It also introduces a weak point, aka shear bolt, controlling what breaks if the system is overloaded. If the chain pins can handle 1500# (or whatever the breaking strength is), and the motors only provide less than 10 percent of that (was it 66#?) then the bolts holding the chains to the arms can be substantially weaker than the pins and still be just fine. If something causes a major failure, like the 800# gorilla jumps on a chain, then the bolts protect the stronger bits
it’s very true that we are not driving things to their max load, the chains are
designed for a failure load in the 800 pound range, but their listed working
load is only ~80 pounds
we should be far below where the chains fail, which gives us a chance of
getting by with normal bolts instead of the hardened pins, it’s just a point to
be concerned about.
what we don’t have any idea about so far is what the strength of the arms is
going to be. I have no concerns about the strength under tension (the bottom
horizontal arm), my concern is the possibility of the upper horizontal arm
buckling under the compression load, or the vertical arm bending (mostly about
the vertical arm bending, the lever arms mean that if the chain is pulling at 66
pounds, the upper horizontal arm is only seeing 33 pounds in compression)
My properties of materials class was around the time of the first moon landing…
Looks like a conservative bending stress for stainless (used 303, good enough for the napkin) is around 66ksi (2/3 of 100k yield, itself125k rounded down). 3/16 of that (rounding width to 1") is a darn big number. Somebody more current than I can double check.
I can’t bend room temp 1" x 3/16 x 12" mystery mild steel by hand without a cheater, although I haven’t tried for a while, and that might have been 1/8 or something else.
what about 3/16 aluminum?
I’m not sure “can bend by hand” is the right measurement, we have up to 130
pounds of force here, I don’t think “by hand” is that strong (is it??)
Edit, found an online beam bending stress calculator for regular steel. One end fixed, the force applied at the other end, figured it with the force against the wide side.
0.02" deflection with 130# over 6" pulling on the end of the arm, although that doesn’t consider twisting. That’s close to a 64th. Doubling up sides is starting to look like a good idea, subject to review by somebody that remembers it better than me. At 12" it’s around 0.16", too much.
Getting a specially shaped pin fabricated by turning on a lathe is
cheap and easy.
The buckling strength ai the kink is a function of the length of the
link, its cross section, and the direction of the force applied compared
to the link’s axis, much as it it is function of the material
properties.
Also, this 130lb estimate that David is using is system wide, not per chain. It’s also an extreme maximum number based on motor capability, not on the geometry of the chains. You would have to overrun the sled 9.18" above the top of the work (centered) to see 66lbs of stress in static chains (with a 20lb sled). I am not accounting for dynamic forces in that math.
That 66 pound number (which is where the 130 is coming from) is the stall force for the motors.
In a static condition the highest possible chain tension with a 20 pound sled is 33.26 pounds for each chain (uder normal circumstances). Obviously the tension forces could (and probably do) spike above that from time to time (sled drag friction, knots in wood, dull router bits, extreme stops/starts or direction changes, etc. etc.) But the thing to note is that those are likely spikes, not continual loads. That means that if a linkage arm flexes at extremely high loads it will be momentary, not continual - which theoretically means that even a tiny flex under the most extreme possible circumstances probably wouldn’t affect overall cut accuracy since most of the time the system will be under “normal” tension conditions (<35lbs per chain). I suppose it could make a sudden vertical turn-around point have a tiny extra chip missing.
I wonder what the deflection would be using 66lbs…
I am not the right guy to ask about calculating such things 
I plan to build a few linkages soon and test them to their breaking point (and measure forces). I will certainly post my findings!
1 Like
Thanks for finding this.
with the top mount arms that I’m doing, we only have 3" hanging out being pulled, so I think we care about a 3"long beam instead of a 6" long beam.
that reduces the deflection to 0.003" for steel or 0.009" for aluminum
If we turn the bar sideways, the deflection and psi go up, but with a 3" beam are still low enough to not matter much (and not permanently bend), with a 6" beam that does get high enough to permanently bend the metal (if I’m reading everything correctly.
I think this means that even if the vertical bar was turned sideways and 130 pounds pull on it, it wouldn’t put a permanent bend in it.
I also think that this means common 6061 aluminum would do the job as well as steel.
could someone else please double-check the numbers?
even for something as small as a 3/32" pin?
In this case, the link we are talking about is 5.5" long, 3/16 x 3/4 and the force is directly down the axis of the link.
given the small amount of deflection according to the calculator if the force was applied at right angles to the end (pulling up on the link), I think it’s safe to say that pushing in won’t cause it to buckle.
@dlang: when doing your bending calc, a more accurate way than taking a
3" bar is to model the actual length of the bar, and add a pin
constraint to the calculator where the pin would go in real life. That
would make a difference to the deflection.
do you have a calculator that will show this? the one linked to doesn’t have this option.
it’s 6" from the first pin to the second pin, and 3" to the third pin. The first two pins connect to links (the first of which will be under compression, the second will be under tension), the third pin connects to the chain.
@dlang I think this one will calculate complex linkages with pins…
https://www.simscale.com/
I’ve used it very little and I’ve only calculated forces on single components so far but I think you can calculate moving linkages.
The linkage kits are available!! 
They are only $30 and that includes all laser cut parts and all hardware needed to assemble the linkages. You can buy them on my Etsy store here: Maslow Linkage
Right now the shipping estimate should be really close to the real cost. If actual shipping ends up being more I’ll cover it, if it’s less I’ll refund you the difference.
Right now I only have the 45˚ version available. Note, the pictures do not show the finalized hardware kit; I will update the pictures with the real hardware soon. Please let me know if you have any questions!
7 Likes
Fantastic! Im going to order one to test imediatly, they look beautiful 
1 Like
Did you sand off the charred surface on the edge after laser cutting? It looks so much prettier than when I cut things.
For the surfaces I very lightly sanded some of them but they weren’t too bad. I wanted them to look nice for the pictures. I didn’t sand the edges at all. I’ve found that a trick for cleaner cuts is sufficient ventilation and plenty of air at the nozzle. Both of those help to disperse and remove any of the vaporized material before it can settle on the surface. For me it’s never quite perfect but usually good enough.
Another big variable is the material. For things like this I like to use high quality baltic birch, it has very few voids and the glue and plys are nice and even. I find that my edge surfaces are usually a dark honey color and not ashy or black at all.
2 Likes
I’d like a set as well if it isn’t too late.
