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Step 7: Cautions: Open Loops and How to Strengthen Them

A classic newbie error I have witnessed personally from people using finger jointed plate construction is leaving flaps of material to try and stand on their own. This is a very easily encountered pitfall of this kind of construction. While joints relying on a third intermediate joining member like angle irons or L-brackets can use the manufactured perpendicularity, care is needed when directly joining plates together, no matter if they are laser-cut, waterjetted, machined via router, or carved out using your own teeth.

Thinking like a sheet metal fabricator, with skillful use of gussets and imitating "I" or "H" profiles, is essential for maintaining rigidity in assemblies. The fact of the matter is, long spans of plate or sheet are always going to be floppy unless backed up by something out-of-plane with it - i.e. turning moment loads ("bending") into tension and compression as much as possible, where most materials are the strongest.

So, I'm here to illustrate several potential failure points of this style of design as well as how to shore up your design against them.

Effect of Edge Taper on Right-Angle Fastened Plates

Shown in the introductory graphic is the classical failure mode. Because of the edge irregularities that lasers and waterjets tend to generate, you cannot assume the sides of the plate are truly perpendicular. The only way to eliminate this positively is with dynamic head or tilting head machines, which are much more expensive. And notice how the specification even says "virtually" eliminates taper - taper-free is defined as 1 degree of taper, and a usual waterjet or badly focused laser cutter will produce something more like 2 or 3 degrees.

Well, a 1 degree error on an edge translates through Abbe error magnification on a 10cm (4") long part to mean an offset at the top of nearly 2mm (.08"). This might not sound that bad except to engineering professors, but it's very visible to the human eye, and furthermore an unsupported edge like that is much weaker than a supported one (remember Step 2?). If the taper is really bad, like 3 degrees, then the part is going to be out 6mm (1/4") or more at the top. Now that is truly horrible.

Hence, the lesson here is to never depend on a cut edge for alignment if it was made with a nonrigid process, e.g. laser or waterjet. The only way to be sure is to produce the part on a router or mill that is known to be perpendicular, known as being "in tram".

Next, we tackle the stiffness issue, or why your unsupported structure is so wubby.

A Typical Two-Plate Structural Element

Image 2 depicts a fairly typical two plate parallel structure that you might find on a robot or some other mechanical implement. At the end, it has a pin or shaft upon which another element, like the next arm segment, or wheel, rides. In the best case, this is tightened against the sidewalls with fasteners, but not infinitely stiff, so it will bend only in the middle. We assume the base is absolutely rigid and firmly attached to whatever this mechanism goes on, so there is no deformation at the base.

Image 3 shows a sideways 10 pounds of force ("lbforce"). Engineering purists would say that this is a fake unit and that I should really say 44 newtons, but for the sake of easier audience connection I'm going to assume most people know what roughly 10 pounds (or 5 kilograms) feels like.

Units aside, the finite element simulation shows the structure deforming sideways with the walls remaining roughly parallel. The total magnitude of the deformation is actually quite low (0.004" or so), but we will see it is the relative stiffness that counts. The shape is exaggerated on purpose by the simulation to show the final shape of the assembly.

Adding Flanges

One method that can stiffen the structure in the configuration is adding flanges to the sides. Think a "c-channel" or similar. The 4th image shows this example structure, and the 5th image is the results of the simulation with the same force magnitude and location. The simulation shows that this arrangement is already about 3 times as stiff as the original.

Depending on the geometry of the flanges, this relative value could be much more. Notice that they also do not reach quite as far as the location of force application and that the vast majority  This was done because of a practical concern, since whatever it is supporting could take up enough space that extending the flanges all the way out is impossible. It therefore represents an example "middle ground" which you are more likely to encounter.

The example's real-life embodiment is the scooter fork shown in image 6. This example only has one flange (like a T-extrusion), but the concept is the same: without it, the two 1/8" rear forks will be extremely wobbly indeed. This structure also sees forces more on the order of 100+ pounds, instead of 10, because of rider weight, cornering, etc.

Adding a Crossing Member

Another tactic is adding what is known as a web. In structural products parlance, the web is the middle of an I-beam, the element that reaches across the two sides. In the 7th image,the web is depicted as the flat plate in the center. Again, it is made to not quite reach the point of force application out of an example practical concern. For instance, an attached arm joint has a hub which is that large, so the web needs to be further away from the shaft.

Even with the end not well supported, the web configuration is the stiffest of them all - 7 times better than the original!

This is why buildings are made from I-beams.

A great example of using an intermediate web is the 4-bar manipulator arm of my own 2.007 robot, shown in image 8. This arrangement was, unfortunately, only of limited effectiveness because there was still a vast unsupported span in front of the grabber end, letting it flex in a similar manner to image 7. Additionally, I neglected to make a second one of those plates - leaving the bottom very poorly supported. As a result, the arm still moved significantly side to side under applied loads, but fortunately this did not affect the robot operation much.

Closed Loop Flexures

The overarching theme is to avoid using materials, especially thin plates, in bending. Support them with material that is out of the bending plane such that the loads are transferred to them and put them in tension or compression. The remaining few pictures are other examples of things being designed to resist wobbling, for better or for worse.

Making structures like those shown in the original FEA simulation in image 3 is an entire science on its own, and the creations are known as flexure bearings (another example, see figure 2). The neat thing about materials in bending is that they are generally very predictable if the deformations are small, so flexures are valued for their repeatability and immunity from "stiction" that a normal hinge could suffer from. They are found in precision machines and instruments for supporting sensitive adjustments.
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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