Watching an Abom79 video I saw an interesting way of fastening parts together with friction: one part has a slot in it that’s too small for the other part, but round holes on both sides of the slot. By using a simple hand tool with two round pins that fit in the holes, one of which is mounted on an eccentric with a handle on it, you can exert a very large force to elastically bend the slot open, allowing the other part (in this case, a ceramic cutting insert for a lathe parting blade) to freely move in and out of the slot.
This is a fascinating idea to me. Bolts and other screws also fasten parts together with friction, but they add weight and tend to vibrate free if they aren’t secured with lockwire. (Loctite isn’t considered adequate in aviation.) Screws are inherently very three-dimensional, while this bending-open-jaws approach can I think be arbitrarily close to planar; you can fabricate it with 2-D cutting approaches. And screws take a long time to insert and remove, while this eccentric approach is a quarter-turn of a handle, like a camlock.
Screws get a pretty good mechanical advantage, but eccentrics can in theory have arbitrarily high mechanical advantage, because the relevant output lever arm is at most the eccentric axis displacement distance and diminishes toward zero like a toggle mechanism when the eccentric approaches top dead center; additionally, you could drive the eccentric rotation through a separate toggle mechanism if need be.
I’d previously seen the MTM Snap mill by Jonathan Ward and Nadya Peek, which uses snaplock connectors milled out of HDPE instead of screws, because Neal Gershenfeld loves snaplock connectors. And they’re sort of the same thing as the flexing-jaw connector in the video, or anyway there’s a continuum between them.
Exploring the design possibilities, I think this is a potentially very exciting mechanism offering many possibilities:
Snap-jaw joints potentially offer a repeatedly-assemblable alternative to screw fasteners with several advantages:
You could build a reusable, very inexpensive, very rapid construction kit using high-strength snap-jaw fasteners, which would allow you to rapidly assemble and disassemble a variety of shapes.
Consider a mating pair of such parts, made of mild steel with 250 MPa yield strength and a 200 GPa Young’s modulus, giving 0.125% yield strain. They’re made from 3 mm steel plate (23.7 kg/m²); the first is 2-D cut with a 20-mm-long slot in its edge that tapers from 2.5 mm wide at the edge up to 3 mm at the base of the slot. The second has a corresponding backwards taper ground or rolled into its edge, so that its edge is the full 3 mm thick, while 20 mm from the edge, it’s been thinned down to 2.6 mm. The slot must thus be elastically opened by 0.5 mm or more, 0.25 mm per jaw, to assemble the parts. Then these jaws can be clamped onto the edge anywhere along its length, not just at predefined locations.
Although there is a stop at the base of the slot, it consists of a tongue; the jaws do not join onto the main body of the second piece for another 20 mm, so the total bend in each jaw is 0.25 mm over 40 mm.
The Von Mises yield criterion says the shear yield stress should be about 0.58 of the tensile yield stress (3-½), or 145 MPa, and the shear modulus G = ½E/(1 + nu), where nu is the Poisson ratio (about 0.26 for mild steels) and E is Young’s modulus, which works out to about 79 GPa, so the shear yield strain is about 0.18%. 0.18% of 40 mm is 0.07 mm, which is a lot less than 0.25 mm. This means that if the jaws are so thick and solid that they are deforming in shear instead of flexure when we open them, we have lost the game; we need them to deform almost entirely in flexure. (I need to learn how to calculate that.)
0.25 mm over 40 mm amounts to a radius of curvature of 3200 mm and a diameter of curvature of 40²/0.25 = 6400 mm.
So suppose we make them 5 mm thick. Assuming pure bending, the jaw’s inner edge is 40/3200 radians of a circle of radius 3200+2.5 mm; its outer edge is the same number of radians of a circle of radius 3200-2.5 mm. This amounts to 0.031 mm of compressive or tensile strain, 0.08% strain, which is comfortably less than the 0.125% yield strain limit of the mild-steel material.
But how much force is this biting down on the other plate with if it tries to pull out? Well, that 0.08% strain gives us 160 MPa stress in the material at the extremes, where it’s applying a 2.5 mm lever arm. But as the strain diminishes toward the neutral axis of the beam, so does the lever arm. We need the integral from -1 to 1 of x² (which is 2/3), times 160 MPa, times (2.5 mm)², times the 3 mm thickness of the material, and we get a torque of 2 N m, which is like 800 N applied at a 2.5 mm lever arm. Dividing this by 40 mm we get 50 N, which is a pretty modest force. You wouldn’t even need a special tool.
But that’s when it’s almost all the way pulled out; it increases from 20% of that (10 N) up to that value as the taper pulls the blades apart, for an average bite force of 30 N. The interesting thing, though, is the size of the energy barrier: steel on steel has a kinetic friction coefficient of about 0.6, so it’s an average of 18 N of friction resisting the pull-out force (plus 30 N × 0.5 mm / 20 mm = 0.75 N). But because that’s over 20 mm, the energy barrier is a very significant 0.36 J. If you don’t manage to pull it all the way out, it will tend to move back into place when there is vibration.
A purely-2D-cuttable version is to use a sort of triangle-wave pattern of teeth on the jaws of one plate and a series of slots in the other plate to accommodate the crests of the triangles.
This conformation of the connector type is not very proof against being twisted, without further support; if we turn it inside out so we have two tapered prongs that stick through a slot against the inside of which they are pressing, we obtain a much better purely-2D-cuttable connector which resists more degrees of freedom. The slot can be, for example, 3.1 mm × 40 mm to locate the connector in all dimensions to a reasonable degree of precision (and if it’s not perfectly rectangular, thinning out to 3.0 mm at the edges, that will improve the precision]; or it could be 40 mm × 40 mm to permit positioning the connector anywhere within it at either of two angles; or it could be longer, say 150 mm × 40 mm, to permit further positioning freedom.
To increase the force without vastly increasing the required cantilevered jaw length, we can use rigid jaws mounted on many parallel flexible thin strips (a section of metal with many parallel cuts through it, perpendicular to the edge but not reaching it), which bend into parallel S-curves to allow the jaw section to move. Since the strips would be bending twice, they’d need to be half as thick to reach the same strain, so 2.5 mm, which also halves the torque (and thus, I think, the force) applied by each one. So to reach a 20 J energy barrier for sliding out of place, we would need about 60 strips, occupying about 150 mm of lateral space and providing about 1500 N of peak bite force, for which you would definitely want a special tool. The energy for opening the jaws would be 0.75 J.
What people normally do in practice in such cases is to use a much steeper slope than the 1:40 slope I’m talking about above, using something closer to 1:1 or even 2:1 or 10:1, creating something more like a hook than an inverted wedge, and a much larger displacement than 0.5 mm. This makes the snap connector self-locking (like a screw or the most common kinds of worm drive) without requiring excessive forces to open it, when the opening forces are applied directly to the snap jaws rather than to the joint they secure. Because rounding over or breaking off the snap hook is an alternate means of failure, typically only one side of the snap fastener moves.
(Providing multiple hook tips, like interlocking sawtooths, is another possibility for reducing the failure risk from the snap hook.)
If the snap jaws are grabbing onto the edge of something or into a slot, rather than poking through a hole or grabbing a small object, having two connected sets of jaws in parallel planes positioned some distance apart along the edge would strongly resist two axes of twisting that a single edge-jaw connection is vulnerable to. And if you want an edge that can be reliably grasped with such an edge-jaw connector, a 2-D-cutting way to get one is, rather than trying to roll a reverse taper into the edge, to assemble something like one side of an I-beam, where a narrow strip of material runs along the edge of a plate of material, perhaps held there by snap connectors protruding through it. If the edge is perfectly straight and there are no jaws clamped onto it, the strip can be twisted around its intersection line, but if the strip is curved or there are jaws grabbing it, it should be held firmly in place.
An exciting thing about hook tips with steep slopes is that they provide further mechanical advantage that’s available to press multiple things together. Suppose your hook tips have a 10:1 slope, so 0.4 mm of bite-down movement is permitted by 0.04 mm of snugging up, and you have 1500 N of bite-down force. That multiplies whatever part of the bite-down force isn’t stymied by static friction, potentially all of it if you vibrate the joint enough, so you might be able to get 15 kN of snugging force. (But, with a 250 MPa yield strength, you need 60 mm² of cross-sectional area in tension to withstand 15 kN, so you’d probably want to make such a thing out of 6mm mild steel sheet instead of 3mm.)
An interesting thing about this is that the numbers for the forces needed to fasten and unfasten, or the costs of fabrication, don’t really depend at all on how wide the actual jaw is (and thus its tensile strength), just the flexure that supports it. This might seem like a distinction without a difference, though: if the flexure breaks under tension, what does it matter that the jaw didn’t?
But I think there is a very clever way around this. The movable jaw always has to work against some kind of fixed jaw (whether pressing toward it or pulling away), and the fixed jaw is rigid and not supported on the flexure. Therefore, why not put the hook on the fixed jaw, which can be arbitrarily robust, and make the movable jaw totally smooth so it isn’t subject to tensile forces? This is backwards from the usual snap-connector design, but I think it has a really killer advantage in terms of strength.
In the case where we’re joining the edge of one plate to the face of another, we can’t do the sawtooth thing to prevent the hook from rounding over or breaking off. Instead, we can use multiple rigid hooks that poke through multiple slots in the mating plate, all preloaded with the same flexure-mounted smooth movable jaw.
There are some disadvantages to the hooked-fixed-jaw approach. It means that the parts being joined have some play in the join, depending on exactly how far down the hook ramp the flexure has managed to force the mating parts, so they aren’t precisely locate relative to one another. And an impact could apply the mass of either of the two parts to the purpose of disconnecting the smooth movable jaw. I think these can be mostly eliminated by using a chain of wedges, like those in a tusk-tenon joint, those used to assemble reusable concrete forms, or those in a cotter pin, with only the last “keystone” wedge in the chain using a compliant snap joint to wedge the whole chain tighter and tighter when there’s vibration. The small masses of the keystone wedge and its immediate wedgee prevent impacts from breaching the energy barrier to disassembly.
Being able to make each connection extremely strong means that you can use fewer of them, which lowers both costs and time for assembly and disassembly.
Of course, if you were to apply 1500 N, you need a fastening and unfastening tool.
At 0.5 mm displacement, a simple eccentric lever tool like the one in the Abom79 video would have an 0.25 mm eccentric offset and thus maximum lever arm. A comfortable handle length of 250 mm would thus have a M.A. at worst of 1000:1, halfway through the movement, when the bite force is only 750 N, and the handle force thus 0.75 N plus friction. The peak handle force is just a little past that, and then the M.A. starts to increase togglewise. With a force budget of 10 N, you’d only need a peak M.A. of 75:1, and thus a handle length of 19 mm. (A pullstring might still be a better way to apply the force, though.)
With the snap-fit fastener, though, there’s almost no friction inside the workpiece, just elastic hysteresis, which is insignificant for most common materials at these speeds. The friction is all inside the tool used to force the snap open, where it’s practical to reduce it with material choice and rolling-element bearings, instead of within the part as with a screw. Consider these scenarios:
These 34 mJ are 4.5% of the 750 mJ needed to activate the mechanism, but we pay them twice: once to load the snap jaw, once to unload it. So it’s only 91% efficient.
Consider the mechanical advantage of the screw. A coarse M6 screw has 1mm thread pitch and might be driven by a screwdriver with a 25mm-diameter handle, so each 79 mm of screwdriver motion produces 1 mm of axial screw motion. This is a 79:1 mechanical advantage. To get 15 kN of snugging force you would need to apply 200 N of force at the surface of the screwdriver; you might need a T-handled screwdriver or something. But with an appropriate safety factor an M6 screw can handle a snugging load of only about 2090 N in strength class 12.9, because its effective cross-sectional area is only 20.1 mm². To handle 15 kN you would need a larger screw --- the 60 mm² cross-sectional area I suggested above would be a little bigger than an M10, but Misumi recommends a safety factor of 3-15 depending on the situation, and so a at least an M24. And these larger screws have coarser thread pitch, further decreasing the mechanical advantage.
McHone says laser cutting steel costs US$13-$20 per hour, and 70” per minute is a common cutting speed, which works out to 12¢-19¢ per meter of cut, but sometimes as slow as 20” per minute, which would bring the cost to 66¢ per meter. (Also they suggest 0.005” precision, which is 127 microns in modern units.) AST Manufacturing says plasma is 0.020” precision (500 microns) on materials thicker than 1”, but laser can hit 0.003” (76 microns) and up to 1575 (!) inches per minute.
OSHCut says the nominal 1200-ipm speeds for the laser they bought are misleading because acceleration is the limiting factor, not cutting speed. So curvy contours, angles, traversing between contours, and especially piercing are slower than cutting the contours themselves, but also they say that on their 3kW Trumpf 1030 fiber laser ¾”-thick steel (19mm) cuts at a maximum of 47 inches per minute (20 mm/s), while 0.04”-thick steel (1mm) cuts nominally at 1160 inches per minute (490 mm/s). They measure curviness in radians per inch, and their plot seems to show that at 5 radians per inch (200 radians/m) the 1160 drops by a factor of 8, I guess to about 150 inches/minute (61 mm/s). Even at 1 radian/inch (39 radians/m) it was down to ¼ of max (I guess 290 inches/minute, 120 mm/s). Still higher curvatures added less penalty; even at 30 radians/in. (1200 radians/m) the penalty for 1-mm steel was only about 17×, so I guess 68 in/min or 29 mm/s. For thicker metal the curviness penalty was less, basically no measurable penalty for the 19-mm stuff. Their plot isn’t super well labeled but one of the thicknesses is supposed to cut at 335 ipm (141 mm/s) and I’m guessing that might be 3mm; at 5 radians/in. (200 radians/m) it was only 2× as slow (70 mm/s?) and even at 30 radians/in. (1200 radians/m) the penalty was only 4× (35 mm/s?).
Another way to look at these curvature numbers is as the characteristic feature size, although especially good CAM software can avoid this sometimes for some designs; a closed convex polygon of any shape is 2 pi radians, so a curvature of 200 radians/m means that your closed polygons are about 31.4 mm in perimeter, while 39 radians/m means they’re about 160 mm in perimeter, and 1200 radians/m means they’re 5.2 millimeters in perimeter, which is pretty impressive if your kerf is close to the typical 0.2 mm. Except that it doesn’t include pierce times, so maybe they weren’t really cutting 6 polygons per second, maybe more like 24 radius-0.8-mm 90° corners per second.
Higher-powered 12-kW lasers can cut 12mm steel at 150 ipm, 64 mm/s, but even for straight cuts, laser cutters from 6 kW to 12 kW on 0.5-mm steel all topped out at 3150 ipm (1.3 m/s). JMT has a cutting speed chart cutting 1-mm steel with 4kW from 280 to 2362 ipm (120-1000 mm/s) and 3-mm steel at 120-380 ipm. Interestingly they needed to use either O2 or N2 gas for such thick steel; air was insufficient. Air could cut thin steel faster, and nitrogen faster still, but oxygen was needed for steel over 6.4 mm.
Plasma is cheaper and faster than laser as of 02018 anyway. This article also gives me the term “XY cutting processes” to cover plasma, laser, and waterjet, and mentions the acceleration limitation. Laser vendor Trumpf disagrees, saying plasma is more expensive per hour, while laser is only US$3/hour in operating costs, and also cuts faster (114 ipm (48 mm/s) in ¼” (6.4mm) mild steel rather than “typical plasma”’s 70 ipm, which commenters say is much slower than typical).
A company in Monte Castro called ZYX Mecanizados (4674-6826, zyxmec...@gmail.com) is one possible vendor of the service; they offer plasma, CNC router, laser, and hot-knife cutting, for up to 1000 × 1300 mm. Their website is down but dates from 02014 and it says they cut lots of things but not ferrous metals. There seem to be some other vaguely relevant companies listed in its category on MercadoLibre, but that is probably not really true. Near here Google Maps lists Plasmacenter (Perón 1898, Lomas de Zamora, 4282-3855 or maybe now 6233-5443), but they just sell CNC plasma, oxy, and laser machines. And in Palermo there’s S.A.D.I. Metales, whose web site says they do CNC plasma (1.6 mm to 12.7 mm) and oxy-fuel (4.7 mm to 300 mm) cutting, but who said they just do laser last time I asked. They sell sheet metal from 1 mm to 6.4 mm in thickness.
Sheet steel is sold here as construction material in a weird mix of medieval and modern units: 1500 mm × 3000 mm × 3.2 mm (0.125”) for AR$28650, which at today’s rate of AR$163/US$ is US$176, or US$39/m²; 1220 mm (4 feet) × 2440 mm (8 feet) × 1.25 mm (18-gauge), 20 kg, for AR$9100, US$56, US$19/m², but it also can’t possibly be those dimensions or it would be 29 kg; 1 m × 2 m × 1.25 mm (18-gauge), 20.5 kg, SAE 1010, for AR$7458, US$46, US$23/m², which ought to be 19.75 kg, which is close enough; 1.22 m × 2.44 nm × 2.0 mm (14-gauge) for AR$15043, 49 kg, SAE 1010 from Hierros Torrent, US$92, US$31/m². These are all in the range US$1.43-US$2.80/kg, with the thinnest gauges costing nearly as much per square meter and thus far more per kg.
So, to get a cost estimate, let’s try scaling down the hook thing a little. Say we’re satisfied with the 2kN snugging load a strength-class-12.9 M6 screw can handle, and we get a 10:1 M.A. from the angle of the hook (so we only need 200 N of bite), and 500 microns is enough. And to get 200 N over 500 microns, let’s say my calculations above are okay and each additional 2.5-mm-wide 40-mm-long strip in 3-mm mild steel would give you 25 N of bite, so you need 8 of them; a 20-mm-wide strip cut lengthwise into 8 straight 40-mm strips with 7-9 cuts (although where do we pierce?). And let’s say the US$15/hour number is about right, and 70 mm/s (one of what I think are OSHCut’s numbers) is about right for these cuts. That works out to 6¢ per meter of cut, or 1.9¢ to cut the springs for each such snap connector. The connector itself might occupy more like 1000 mm² (0.001 m²), so the steel thus used costs about 3.9¢, but it can also be serving other roles as structural support.
(At 200 N we don’t need a special tool with eccentrics and bearings and stuff. We can comfortably use snap-ring pliers with an M.A. of 3:1.)
A box of 50 15mm M6 screws costs AR$540 or US$3.31, or 6.6¢ per screw, but those aren’t strength class 12.9 or actually any declared strength class. A box of 25 20 mm class-12.9 M6 screws costs AR$656, 8¢ per screw. Drilling and tapping the holes for a screw costs extra, probably a comparable amount.