’s not particularly good for soft objects with sloped sides, like the insole shown above. It works fine for rigid objects and should suffice to figure the modeling workflow.
The bCNC Auto-Level probe routine scans a grid over a rectangular region:
Which Meshlab turns into a solid model:
That’s the bottom of the insole probed on a 5 mm grid, which takes something over an hour to accomplish.
Focus the camera at whatever distance needed to clear the longest tooling you’ll use or, at least, some convenient distance from the platform. You must touch off Z=0 at the surface before using bCNC’s probe camera alignment, because it will move the camera to the preset focus distance.
Align the camera’s optical axis perpendicular to the table by making it stare into a mirror flat on the platform, then tweaking the camera angles until the crosshair centers on the reflected lens image. This isn’t dead centered, but it’s pretty close:
The camera will be focused on the mirror, not the reflection, as you can tell by the in-focus crud on the mirror. Whenever you focus the lens, you’ll probably move the optical axis, so do the best you can with the fuzzy image.
You can adjust small misalignments with the Haircross (seems backwards to me) Offset values.
A cheap camera’s lens barrel may not be aligned with its optical axis, giving the lens a jaunty tilt when it’s correctly set up:
With the camera focus set correctly, calibrate the camera Offset from the tool (a.k.a. Spindle) axis:
Put a pointy tool at XY=0
Touch off Z=0 on a stack of masking tape
Put a dent in the tape with the bit
Move to the camera’s focused Z level
Make the dent more conspicuous with a Sharpie, as needed
Register the spindle location
Jog to center the crosshair on the dent
Register the camera location
Calibrate the Crosshair ring diameter thusly:
Put an object with a known size on the platform
Touch off Z=0 at its surface
Move to the camera’s focused Z level
Set the Crosshair diameter equal to the known object size
Adjust the Scale value to make the Crosshair overlay reality
For example, calibrating the diameter to 10 mm against a shop scale:
At 10 mm above the CD, setting the camera’s resolution to 11.5 pixel/mm:
The smaller and more rigid CNC 3018-Pro should be able to engrave text faster than the larger and rather springy MPCNC, which could engrave text at about 50 mm/min. This test pattern pushes both cutting depth and engraving speed to absurd values:
Compile the GCMC source to generate G-Code, lash a CD / DVD to the platform (masking tape works fine), touch off the XY coordinates in the center, touch off Z=0 on the surface, then see what happens: