Step 3: Finger Joints for Non-Perpendicular Angles

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 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?


A gusset 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...
Yet another incredibly informative and well written instructable, nice job! Love the FEA’s and especially enjoyed your notes on set screws. My goto sources are always McMaster and ServoCity. Similar to your RoyMech site I’ve used http://www.gizmology.net/ for reference many times.
I knew I was forgetting something! Gizmology has been added to the end - I may sprinkle relevant links in the middle too.
http://web.mit.edu/2.75/fundamentals/FUNdaMENTALS.html is the correct link now, it's a great resourc, especially for offline use. THANK YOU FOR THIS INSTRUCTABLE!
<a href="http://web.mit.edu/2.75/fundamentals/FUNdaMENTALS.html" rel="nofollow">http://web.mit.edu/2.75/fundamentals/FUNdaMENTALS.html</a>&nbsp;whoops.&nbsp;
nice one
Re using one part to template tthe other, &quot;dimpling&quot; -- mention transfer punches here?
Probably worth it. I was definitely in &quot;slummin' high school&quot; mode then, when we didn't have a set of center punches much less transfer punches! I'll look to adding it in.
Wow that was incredibly comprehensive! Are there still robot combat competitions going on?
Hell yeah. Primarily small weight classes and these days grassroots-level and builder run. The big event is RoboGames: http://robogames.net/index.php and Combots: http://combots.net/, and on the east coast, NERC: http://www.nerc.us/ <br> <br>Various other local clubs and organizations exist also. A current listing of events is on buildersdb: http://buildersdb.com/
This might be my new favourite Instructable. Great info!
Thanks for sharing that. <br>One suggestion to add for using set screws in transmitting torque on shafts (only works if the shaft and hub are the same material and ends flush) is to use the set screw as a key - drill and thread the keyway parallel to shaft on the joint between the shaft and hub.
Wow, that is some invaluable mechanical design info. I thoroughly enjoyed the read and I feel like I just took an engineering class, an incredibly fun one. Seriously, amazing detail, thanks a bunch! <br> <br>Simply out of pure curiosity, why weren't taped holes used over T-slots more often? I'm guessing that it didn't fit the 2D fab theme of the class? <br> <br>PS: Working in that shop must have been like a dream come true, I'm olive green with envy :)
Purely as a matter of convenience. The t-nutted holes are not nearly as strong as a properly drilled and tapped hole due to the number of inside square edges. It's a matter of recognizing when the structural loads in the device can be borne by material-on-material interference (the slots and tabs) and then having the fasteners (t-slots) only be there to keep it all together. There are far more instances when drilling and tapping is stronger than using t-nuts.
Excellent! Thank you! <br> <br>Suggestion for an addition: how do you align parallel guide rails on which bushings will slide? Also, how do you keep things sliding freely when temperatures change? <br>Specifically, in my 3D printer project I have an aluminum carriage supported by 4 bronze bushings that slide on guide rails. The print-bed is bolted to the carriage and is heated. As the print bed heats up, it expands, applying force to the bolts that stand it off the carriage, which in turn bend the carriage, which in turn misaligns the bushings.
The design you describe is a classic &quot;overconstrained slide&quot;. It's very sensitive to change in the center distance (gap) between the two rails regardless of what you do to the bushings. <br> <br>Generally you have only 3 bushings - two on one axis to constrain it against planar motion (up/down, left/right) and against tilting/pitching, which are two rotations. And one on the other to make sure it does not pivot on the first axis (rolling). The result is only one motion possible (along the rail). Four bushings adds another constraint which is technically unnecessary, and for it to not impede the motion of the slide, they all have to act perfectly in line and on the same axes. Any misalignment of the rails or of the bushings, then would seize up the slide, as you've noticed. <br> <br>The solution is usually to use 3 bushings - two on one rail, one on the other, and also 'float' the 3rd bushing on a mount which is compliant to misalignment in the center distance. For small applications it's sufficient to just use one of those rubber-mounted self-aligning bushings. <br> <br>In addition, your issue seems to involve flexing of the entire carriage structure which can bind up the two-bushing side too, unless they are also self-aligning. Short of isolating the hot build bed from the carriage, perhaps one or more of the bushings on the two-bushing rail should be also flexible types. It's less rigorous machine design but also a practical solution.
Sup everyone, <br> <br>Feel free to chat amongst thyselves and ask questions. Interesting discussions could very well get folded into the document for everyone to reference.
Well done.
That was great! Now can you come over and help me build my Spencer Aircar?

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