3D Printing with Forth
Part I

November 20, 2021

FORTH DAY!

Brad Nelson / @flagxor

Overview

Intro to 3D Printing
G-code and printer control
Constructive Solid Geometry
Signed Distance Fields
Deciding the Path
Fixing my microwave

Reprap

Adrian Bowyer, University of Bath 2005
Open-source 3D Printer that can print itself

https://reprap.org/wiki/RepRap

Prussa i3 (2012, kit 2015)

https://reprap.org/wiki/RepRap

Rectilinear Printer
Moving Heated Bed
Moving Extruder Motor

Kossel (2012)

https://reprap.org/wiki/RepRap

Delta Printer
Stationary Glass Bed
Stationary Motors

My FLSUN Kossel

Kit Version of Kossel
Added Metal Heated Bed
~$200 in 2017

My FLSUN Kossel

Kit Version of Kossel
Added Metal Heated Bed
~$200 in 2017

My FLSUN Kossel

Kit Version of Kossel
Added Metal Heated Bed
~$200 in 2017

My FLSUN Kossel

Kit Version of Kossel
Added Metal Heated Bed
~$200 in 2017

My FLSUN Kossel

First control board weird
FLSUN good about replacing

Materials

PLA - Polylatic Acid
- Polyester made from corn, cassava, sugarcane, or sugar beet pulp.
- Used for recyclable utensils.
- Melts at ~155°C (~311°F).
ABS - Acrylonitrile butadiene styrene
- Mixed terpolymer made from natural gas and petroleum.
- Used for Legos.
- Melts at ~200°C (392°F).

Filament Spool

ATMEGA2560

54 Digital I/O Pins (12-15 can do PWM)
16 Analog Input Pins
5V, 256KB Flash, 8KB SRAM, 4KB EEPROM

Control Board

https://i.stack.imgur.com/8SbR7.png

Marlin Fireware

Open-source G-code control software
Over 150 commands
Tethered or SDcard operation

G-code

Computer Numerical Control (CNC) Language
Appeared 1950! Standardized in 1980 - RS-274
Single letter codes to control:
- X, Y, Z position/movement
- Filament extrusion
- Extruder and bed temperature
- Rebasing / speed

G-code Example


M107 ; fan off
M190 S60 ; set bed temperature to 60
M104 S200 ; set temperature to 200
G28 ; home all axes
G1 F5000 ; set speed 5000mm/min
G1 X0.000 Y0.000 Z5.000

M109 S200 ; wait for temperature 200
M21 ; set units to millimeters
G90 ; use absolute coordinates
M82 ; use absolute distances for extrusion

G92 E0 ; set zero position (E=extruder)
G1 F9000 ; set speed 9000mm/min
G1 X0.000 Y0.000 Z0.300

G-code Example


G1 X-11.600 Y-9.800 E0.009
G1 X-11.300 Y-9.800 E0.018
G1 X-11.000 Y-9.800 E0.027
G1 X-10.700 Y-9.800 E0.036
G1 X-10.400 Y-9.800 E0.045
G1 X-10.100 Y-9.800 E0.054
G1 X-9.800 Y-9.800 E0.063
G1 X-9.500 Y-9.800 E0.072
G1 X-9.200 Y-9.800 E0.081
G1 X-8.900 Y-9.800 E0.090
G1 X-8.600 Y-9.800 E0.099
G1 X-8.300 Y-9.800 E0.108
G1 X-8.000 Y-9.800 E0.117
G1 X-7.700 Y-9.800 E0.126
G1 X-7.400 Y-9.800 E0.135

Movement & Extrusion


G1        ; Linearly interpolate (E.g. G0 goes straight there)
  X0.000  ; X coordinate
  Y0.000  ; Y coordinate
  Z5.000  ; Z coordinate
  E0.3    ; Extrusion position

Describing 3D Models

Platonic Solids
Triangle Meshes
Non-Uniform Rational B-Splines
Voxels
Constructive Solid Geometry

Constructive Solid Geometry

https://en.wikipedia.org/wiki/Constructive_solid_geometry#/media/File:Csg_tree.png


: model
   gpush
       6 mm -7500 um 1500 um - 1 mm translate
       4 mm 3 mm 1 mm prism
   gpop
   gpush
       0 7500 um 10 mm - 5 mm translate
       5 mm 3500 um cylinder
   gpop
   difference
;

Units


: um ;
: mm 1000 * ;
: cm 10 mm * ;

: signoformat ( n -- n d ) s>d swap over dabs ;
: n. ( n -- ) signoformat <# #s rot sign #> type ;
: mm. ( n -- ) signoformat
               <# # # # [char] . hold #s rot sign #> type ;

Printer Head

Track position
Extrusion and flow rate


variable x   variable y   variable z   variable e
variable flow  30 flow !

Signed Distance Fields

Function mapping position to signed distance from the surface of an object
For example a sphere: \[ S(x,y,z) = \sqrt{x^2+y^2+z^2} - r \]

Sphere / Cylinder


: sphere ( r -- n ) x @ square y @ square + z @ square + sqrt swap - ;
: cylinder ( h r -- n )
   x @ square y @ square + sqrt swap - swap z @ abs swap - max ;

Rectangular Prism


: prism ( x y z -- n )
   z @ abs swap - swap y @ abs swap - max swap x @ abs swap - max ;

Union


: union ( a b -- n ) min ;

Intersection


: intersection ( a b -- n ) max ;

Inverse


: inverse ( n -- n ) negate ;

Difference


: difference ( a b -- n ) inverse intersection ;

Transforms


: translate ( x y z -- ) z -! y -! x -! ;
: scale ( x y z -- )
   z @ swap 1000 */ z !
   y @ swap 1000 */ y !
   x @ swap 1000 */ x ! ;
: uscale ( s -- ) dup dup scale ;

Geometry Stack


create geostack 300 cells allot
variable geosp  geostack geosp !
: gunipush   geosp @ !   cell geosp +! ;
: gunipop   cell geosp -!   geosp @ @ ;
: gpush   x @ gunipush y @ gunipush z @ gunipush ;
: gpop   gunipop z ! gunipop y ! gunipop x ! ;

Complex Shapes

Filling Each Layer

Flood fill each layer
Alternate horizontal / vertical bias
Represent x,y as a x+y*slicelength single value
Emit G-code as you go

Floodfill Stack


create floodstack slicelength 100 * cells allot
variable floodsp   floodstack floodsp !
: flooddepth   floodsp @ floodstack - cell / ;
: unflooded   floodsp @ floodstack <> ;
: floodpush   floodsp @ ! cell floodsp +! ;
: floodpop   cell floodsp -! floodsp @ @ ;

https://en.wikipedia.org/wiki/Flood_fill#/media/File:Smiley_fill.gif

Floodfill


variable floodorder
: toggleorder floodorder @ invert floodorder ! ;

: horiflood ( pos -- pos )
   dup 1- floodpush
   dup 1+ floodpush
   dup slicelength - floodpush
   dup slicelength + floodpush ;
: vertiflood ( pos -- pos )
   dup slicelength - floodpush
   dup slicelength + floodpush
   dup 1- floodpush
   dup 1+ floodpush ;

Floodfill


: flooddrain
   begin unflooded while
     floodpop
     dup c@ if
       0 over c!
       floodorder @ if horiflood else vertiflood then
       pointify
       2dup dist 500 um > if 9000 speed moveto
         600 speed else lineto then
     else drop then 
   repeat
;