Tag Archives: Conic Slicing

3D Printing: Conic Slicing for Rotating Tilted Nozzle (RTN) / 4 Axis

State: early draft, mostly simulations with a few tests with 3-axis printer only

Conic sliced overhang model, printing with Rotating Tilted Nozzle (RTN) 90° overhang structure without support


  • 2021/03/08: slicer4rtn 0.2.3 reached (still unreleased), better prints, documenting various settings in more details
  • 2021/03/05: added proper ZHAW reference in the introduction and a few notes
  • 2021/02/27: removed some redundant illustrations and remade some of them, outside-cone vs inside-cone mode & printing
  • 2021/02/26: added inside-cone printing example for inner overhang mode, also early information of slicer4rtn; more animations to observe details of produced G-code, using now also OpenSCAD to simulate G-code and actual nozzle position
  • 2021/02/24: better tests with 20mm cube and overhang structure, included two short G-code simulations as videos, added 20mm sphere and 3D Benchy and discover first issues with volume decomposition and overhang recognition
  • 2021/02/23: first write up, pseudo code and first attempt to conic slice 20mm cube


The main idea is to utilize existing 3D printing slicers but create conic slices for the Rotating Tilted Nozzle (RTN) 4 Axis Printer. ZHAW published in their announcement in 2021/01 something about utilizing existing slicers, but the details remained concealed and later published as a paper but I did not want to wait and pondered on the problem, and came up with a solution. In its current state it’s purely theoretical and untested for now (2021/02) barely tested yet.

Michael Wüthrich confirmed my solution is comparable with their solution. ZHAW planned their paper to be published sometime 2021. So, the main credit goes to ZHAW and the researchers (Prof. Dr. Wilfried Elspass, Dr. Christian Jaeger, Michael Wüthrich, Maurus Gubser, Philip Bos and Simon Holdener) there, I was just impatient and tried to find a solution with the information available.

I also adapted some of the notions Wüthrich introduced in the Novel 4-Axis 3D Printing Process to Print Overhangs Without Support Material paper, e.g. “outside-cone” and “inside-cone” printing as featured in an earlier blog-post already.

Non-Planar Conic Slices

The 4-axis Rotating Tilted Nozzle (RTN) physical setup implies its slices are of non-planar conic shape, allowing to print overhangs without support structure, such as:

Conic slices of an overhang model

I also like to master the conic slices properly as they promise to become a subset of 5 axis printhead (PAX) features too – so it’s worth the effort even if the RTN itself might be too limited in its application with its fixed tilt – we will see.


In a nutshell the steps are following:

  1. sub-divide faces of the model (fine-grained)
  2. map model to inverse conic space
  3. send to slicer
  4. remap G-code to conic space
  5. adding Zrot to G-code

Conic Space Mapping

(x1,y1,z1,rot) = conicSpaceMapping(cx,cy,x,y,z,dir);


  • cx, cy are the conic axis coordinates
  • x, y, z are the input coordinates
  • x1, y1, z1 are the output coordinates
  • rot the rotation angle x,y vs cx,cy
  • dir is either direct (default) or inverse
function conicSpaceMapping(cx,cy,x,y,z,dir='direct') {
   dx = x-cx; 
   dy = y-cy;
   d = sqrt(dx*dx + dy*dy);
   rot = atan2(dy,dx);
   return (x,y,dir=="direct" ? z-d : z+d,rot);


The entire procedure goes like this:

m = subDivide(loadModel("cube.stl"),5);
cx = m.minX + (m.maxX-m.minX)/2;
cy = m.minY + (m.maxY-m.minY)/2;
for(i=0; i<m.vertices.length; i++) {
    m.vertices[i] = conicSpaceMapping(cx,cy,


foreach(line of read_file("temp.gcode")) {
   if ma = line.match("G1 Z([\-\d\.]+)")   // new layer
      z = ma[0];
   else if (x,y,r) = line.match("G1 X([\-\d\.]+) Y([\-\d\.]+)(.*)") {
      (x1,y1,z1,zrot) = conicSpaceMapping(cx,cy,x,y,z,'direct');
      puts("G1 X${x1} Y${y1} Z${z1} A${zrot} ${r}");
   } else

Note: the pseuco-code is incomplete as extrusion E is not yet taken care of, as soon I found a definitive solution I will write it up.


I implemented the pseudo-code with some more details like taking care of G-code E extrusion as well and fine-step linear extrusion – here some early tests using OpenSCAD as STL & G-code viewer and Slic3r as actual slicer:

20mm Cube Conic Sliced

Snapshots of progress of conic sliced 20mm cube:

20mm cube conic sliced G-code
20mm cube conic sliced with rotating tilted nozzle simulation

Overhang Conic Sliced

Snapshots of progress of conic sliced Overhang:

Conic sliced overhang model
Conic sliced overhang model including rotating tilted nozzle simulation

Gallery of Conic Sliced Models

Using Cura as STL and G-code viewer only:

Issues to Resolve

  • test actual G-code in real life
    • verify Axxx / Zrot , verified with G-code simulator coded with OpenSCAD
    • verify Exxx interpolation
  • find good pre-processing face sub-division strategy
    • in its current form the algorithm requires fine-grained sub-divided faces otherwise inaccurate G-code is created which cannot be recovered
  • slice more complex parts
    • 3D Benchy: requires more thorough examination, e.g. volume decomposition to segment roof apart:

  • document all details
  • release source code to public


Some close-ups of conic sliced models:

Outside- vs Inside-Cone Printing

As pointed out in the previous blog-post, the RTN has two main modes of operation, outside-cone and inside-cone printing to cover outside overhangs and inside overhangs – the slicer must recognize those and switch operation mode. Further, these two modes cannot easily be mixed, and need to be segmented or separated, hence speaking of volume segmentation.

This poses significant grow of complexity from just planar slicing, the 4 axis RTN provides features to print 90° overhangs without support structure, but only when the part can be properly analysed and segmented so that those operational mode can be applied.

The difference between inside- and outside-cone printing is to change the order of conic mapping for the model and post slicing:

outside-cone mode

  1. map model inverse conic
  2. slice model
  3. map G-code direct conic

inside-cone mode

  1. map model direct conic
  2. slice model
  3. map G-code inverse conic, Zrot + 180°


The pseudo-code turned into an actual application I named slicer4rtn and is a command-line tool, slicing STL into G-code:

USAGE Slicer4RTN 0.2.3: [<opts>] <file.stl> ...
       -v or --verbose      increase verbosity
       --version            display version and exit
       -k or --keep         keep all temporary files (temp.stl, temp.gcode)
       --subdivide=<n>      set midpoint subdivisions (default: 2)
       --mode=<mode>        set cone mode, either 'outside' or 'inside' (default: 'outside')
       --output=<fname>     override default naming convention file.stl -> file.gcode
       --axis=<axis>        set axis count of printer: 3, 4 or 5 (default: 4)
       --angle=<angle>      set angle of cone (default: 45)
       --center=<cx,cy>     set conic slicing center (default: 0,0)
       --bed-center=<cx,cy> set bed-enter, only affects output G-code (default: 100,100)
       --fixed-rot=<angle>  set fixed rotation angle, usable if --axis=3 but 4-axis or 5-axis printer is target
       --zoff=<v>           define z-offset, will be added to G1 … Z<v>
       --erate=<f>          define extrusion rate (multiplier, default = 1)
       --efmin=<v>          define extrusion factor minimum, (default = 0.01)
       --efmax=<v>          define extrusion factor maximum, (default = 3)
       --motion-minz=<v>    define minimum Z level for motion (without extrusion) (default = 0.2)
       --max-speed=<s>      define maximum speed (default: 0)
       --recenter           recenter model X- & Y-wise
       --core-slicer=<slicer> set slicer (default 'slic3r')
       --slicer.<k>=<v>     add additional slicer arguments, e.g. --slicer.fill-density=0
       --<k>=<v>            all other arguments not for slicer4rtn will be passed to the core slicer (slic3r)

       ./slicer4rtn sphere.stl
       ./slicer4rtn overhang.stl --output=sample.gcode
       ./slicer4rtn overhang.stl --axis=5 --output=sample.gcode
       ./slicer4rtn overhang.stl --axis=3 --output=sample-belt-printer.gcode --fill-density=5

and actual usage looks like this:

% slicer4rtn cube.stl 
Slicer4RTN: processing 'cube.stl'
Slicer4RTN:    #1/5 read stl
Slicer4RTN:       #1/2 subdivide (44 vertices)
Slicer4RTN:       #2/2 subdivide (188 vertices)
Slicer4RTN:    #2/5 map vertices
Slicer4RTN:    #3/5 write temporary stl
Slicer4RTN:    #4/5 slice stl
=> Processing triangulated mesh
=> Generating perimeters
=> Preparing infill
=> Infilling layers
=> Exporting G-code to temp.gcode
Done. Process took 0 minutes and 0.570 seconds
Filament required: 706.4mm (5.0cm3)
Slicer4RTN:    #5/5 remap gcode to 'cube.gcode'
Slicer4RTN: done.

I gonna release slicer4rtn eventually, in its early version the model currently can only be sliced for outside-cone or inside-cone printing, so the volume decomposition or segmentation needs to be done separately. For now it helps me to verify some of the 4-axis and 5-axis printer designs I work on.

Ashtar K RTN printing conic sliced 20mm cube (close up, animation)
Ashtar K RTN printing conic sliced overhang model without support structure (close up, animation)


Defines the outside- or inside-cone mode printing/slicing:

  • outside (default): for outside going overhangs
  • inside: for inside going overhangs

Note: currently you need to define those manually, there is no auto-detection which is where (aka volume decomposition/segmenting).


By default the STL is midpoint divided 2 times (iterations), you may disable it with --subdivide=0 or increase the value which will generate a lot of triangles. In order the procedure to work a fine-grained model is required, especially for very simple models like a cube.


By using --axis=3 the resulting G-code is non-rotating nozzle yet tilted, like a belt-printer setup, for targeting 5-axis / Penta Axis (PAX) choosing --axis=5 and it sets the G-code B45 (Trot = 45°) for each G1 statement.


By using --angle=30 the slicing cone angle can be changed:

It might help to experiment to print with ordinary vertical nozzle (non-tilted) to print 90° overhangs, something like this:

--angle=22.5 or a bit less with --axis=4, but printing on a vertical nozzle

As soon I tried it in real-life I will document using slicer4rtn with ordinary setup as well.
Update 2021/03/03: first tests are promising, actually a breakthrough printing 90° overhangs with a vertical nozzle – the most common 3-axis 3D printer setup.


Unlike with ordinary slicers, conic slicing requires to set a center of the conic slicing, it may not be necessarily in the center of the model, but offsetted, this is done with e.g. --center=50,10 as to the STL file; by default --center=0,0.

Note: not all STL files are properly centered, they may be off already; this directly affects the conic center position. Use --recenter switch to force the STL to be centered X- & Y-wise.

Print3r & Slicer4RTN

As of print3r 0.3.2 or later slicer4rtn is supported as well:

  • .config/printer4/printer/<yourprinter>.ini and make a copy like .config/print3r/printer/<yourprinter>-rtn.ini add following lines:
display_update = off
slicer = slicer4rtn
external-perimeter-speed = 10%

and alter the start-gcode line with increasing Z motion as well, e.g for my Prusa-i3 clone it has a M6 threaded rod, which means one revolution (200 full steps) 1mm Z motion, hence

start-gcode = ".....\nM203 Z6\n...."

increased Z motion speed to come close to X- and Y- speed, it creates more even extrusions, nicer prints.

Actual use with print3r goes then like this, my Prusa-i3 clone named y3228-rtn now:

% print3r --printer=y3228-rtn --random-placement print overhang4l4mm.stl
% print3r --printer=y3228-rtn --layer-height=0.3 --fill-density=5 print overhang4l4mm.stl
% print3r --printer=y3228-rtn --scad print 'sphere(10)' --fill-density=5

it slices and forwards the G-code according your setup.

Test Prints

As soon I built the RTN printhead on one of my printers I will post photos of the first prints. For now (2021/03) I only printed conic sliced pieces on a 3-axis 3D printer.


As I progress I will update this blog-post.

With conic sliced G-code there are many first layers . . .

That’s it.

3D Printing: Rotating Tilted Nozzle 4th Axis Option – Draft

Status: just collecting information and start a simple design


  • 2021/03/01: added brief animation of simulated print of conic sliced overhang model
  • 2021/02/23: added brief animation (Zrot=-180° .. 180°)
  • 2021/01/31: maturing printhead with heatsink fan and part cooler
  • 2021/01/28: Outside/Inside Cone printing explained with example, Considerations (Pros/Cons) added
  • 2021/01/27: more detailed illustrations and slicing renderings, published as a draft
  • 2021/01/22: adding conic slicing examples
  • 2021/01/21: first version with rotating bowden printhead

RotBot by ZHAW School of Engineering Zurich

RotBot by ZHAW School of Engineering Zurich (2021/01/13), rotating tilted nozzle

As featured on Hackaday January 16, 2021 and other sites, a “Novel 4-Axis 3D Printing Process to Print Overhangs Without Support Material” by ZHAW School of Engineering (Zurich, Switzerland), from the abstract of the paper:

[..] a novel 4-axis FDM printing process with a newly designed printhead, for the printing of overhangs without support structures. With conventional FDM printing, overhangs of more than 45deg–60deg must be supported.

For this novel printing process, the printhead is rotated 45° around a horizontal axis and equipped with a vertical, rotational axis. The printhead no longer follows layers parallel to the build platform, but moves on the surface of a 45deg cone. The printing cone increases in diameter from layer to layer. With this cone-shaped layers, the printable angles increases by 45°, which leads to printable overhangs of up to approximately 100°.

New slicing strategies for this printing process have been developed to slice the parts for the novel printing process. The feasibility of the concept has been prototypically demonstrated. The novel design achieves the advantages of higher speed and quality with lower cost at the same time.

A brief video sequence of printing (YouTube) shows the machine movement. Unfortunately, as of 2021/01 not much more details have been published by ZHAW except a paywalled paper [sigh] which contains useful overview of their research. I contacted ZHAW and Michael Wuethrich mentioned that they are in negotiations with different companies to develop a product (2021/01) and eventually release the details of their slicing approach with pre- and post-processing while using an ordinary slicer.

Update 2021/02/27: I started with a 4-axis conic slicer.

Rotating Tilted Nozzle (RTN) Option

I thought to try my own implementation of this Rotating Titled Nozzle 4 Axis option. The main idea to keep the entire hotend in Bowden style and rotate that around only once (non-continuous) with all wires, that would simplify things greatly:

The challenge is the +/-180° position when the nozzle opening looks forward, where the printhead bowden tube (and all cables) comes most close to the X beam. As a consequence only -180° to +180° rotation is allowed and not multiple revolutions.

It would also mean, once the printhead reaches -180°, and it has to rotate to +180° and decrease from there again to fulfill 360° rotation – whether this is suitable has to be seen, this likely creates a seam there.

The main advantage of this simplified 4 axis approach is to use existing pieces plus just an additional NEMA 17 motor.

Update 2021/01/26: Wuethrich from ZHAW mentioned that they started first also with a full printhead rotating but then switched to the more complex continuous rotating printhead to avoid a seam, have direct drive extruder, faster prints as simpler decision making to change rotation direction and no start/stop of rotation and de/acceleration when reaching -180/+180° position.

Single Revolution with Rotation Shadow

As I pondered on the limits of single rotation approach, there is a range where the bowden tube (and all wires with it) is touching and bending on the X carriage or printhead holder – let’s call it the rotation shadow – ideally it would be zero or slightly sub-zero to have a bit overlap to conceal a possible seam with “ironing” the section (move nozzle over section without extruding).

E3D Volcano

My first attempt is modeling with E3D Volcano hotend like the RotBot by ZHAW:

Micro Swiss / CR 10 Hotend

And as alternative the smaller Micro Swiss / CR 10 printhead which gives significant more space for the bowden tube (and all wires with it) to bend or flex near -180/+180°:

Comparison Volcano vs Micro Swiss

At this point I continue with the Micro Swiss option, as the smaller heatsink gives me more space to make full 360° turn with -180° to +180° and have ~0° rotation shadow, perhaps even sub-zero as of overlapping.

Slicing for Rotating Tilted Nozzle: Conic Slicing

I had to visualize the novel conic slicing approach as mentioned in the article and in the video:

f(Z rot, C height, R) ⟹ X, Y, Z

X = sin(Z rot) * R
Y = -cos(Z rot) * R
Z = C height / sqrt(2)

Z rot = atan2( -Y, X )
R = sqrt( X*X + Y*Y )
C height = Z * sqrt(2)

A single conic slice is covered by Z rot, C height and R, whereas slices are separated by increasing Z offset to C height, forming conic slices on top of each other:

Let’s inspect the motion of a single layer: it’s curved – obviously – in X, Y and Z – this means, the Z axis has way more motion than in cartesian XZ Prusa-Mendel setup where the Z axis only changes once a layer is finished, here with cone-slicing every trace or track all traditional 3 axis are in motion, plus the 4th – the tangent on that conic trace.

Planar vs Conic Layers
Multiple solids sliced planar and in conic manner

See more details on Conic Slicing for Rotating Tilted Nozzle (RTN).

Different Print Modes

The 45° tilted printhead allows three print modes:

  • non-rotation nozzle with planar Z layers (with ordinary slicer), acts like belt-printer in one direction: overhangs in one direction without support
  • rotation nozzle with planar Z layers (requires dedicated slicer), might support near 90° overhangs of a certain length in all X/Y plane directions as well – but needs to be tested
  • rotation nozzle with conic Z layers (requires dedicated slicer or pre- and post-processing while using ordinary slicers)

And by choosing the position of the “axis” of the conic slicing within the model and the cone direction matters then as well:

The last piece with inside and outside looking overhangs requires a switch of nozzle direction, e.g by default the sliced cones are ordered ▲ (outside-in or outside-cones) where outward overhangs work, but for inward overhangs the opposite direction of the nozzle looking outside is required ▼(inside-out or inside-cones), like this piece:

So the slicing software needs to recognize this, and the sliced cones switched either ▼ or ▲ according Z level.

These aspects opens a whole new range of considerations how to orient a piece and where to position the newly introduced slicing axis, and which kind of cones need to laid at which level.

Issues to Resolve

  • Heatsink fan mount: needs to be mounted for both variants, Micro Swiss and E3D Volcano ideally
  • Part cooler:
    • have the part cooler rotate on Z axis as well? yes for now
    • using a flexible pipe to blow air near the nozzle instead

  • Z rotation calibration:
    • alike with X or Y stop, but a trigger rotating from one direction only and then set a angle offset
  • Z rotation motor mount adaptable for different kind of printheads
    • keep it modular
    • ensure the nozzle end is centered (allow simple center calibration)
  • Properly document design and features of Rotating Tilted Nozzle as there isn’t much detail information available
  • 3D printer firmware support
    • Marlin: support for 4th axis?
  • 3D slicing software support



  • conic layers: printing 90° overhangs without support, given some conditions are met:
    • overhangs must be horizontally or vertically rotational symmetric and aligned with the cone axis to switch from outside to inside cone printing or vice-versa (to do: more use cases explored and documented)
  • conic layers: stronger pieces as layers cross X, Y and Z in non-planar manner, mechanical forces distribute further than just planar layers
  • planar layers / rotating nozzle: perhaps close to 90° overhangs (speculative) requires new overhang algorithms in slicer


  • additional mechanical complexity
    • fine-tuning nozzle center calibration
  • additional slicing software complexity
    • new slicer software supporting different printing modes (conic layers, planar layers w/ rotating nozzle)
    • conic layers: more things to consider (preferably recognized by the slicing software):
      • overhangs must be horizontally or vertically rotational symmetric and align with cone axis to take advantage of it (complex compartmentalizing of different cone-direction per overhang and newly introduced seams between those)

Ashtar K with Rotating Tilted Nozzle (RTN)

The additional Y offset is about 20mm, and losing apprx. 50 mm in Z build volume in its current form:

Ashtar K RTN (animated)
Ashtar K RTN printing conic sliced overhang model (animated)

I will update this blog-post as I progress or find other people with alike ideas and summarize the findings.


See Also

That’s it.