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
, 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.