# 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:

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.

# Question

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?

• @R..GitHubSTOPHELPINGICE And so have others, like Joel Dec 3, 2020 at 12:08