How to always have short bridges with complex shaped overhangs / gaps - OpenSCAD and Fusion 360

How to Always Achieve the Optimal Bridging Angle

In most slicers, you can only set a single bridging angle, which then applies to all overhangs. This isn’t ideal for circular overhangs or those with complex paths. Ideally, the bridging should always be perpendicular to the wall of the overhang. This design trick allows you to achieve that.

We will increase the height of the gap by one filament layer and fill this additional layer with rectangles that are exactly one layer high and perpendicular to the gap's wall.

My demo files were created using OpenSCAD and Fusion 360, but the concept can easily be adapted to other design tools.

The Problem

Let’s first look at a model with an internal, fully covered gap:

When cutting off the top surface the gap looks like this:

If we slice this model we will get bridges like this. Note that my bridging angle is set to 0°:

At the bottom left the bridges are perfectly perpendicular to the gap but at the top they have the worst possible orientation, leading to very long bridging distances. This cannot be fixed, since in the usual slicers we can only specify one bridging angle per layer, if at all. No matter how we choose it, at some point along the circle the bridges will be tangent and will therefore have to span extremely long distances.

The Solution

The idea is to increase the height of the gap by one layer height and to place small rectangles in this additional space. The rectangles lie perpendicular to the gap and will thus be sliced with perimeters that are perfectly perpendicular to the gap.

The following figure shows the concept:

Width of the rectangles

The width of the rectangles must always be exactly a multiple of twice the width of the wall lines layed by the printer. For example, if you use a 0.4-mm nozzle, a wall line is typically around 0.45mm wide if not modified in the slicer's settings. Therefore, our rectangles would need to be 0.9mm (one perimeter), 1.8mm (two perimeters), 2.7mm (three perimeters) wide, and so on. By choosing the width of the rectangles this way, we prevent the slicer from generating infill that would hang freely in the air.

You can set the wall line width in your slicer. The comments in the scad-files explain in detail which properties of PrusaSlicer and OrcaSlicer control the wall line width and how to calculate a weighted wall line width if you set different values for external and internal walls. Nonetheless, I recommend to always set the same width for external and internal walls because this way you have the most freedom to chose the width of the rectangles.

In the SCAD circle example, I chose a width of the rectangles that is exactly twice the width of the walls produced by the printer. Since we saw that each wall usually consists of multiple wall lines (perimeters), it is calculated as follows:

width = 2 * lineWidth * wallCount

The rectangles can be narrower than the calculated width but must not be wider to avoid infill. So if for instance you print with 4 perimeters you can choose the rectangles' width to be 2, 4, 6, or 8 wall lines. If you would choose a width larger than 8 wall lines, the rectangle wouldn't be completely covered by 4 perimeters on each side and the rectangle's center would be sliced with infill that has nothing to lay on.

Number of rectangles

The number of the rectangles depends on the length of the groove. We need to make sure there are tiny gaps between the rectangles so that the slicer actually adds perimeters to each one individually. Thus, we calculate the circumference of the inner radius of the gap and divide it by the width of the rectangles:

count = (PI * innerDiameter) / width

Please note, that the images show half circles but the formula considers a full circle.

In some cases, especially if the gap has sharp turns, it might be necessary to reduce the number of rectangles manually to avoid overlapping of rectangles which again would lead to infill. If you have to adjust the number of rectangles manually it is usually a good idea to make the rectangles as narrow as possible (2 wall lines). See the comments in bridging-path.scad for details.

Slicing

Doing so results in bridges as shown in the following image:

The top model has supporting rectangles while the lower one is the original model. Taking a look at the details we can see the rectangles (green emphasis) and how the perimeters are perfectly perpendicular to the gap:

Conclusion and Complex Paths

Please see the OpenSCAD files for more details and actual implementations.

For more complex paths the calculations are different since the orientation of the rectangles cannot simply be determined by rotating it by a fixed angle but the tangent of the path at the respective position has to be considered. See the file bridging-path.scad for an example implementation and an in-depth explanation in the file's comments.

Fusion 360

In Fusion 360 you can achieve the same with the "Pattern on Path" tool.

Follow these steps:

1. Create the gap you want to bridge along a path. In my example I used a Fit Point Spline and offset it to both sides.

2. Copy the path (the original Fit Point Spline) to a new sketch. Raise that sketch such that it lies one layer height (e. g. 0.2mm) below the top of the gap

3. In that new sketch draw a new rectangle perpendicular to the path. The rectangle should be long enough to bridge the gap everywhere. In my example I offset the spline by 3mm to both sides, creating a 6mm wide gap and chose the rectangle to be 7mm long. Choose the width of the rectangle as explained above depending on the wall line width of your printer.

4. Extrude the rectangle by one layer height. Make sure to create a new body (don't join).

5. Select the newly created body and select Create -> Pattern -> Pattern on Path. In the Pattern on Path dialog set

   1. Object Type: Bodies

   2. Objects: the body of the rectangle, should already be selected

   3. Path: Select the path

   4. Orientation: Path Direction (!important)

6. Drag the blue arrow along the path to the end of the gap

7. Adjust the quantity of the copies of the rectangle such that tiny gaps remain between the rectangles at the sharpest turn of the path

8. Click OK

For illustration see the enclosed bridging-path-fusion360.f3d file.

I hope this helps.