New Diagnol Tie for Reduced part count and build time

Hello all!

I'm now contributing something that I think could be significant for the Darwin design.

Nophead noted somewhere that it was taking a lot of time to print the diagonal tie blocks as there are 20 of them. That's a lot of parts which takes a lot of build time. It was suggested somewhere else--couldn't find it again with the half-hearted effort I put into it--that we should modify this to eliminate the steel rods from the design.

Here is an idea for that, STL and JPEG's included!

I got the idea from tie strapps used in warehouses to strap stuff to pallets. You basically use it as a cinching buckle with two straps. For our purposes we could use Nylon strapping or even just scrap cloth a person has laying around. No need for the braces at the corners now. Just make a loop out of the strapping of your choice and throw it around a likely corner. Two such straps from diagonal corners with a Strap Binder in the middle gives you adjustable, collapsible, re-usable diagonal bracing for the reprap. Bonuses include smaller part size, reduced hardware count, decreased build time, decreased build resources.

***Edit***

Got my lazy butt around to making a couple pictures to explain things...

The general idea of how things go together. Red is the strap, Blue is the Binder.

Strap01.bmp

Now, we need to know how to thread the straps into the binder....

untitled.bmp

Now, for a bit more specific information to give us an idea of volume and possible print time...

Output coordinate System: -- default --

Density = 0.00 grams per cubic millimeter

Mass = 4.12 grams

Volume = 4119.15 cubic millimeters

Surface area = 3692.64 millimeters^2

Center of mass: ( millimeters )
X = -1.02
Y = 2.76
Z = -10.00

Principal axes of inertia and principal moments of inertia: ( grams * square millimeters )
Taken at the center of mass.
Ix = (1.00, 0.01, -0.00) Px = 207.00
Iy = (-0.00, -0.00, -1.00) Py = 1762.83
Iz = (-0.01, 1.00, -0.00) Pz = 1941.75

Moments of inertia: ( grams * square millimeters )
Taken at the center of mass and aligned with the output coordinate system.
Lxx = 207.34 Lxy = 23.88 Lxz = -1.87
Lyx = 23.88 Lyy = 1941.42 Lyz = 0.01
Lzx = -1.87 Lzy = 0.01 Lzz = 1762.83

Moments of inertia: ( grams * square millimeters )
Taken at the output coordinate system.
Ixx = 650.76 Ixy = 12.29 Ixz = 40.13
Iyx = 12.29 Iyy = 2357.74 Iyz = -113.71
Izx = 40.13 Izy = -113.71 Izz = 1798.50

***End of Edit***

Tell me what you think!

Demented

Edited 1 time(s). Last edit at 08/08/2008 07:09AM by Demented Chihuahua.

I'm sorry, but I can't really visualize how you're intending to set this up...

Sorry, should have at least tried to explain it.

The two loose ends bend over either side of the closed end. The strapping gets wrapped around in a certain way so that the tension on the strap causes friction on the strap stopping it from unwinding. You have an adjustable tensioner in this way. Kinda like the plastic strap pieces for a back back strap. Adjustable friction fasteners...

Made some changes to the files. Added the RepRap logo. Didn't really know the dimension of the drop thingy. Just faked it.

Demented

More info from SolidWorks on this part...thought it would be interesting

Output coordinate System: -- default --

Density = 0.00 grams per cubic millimeter

Mass = 4.12 grams

Volume = 4119.15 cubic millimeters

Surface area = 3692.64 millimeters^2

Center of mass: ( millimeters )
X = -1.02
Y = 2.76
Z = -10.00

Principal axes of inertia and principal moments of inertia: ( grams * square millimeters )
Taken at the center of mass.
Ix = (1.00, 0.01, -0.00) Px = 207.00
Iy = (-0.00, -0.00, -1.00) Py = 1762.83
Iz = (-0.01, 1.00, -0.00) Pz = 1941.75

Moments of inertia: ( grams * square millimeters )
Taken at the center of mass and aligned with the output coordinate system.
Lxx = 207.34 Lxy = 23.88 Lxz = -1.87
Lyx = 23.88 Lyy = 1941.42 Lyz = 0.01
Lzx = -1.87 Lzy = 0.01 Lzz = 1762.83

Moments of inertia: ( grams * square millimeters )
Taken at the output coordinate system.
Ixx = 650.76 Ixy = 12.29 Ixz = 40.13
Iyx = 12.29 Iyy = 2357.74 Iyz = -113.71
Izx = 40.13 Izy = -113.71 Izz = 1798.50

Demented

I'm still not completely clear to me how this works. Is it similar in principle to the belt tension adjusters on the strap in the picture at [www.skoobadesign.com]? I've seen many of those, but nothing like what you have sketched.

In other news, that's a pretty spiffy material you've got there. It has volume and mass, but no density!

Kinda similar but this bit is made to take two ends and attach them together. So you can have the ends of a strap come together and be connected.

Yeah, didn't choose a model material. Didn't think it was necessary at this point. People can multiply by there materials density to get the actual mass and such.

Also, made a quick and dirty drawing for the dimensions. Gonna have to change things around here eventually to make it better but just to give you an idea of the size.

All dimensions are in millimeters.

Demented

until now I thought I understood how that thing should work.
Now you come up with the two ends, and I'm totally lost in confusion.

Would you mind drawing the strap with that thing attached ?

'sid

Here is the idea for the diagonal support with a bit more explanation since I really do suck at explaining things. :-)

An overview of how the pieces go together generally. Diagonal corners being strapped together. Strap in Red. Strap Binder in Blue.

Strap01.bmp

Now, a detail of the intersection of the blue and the red--the strap and the binder.

untitled.bmp

There is text there so pay special attention.

Hope that helps.

Demented

A picture is worth 1000 words!

Whatever the strap is made from has to have no give in extension compared to M8 studding.

Edited 1 time(s). Last edit at 08/08/2008 10:14AM by nophead.

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[www.hydraraptor.blogspot.com]

nophead Wrote:
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> A picture is worth 1000 words!
>
> Whatever the strap is made from has to have no
> give in extension compared to M8 studding.


I think a little bit is OK because you keep it under constant tension and you can always cinch the straps down if it starts to feel a little loose.

Interesting idea, but I'm not sure that just throwing it around a corner block wil be an effective means of securing the ends, especially since you need 2/corner block... I'll have to think about that more.

Tension isn't the same as stiffness. Once it has taken up the slack it only increases stiffness if the material has a non linear Young's modulus. Things like HDPE certainly do, but whether they ever get as stiff as steel before they shear I don't know.

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[www.hydraraptor.blogspot.com]

Agreed, tension and stiffness are different. However, I don't think we need stiffness here, only tension. We are basically making strong little triangles. A good triangle can certainly be made from two sticks and a string as long as There is a force tending to push the vertice where the two sticks meat toward its string hypotenuse and thus forcing the two sticks into a straight line. We have that very situation here.

Also...yes, just looping the straps over the corners is not the way to go. We should modify the corner blocks to give a nice attachment point. Not too hard. Even if you don't, however, you should still be able to get away with just looping them around the studding where the old diagonal tie would have gone. Should work just fine.

Demented

Quote

However, I don't think we need stiffness here, only tension. We are basically making strong little triangles. A good triangle can certainly be made from two sticks and a string as long as There is a force tending to push the vertice where the two sticks meat toward its string hypotenuse and thus forcing the two sticks into a straight line. We have that very situation here.

No I entirely disagree: tension is no benefit, we need stiffness.

What we have is squares that are already strong against vertical or horizontal forces because that involves compressing or stretching a steel bar, but they are weak against skew forces which try to make them into parallelograms because that involves bending a steel bar or a plastic block. I can easily bend an M8 rod a few mm over its length by hand but I can't stretch it.

Adding tension across the diagonals makes no difference at all to the stiffness of the square. The Young's modulus of steel does not increase with tension (as far as I know). You have to add something that is stiff across the diagonals. Because one diagonal extends when the other compresses you can get away with something that is only stiff in extension. That is why I suggested steel cable.

Some tension is required to take up the slack and ensure that one cable is being stretched but any further tension would not increase the stiffness unless you were using a material that had a Young's modulus that increases with tension. Some plastics do just that, for example, it is very hard to snap HDPE because it gets stronger as you stretch it, but I can't imagine a plastic like that being stiff enough to have no give compared to M8 studding unless it was very thick. Possibly carbon fiber would fit the bill.

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[www.hydraraptor.blogspot.com]

I must agree with nophead, its stiffness that's needed (at least that's what I can see, 'cause I never touched a darvin yet)
But stiffness can be achieved in various ways.

Thinking of a bicycle wheel where one half of the spokes handle the pull and the other half the pushforces (normally, ther are many ways to spoke a wheel though..)
A single spoke can handle almost no force at all but altogether they can carry huge loads.

So why not thinking about a central connector for something like (or) bicyclespokes, they are cheap (noone really needs stainless steel spokes on a darvin) and they can be bought everywhere in the world.
It's easier to have access to bicycle spokes than to steel rods I think.

I'm sorry I was only thinking out loud

'sid

Quote

So why not thinking about a central connector for something like (or) bicyclespokes

That's quite a nice idea, but I suspect that getting a suitable hub would be the problem there. Unless you got a couple intended for normal bike wheels, and sawed them in half. And then all you have to do is to take some suitable 'rims'... it all seems to be getting a bit fiddly, no?

But it has given me some interesting thoughts for other projects. Hmm.

You have a four bar linkage here. It tends to swivel about it's corner brackets--they would crack in real life--and we want to cause them to resist this linkage action. Since the bars cannot slip through the corner blocks--screws and bolts and such--adding a force to them that pulls diagonally through the center of the square constrains that motion. That member through the center--in our case the strap--undergoes no compression. It is a pure tensional element.

A picture...

Example.bmp

The red again is the straps. Notice that when you apply a force that would cause a collapse in a four bar linkage, the strapping would have to elongate. Since we are assuming a fairly sturdy strapping, it can't and we are saved from collapse. All the forces are taken by one or the other tensioning element as one is getting longer and the other could get shorter. Since they cannot stretch--ideally--they will not move.

Honest guys, this does work. I've played with this kind of thing both as a child and in college to learn statics. Don't trust me on it. Make yourself a grown up toy and fiddle with it.

Now, as to whether my strap binder will be strong enough or the strapping we choose sufficiently unstretchable is to be seen. However, that is a material choice issue IMO.

Demented

Quote

Since they cannot stretch--ideally--they will not move.

Agreed: adding something that will not stretch will make the structure stiff. What I am saying is that in practice everything will stretch to some extent. Adding more tension, after you have taken up the slack, does not make the structure any stiffer.

So the stiffness is down to the Young's modulus of the diagonals. Most plastics and fabrics will be nowhere near as inelastic as M8 studding. Putting more tension through them does not improve this.

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[www.hydraraptor.blogspot.com]

Yep, its all down to how much stiffness you need.

I had a kit of parcel strapping with plastic blocks just like Demented has described. The strapping was very strong with very little elongation, so I feel it may do a good job. It may be a bit fiddly to set the tension balance between alternate braces to keep it square.

Wheel spokes in a bicycle are actually all in tension all the time. (ok the bottom one may be slack). What happens is : the hub HANGS on the upper spokes from the top of the rim. The horizontal spokes are tensioned by the resulting force which is trying to squash the rim into an oval - they hold the sides in. The bottom spoke does nothing. Obviously, each inbetween spoke carries a proportional fraction of those tensional forces.
You will also notice that the spokes are spread to the left and right of the wheel's centre in order to resist side loads. They also dont rin to the very centre of the wheel - because the bearing has to go somwhere but also they can then be displaced angularly (is that a word?) so that they can carry tortional forces about the axis (pedal power on the rear or brake loads with hub mounted brakes)

Sure on the modulos of elasticity but I think we are getting carried away with how much stiffness this machine will need. It isn't undergoing any crazy forces. It just needs to stand up to gravity and the slight vibrations from itself.

I think this strap idea will do just that.

Demented

Accelerating the the X-axis and the extruder, which must upwards of 1Kg, with the y motor is certainly going to generate a significant force. The motors are rated at 1Nm. I am running at about 25% power, so say 0.25Nm. The belt radius is around 7mm, so I think the thrust is about 0.25/.007 = 35N. Do you think your strap will extend less than 0.1mm over about 700mm when pulled with 35N?

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[www.hydraraptor.blogspot.com]

nophead Wrote:
-------------------------------------------------------
>
> Do you think your strap will
> extend less than 0.1mm over about 700mm when
> pulled with 35N?
>

~8 lbs force? ROTFLMAO! With carbon filament, maybe. Anything else? No way!

What about using steel cable(the thin type) or wires instead of plastic straps? Possibly using multiple cables on the same diagonal for extra strength.

Gene Hacker Wrote:
-------------------------------------------------------
> What about using steel cable(the thin type) or
> wires instead of plastic straps? Possibly using
> multiple cables on the same diagonal for extra
> strength.

Good luck on ever getting it adjusted so that it isn't warped.

They sell cable tensioners
[www.biconet.com]
and swivels
[www.ederflag.com]
and you probably could get away with using an eye-bolt for tensioning without the tensioner
[www.biconet.com]
but with all the crimps and stuff it's probably cheaper to just use a metal rod.

They make very good poly-line now, a 1/8" (3 mm) line is rated over 2000 lbs (900 kg) and has very little stretch. A 1/2" rope of the same material is rated 34000 lbs (15000 kg). With some clever knot tying you could keep the frame square without all the extra small hardware.

Tanex Polyester strapping comes in 9mm wide strap and is what is used on medium weight strapping applications for pallatizing products for shipping. It is exactly the stuff I saw in the warehouse using the strap binder. It is rated at a strength of 1,890 N or 425 lbs. The stuff is made to not stretch because you are putting it under constant tension and load and if it stretches the load falls over in the truck and you loose money.

[www.signode.com]

Honestly, you guys are drastically over estimating the forces on this machine. Even if Nopheads rough calculations are correct, they get divided in half because there are two halves of the machine sharing the load. 17.5 N is far under the 1,890 N strength limit of this line and should, therefore, deflect very little over 700 mm. Even if this one isn't enough, it is the smallest I could find and the values on this stuff just go up.

Demented

Yes it may be halved but then again there is the fact that when the carriage is being "thrown" back and forth when it in the center each side of the frame will have equal force and vibration being throw at them. But the carriage is rarely just parked in the center of the cart bot. So it is best to round up and get something that get as close to 35N as you can. Because there is probably some extra torque/force/vibration that will come from somewhere you did not think about.

Anyways....
After I get my Darwin printing parts nicely I was thinking about testing the cable and eye bolt idea. Mainly because even though it might give it will probably give a bit less than plastics and fabrics. Also all this speculation is nice but, but in the end if you have an idea, don't let us kill it. Go out try it out. If then it does not work we can scratch that idea from the list.

I started this topic earlier [forums.reprap.org] not because I wanted to reduce the need for threaded rods, but mostly because of the weight aspect. The machine is very heavy (I estimate 15 kg at least, but I don't have a person-scale at home). If you want to call it a desktop factory, it should be in the range of weight of an ordinary printer. Perhaps allow 5 times the weight. Now it's at least 5 times as heavy, and future versions will have extras that would also add more weight.

Switching to M5 or M3 threaded rod is also a good option. You have the power of two to your advatange: it gets lighter quadratically when you reduce the rod diameter. All you need is a pair of washers to make them fit in the current diagonal ties. You'll have ~ 7.1 times the weight loss off 3 mm vs. 8 mm ( (pi*(8/2)^2)/(pi*(3/2)^2)=7.1111 ).

Empirically I got these numbers:
M8 diagonals weighing 400g each (I weighed 6.67 g/cm of rod) versus
M3 diagonals weighing 26g each (I weighed 0.44 g/cm of rod).
6.67/0.44 = a weight reduction factor of 15.16. I don't know why these empirical numbers are so far from theory. Both rods look like they're from stainless steel, but the M3 rod looks less shiny, so it could be a lighter alloy?! Also, both M3 and M8 are not exactly 3 or 8 mm in diameter because of the thread.

Empirically the weight would be down by ~ 7.47 kg (from ~ 8.00 kilo's). If M3 are sufficiently stiff, this would reduce transportation costs of parts, transport costs of complete RepRaps, material costs and the number of people having a back-ache. Besides, you'll cut a M3 rod a hell of a lot easier (reduces build time!).

If the reduction is closer to the theoretical number I calculated (half of what I weighed), it's still down by 6.88 kg!

The entire Darwin loses a third of its weight!

I didn't know about the Young modulus until now, thanks nophead for the theoretical background. I'm an amateur when it comes to mechanics, but I did have the feeling that this effect would be relevant to this discussion and that it's the amount of stretch that is essential.

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Regards,

Erik de Bruijn
[Ultimaker.com] - [blog.erikdebruijn.nl]