when we are talking about trying to get accuracy of <.5mm in the final machine,
even 1% stretch seems like a lot. We’re starting to worry about chain sag when
it hits .1%
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Another great triangular kinematics design! This might be my new favorite (old was the top ‘pantograph’).
Me too, I even modeled it with shoelaces tied to nails to try to figure out angles that would work, with no luck.
If our loop is approx 1 meter, that means that the stretch would be 1cm at 1%. Even halved (cord on both sides), that would be 5mm of error. Our tolerance for stretching is probably closer to .1%, the less the better. I don’t think even kevlar can meet this, and that’s the least stretchy cord we can get.
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I agree, maslow is not suited for grooving in the side of things… I wasn’t intending to groove into the side quite like that. I was thinking of something more like a stack. Perhaps two rings out of 3/8" ply for the chains to ride on plus three more rings that have a slightly larger circumference cut from 1/8" ply. Stack them thin-thick-thin-thick-thin. That would effectively give you two "grooves, they’d be square sided, flat-bottomed grooves. It would be sort of a large, squat, double decker bobbin. If you are using Maslow to cut them I’d design some registration holes in all the layers to make it easier to get the two critical thicker rings lined up with each other.
Chain mis-alignment might cause a chain to snag and jump the groove, but you could bevel/chamfer the inner edges of the 1/8" layers to help.
With a quality plywood I don’t think it would be an issue but if you’re worried about surface consistency you could always wrap the tracks with a stiffer material (plastic, rubber, leather, metal…).
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Instead of grooves, could we just screw the chains to the outside a plywood ring, on the parts of the ring that we don’t need movement? Then, with slightly offset motors, we might get things to line up on their own from there…
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Ha! I love it! I used a piece of ribbon, my fingers, pins and a pencil to try to figure it out! It turns out we were really close, instead of pins or nails all we needed was a cylinder 
I even had my ribbon in a loop! So close!
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I like this idea, but does it work with our angles? (10-80)
Where do the screws end up?
Figure the ring needs to be 12-16" diameter (clearing handles on large routers)
The idler about 2" diameter (i think this needs to be a good ball bearing idler for the reasons logan gave in his link vs ring post)
I was thinking along those lines too. Instead of stacking thinner sheets in between, I was thinking of using Maslow to route out a dado in the edge of two circles before cutting out, and stack them (dado down) on top of a third circle. That would end up like you described, a double decker bobbin.
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That’s a much simpler (and better) idea!
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For those of us without a temporary sled, this method could be used to make those dado impressions and for the circular cuts
I think it will. Back of the envelope: with a plywood circle of inside (radius) 8" and outside radius of 11", and a 2" sprocket with 2" clearance, the loops would need to be free from about +/- 140° from the top of the sled. That would leave about 80° at the bottom of the sled for attaching. Attaching would hinder rotation of the sled, so the attachment points would need to be low enough to avoid that.
Preventing the crossing links from catching could be as simple as putting some PVC around one side and attaching to the sprocket hook to prevent pinching where the chain meets the sled ring.
This might eliminate the need for the dadoes at all, and allow the loops to be closer to the same plane at the sprocket.
I think completely the opposite 
it will be an advantage and have offset. if you take a cylinder and try and balance it with two rubber bands. It’s not easy if both are in the middle.
and we talk about under 1 "so torsion will not be a problem. (weight × length)
The difference is the loops are pulling at different angles, so that would introduce the torsion. If the chain is close enough to rub, I doubt it will be noticable, especially compared to the torsion imparted by the router bit 
Yes!! I totally missed the offset motors part. That would minimize the tendency of the loops to . . interact. . and would eliminate the issue of the loops being on different planes than the motors.
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yes, but add the surface to the sled against the workpiece so you have another calculation
You don’t need to offset the motors if you can have the chains go between the two rings with the idlers offset (see the bearing holder I posted way up on this thread)
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We are not tethering tons of ships, though. Their rating is the maximum deflection at the rated weight.
It might not be easy if they are in the middle but it’s impossible if they are spread apart. Imagine your two rubber bands and a can of spray paint. Set the can on its side on the floor with the base of the can against the wall (parallel to the wall). If you put one rubber band around the cap and one around the base there is no way you could pick up the can with only the bands AND keep it’s base parallel to the wall (keeping your hands in the original planes of the two bands). You’d need another force in order to counteract the torsion imparted by the offset. With the design we are talking about the torsion is very small and the sled (base of the can) is very large and rests against the work piece. This is the force that keeps things from turning. Not the spacing of the chains.
Imagine the same can in the same place but with a single rubber band around it’s middle, right at the center of gravity. If you grabbed the band at two places and lifted carefully it could be lifted without any lateral torsion and the bottom of the can could be kept parallel to the wall.
I’m not saying the torsion is a big problem but with offset chains there will be torsion - weather or not it causes problems is yet to be proven. (with offset chains there will always be more friction on one side of the sled).
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So what’s the rated weight?