Background: What's a Belt Printer's Coordinate system?

For "normal" Cartesian (Portal, Cube) or Cylindrical (Delta) coordinate printers, the same Design Consideratons are to be kept in mind. But on a Belt Printer aka Printer Mill, the conversion from cartesian design space to cartesian or cylindrical printer coordinates is not applied in the same fashion, and as such some considerations based on subsequent laying down of full levels do not apply the same: While there is a common alignment of two axis, the third axis is tilted forward and the printhead does move in the angled X'Y'-Plane. While the Belt moves only in one direction, never backwards, there is a component of negative movement in that direction by lifting the printhead...

The formula for how the new coordinate system is translated to is thus as follows $$X'=-X$$ $$Y'=\cos(\alpha)Z$$ $$Z'=Y-\sin(\alpha)Z$$ To Illustrate this: The Red-Green-Blue is the orthonormal cartesian coordinate system. and the Magenta-Yellow-Cyan is the coordinate system the printer moves in: enter image description here

The most common angle for currently available designs is 45° as in the Blackbelt or the coming Creality Belt Printer (pre-production in December 2020), making the math for the slicer somewhat easier as $\sin(45°)=\cos(45°)$. As a result of all the math, there is a Cura Derivate, the BB Cura 3.6.2.


What impact does this movement pattern of laying down in an angle upwards have on considerations that have to be taken in the design stage of a model for 3D printing?

  • $\begingroup$ Maker's Muse has a video talking a bit about this. $\endgroup$ – R.. GitHub STOP HELPING ICE Dec 3 '20 at 1:30
  • $\begingroup$ @R..GitHubSTOPHELPINGICE And so have others, like Joel $\endgroup$ – Trish Dec 3 '20 at 12:08
  1. The first and most important design consideration is the overhang. Normally, when designing a part, you would make considerations based on the fact that gravity will act on the part from the "bottom" towards the top. As a result, when I am designing a part, I am always mindful of the fact that anything which protrudes outside of the intended printing base will be subject to "overhang" forces. Therefore, based on the layer height and nozzle diameter, there is a limit to the maximum overhang angle that can be serviced by the printer. Just as a side note, printers that co-extrude dissolvable supports, do not have overhang problems.

  2. Additionally there are structural considerations with the laminations being at an angle, especially with holes that are intended to have heat-set inserts. Normally, when applying an insert the pressure is perpendicular to the layers. However, depending on where the hole is needed and how the part was printed, the inserting process could promote delamination of the layers and early part failure. It could be even worse with holes that are being threaded subsequent to printing.

  3. Because the first few layers are going down at an angle, the layer adhesion will be unknown.

At design time, all you would need to do is keep an eye on those overhangs. I'd start all models on a plane that was at a 45degree angle. That way I can see the effect of having it being printed on its side rather than perpendicular to the bed.

"The first 3D-printed boat, 'built' by the world's largest 3D printer" was also printed with the nozzle at an angle to the bed; and that seems to have worked out well.

  • $\begingroup$ The design of a belt printer puts the printhead to print in layers tilted by some 45° to the XY-plane. How would this impact the design considerations? $\endgroup$ – Trish Dec 2 '20 at 13:11

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