It is possible to use these joints for non-perpendicular angles. However, it's important to clarify what is meant by "nonperpdendicular angle".
Refer to the mate seen in the first image. Because the assumption is that these 2D fabricated pieces have straight sides. After all, we're not talking about 5-axis machining here! To intersect two plates at a non-perpendicular angle, there can only be edge contact, plus several much smaller planar (face) contacts.
The second image, which shows the sloped side of Jamison Go
's robot Dominant Mode from the title section, is technically a perpendicular joint. That is, if the sides of the cut pieces are all perfectly square and perpendicular, there exist planar contact amongst the faces in the finger joint. One of the pieces involved in the joint may be trapezoidal, but from its perspective, the mating piece extends straight 90 degrees out in space.
Non-perpendicular joints are not handled well by 2D construction methods. There will be large gaps involved, and the face contact area is reduced significantly compared to a perpendicular one. But perhaps most importantly, there's not really a way to fasten the pieces together.Tab and Slot Length
The 3rd image shows a geometrically derived nonperpendicular joint with equations for the length of the slot and tab with respect to angle. The driving factors are the two material thicknesses t
, and the joint (included) angle θ
. Notice that the equation degenerates into trivial form as the angle becomes perpendicular - at 90 degrees, the length of the slot is just the mating material thickness T. At 0 degrees, the slot is infinitely long, because why are you trying to make objects intersect in real life?Gusseting
might be one solution to fastening mating plates at non-perpendicular angles. Basically a triangle which mates with the two plates and gives them structural support, and commonly seen in welded tube frames
as triangles in the corners.
We extend the concept here to use an open or closed finger joint setup to brace the two mating plates with a 3rd orthogonal plane of material. With a gusset, these joints can become reasonably strong, but only if the gusset itself is well-secured. Care should be taken to make sure the final assembly is actually, you know, assemble-able. A closed gusset might make one plate impossible to slide on and secure!
Overall, though, my opinion of nonperpendicular angles is that they shouldn't be recommended practice because of the ugly panel gaps and reduced strength. This doesn't mean I haven't built any...