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Underslung Delta Effector

Posted by aflactheastronaut 
Re: Underslung Delta Effector
May 21, 2019 02:17AM
A magnetic ball joint will have no movement until the seating force is overcome. (Edit: A rod end will have a small inherent movement particularly if working dry)
The flex in an effector made of 1.6mm FR4 is very much less than error such as flexing in smooth rods, belt stretch stepper position compliance etc..
edit [reprap.org]

Edited 2 time(s). Last edit at 05/21/2019 03:29AM by leadinglights.
Re: Underslung Delta Effector
May 21, 2019 06:38PM
Attractive force between magnet and iron drops with distance between them quite quickly. It is similar to the force between two magnets:

That does not mean that your magnetic joints will not have any play at high accelerations! They can temporarily disconnect and reconnect again without staying disconnected. In a sense they can have bigger play than rod end when your accelerations are high enough ... and your speed is small enough.

Imagine that your magnetic joint is made from two cylindrical magnets (magnet/iron combination will be a bit worse) with diameter of 5 mm and length of 5 mm too. I.e. we follow the orange line on the chart above.
Lets say you have 0.2 kg object pulled by a magnet with acceleration of 10 m/s² up to maximum speed of about 0.05 m/s. Your magnet will reach the maximum speed in 5 ms and travels the distance of about 0.125e-3 m in that time. The required force is 2 N. But your magnetic joint has a maximum holding force only 1.25 N (orange line on the chart). Your magnetic joint will temporarily disconnect. But the joint will not break apart. It will reconnect again significantly sooner than in 40 ms. The reason is that your joint reaches the maximum speed very quickly and from that time on it does not accelerate but it still pulls your 0.2 kg object with significant force allowing the object to accelerate and catch up with the magnet. Here is a proof that the reconnection will happen in our example:
  • from the orange line on the chart we see that there is still pulling force of 0.5 N when there is a gap of 1.97 mm between the magnets
  • the maximum acceleration achievable with 0.5 N force on 0.2 kg object is 2.5 m/s² and this acceleration will need time of 40 ms to reach the distance 1.97 mm (within which the pulling force is at least 0.5 N)
  • but your magnet had travelled only 0.000125 + (0.04 - 0.005)*0.05 = 1.875e-3 = 1.875 mm in 40 ms and that is smaller than 1.97 mm in the previous point
  • that means the magnetic joint will reconnect
Note: It is possible that the chart does not show the force in Newtons. But it does not change anything in principle. You can adjust the example to different forces by changing the mass or the magnet sizes.

So claiming that magnetic joints have no play is misleading since it is true only when your accelerations are low enough.

This board is full of claims similar to this:
I have no problem of disconnection [of magnetic joints] even at printing at 3000 mm/s accelerations and 100mm movement speeds.
Well, of course there is no problem. The acceleration setting is pathetic. You can have that in a cartesian printer which will cost you at most half the price of a delta and will be so much easier to calibrate!

The problem is that there is nobody on this board who posts samples of prints with magnetic joints at accelerations of at least 1 G (10000 mm/s^2). There are also no good posts at which accelerations the magnetic joints start to rattle (temporarily disconnect) when infilling small gaps.

I think magnetic joints are a poor choice for a delta because their poor holing force per gram ratio but I like it when people use them. Maybe somebody of magnetic joint users will post some useful data and maybe even sample prints in the end. Data and sample prints at accelerations worth a delta. One can still hope.
Re: Underslung Delta Effector
May 21, 2019 09:37PM
Interesting post, @Hercek.

It's not clear whether your cylindrical magnets are magnetized radially or axially. Radial magnets would be a better approximation than axial, with a line of contact where a steel ball and countersunk magnet (which is the typical arrangement) has a circle.

I'd add:

  1. The forces in a delta are never at right angles to the plane of the attachment circle, because the carriage only ever moves vertically, the magnet is inclined about 60 degrees, and the rod is at various angles to that. Similarly at the effector... it moves only horizontally, and the magnet is inclined. I'm not sure how this affects your argument regarding detachment and re-attachment.
  2. For a lot of the motion, the magnetic joints are in compression, not tension, so holding force is irrelevant.
  3. The countersinks in the magnets are 90 degrees, so in some orientations the force of the motion is pressing the magnet "sideways" against the ball, even though the motion is in a different direction.
  4. There is a much stronger magnetic field at the corners of the magnet... sizing the ball and magnet so that the ball touches at these corners will improve the strength of the joint. The typical 10mm ball and 12mm magnet are not optimal.

Edited 1 time(s). Last edit at 05/21/2019 09:46PM by frankvdh.
Re: Underslung Delta Effector
May 21, 2019 09:39PM
A magnetic ball joint will have no movement until the seating force is overcome. (Edit: A rod end will have a small inherent movement particularly if working dry)
The flex in an effector made of 1.6mm FR4 is very much less than error such as flexing in smooth rods, belt stretch stepper position compliance etc..
edit [reprap.org]

You are correct when using the specs for 2 magnets of the same material in direct contact to each other with the force being applied parallel to the magnetic poles, once they are no longer in contact then the "seating force" has a different set of calculations. In the case being discussed hear, the magnets are indeed separated and the force is not being made/applied parallel to the poles and as a result only a fraction of the force being created along the magnetic poles is required to see movement/separation of the joint. This results in alignment being out of square and the arms technically changing in length impacting the calculations using the rod length.

I don't know the exact specifics of hardens mag balls and arms (and not about to cut up a set just to see), but I think most would be happy to accept that there is a gap between the magnets and that gap is for the majority of the contact area making it a pretty significant gap when you consider one magnet is a sphere and the other does not match that sphere with a "cupped" magnet on the opposing side.


[*] For a lot of the motion, the magnetic joints are in compression, not tension, so holding force is irrelevant.

Well that's not correct, all the joints are under tension most of the time (this is what keeps the effector aligned), sure in horizontal movements some joints will increase the tension and some will reduce it. The thing is 99.99% of the time the joints are still under tension (even if reduced under movement) as the effector alignment requires tension between the joints (and the joints to be accurately aligned) in order to hold the effector level. Now in movements directly down you do get compression of the joint, but you also get tension out sideways as the arm "cup" attempts to move around/away from the ball due to there being basically nothing constraining the join to hold its position and prevent it leveraging it's way out of alignment.

Edited 3 time(s). Last edit at 05/21/2019 09:49PM by Redemptioner.
Re: Underslung Delta Effector
May 22, 2019 05:57AM
I'll do some testing at 1G when my arms and smart effector arrvies hercek. I'm prolly never gonna set it to 1G for printing tho as it will introduce other problems but I can try to push the limits and get some videos of it.
Re: Underslung Delta Effector
May 22, 2019 06:14AM
Firstly, Thank you hercek for this and the earlier explanation on the steel cords. Having now investigated I agree that steel cords are problematic and your data is good.
On the use of magnets for ball ends I am less than convinced so let me put my arguements forward.
Looking just at the rigidity of a magnetic coupling I see the magnet and the iron bit (or second magnet) being held together by a force. One part, say the magnet, is connected the the effector and the second to the motor through the rest of the linkage - effector rods, carriages, toothed belt and smooth rods. This will have typically a degree of springiness. Here I make a couple of assumptions: 1) that the elasticity of the bits between the magnet and the motor can be moddled as a single spring and 2) that the stepper motor is perfect. Assumption 1 is true at printer speeds and assumption 2 is waaaaayy false but the best I can do.
When the motor pulls the iron block away from the magnet the spring gets stretched until the magnetic attractive force is overcome and at that point the spring pulls the block away. Unless this pull away is damped there is little or no chance that the magnet will recapture the block. There is no room for jiggling aboutso the movement in a good ball joint should be less than in a ball rod-end - which will have some play inherent in the design.
The above is not true if there are for e.g. severe mechenical vibrations that pull apart the magnet/ball and then pushes them back together again. It is also not true if the magnetic circuit is somehow compromised - and this brings me to my second argument.

Many/most people who have tried to make a magnetic coupling (including myself) have tried to use a ferromagnetic cup to fit against the ball. This will only compromise the magnetic circuit by offering an alternative route for the magnetic field.
The diagram below represents a magnetic ball jointI made with a ferromagnetic cup. The attraction with the ball fully in the cup is about 12 Newtons but the cup offers an alternative path where the ball can slide sideways and away from the central position. This is shown in the second part of the diagram with imagined lines of magnetic force - in the case of my coupling this allowed 0.5mm of force with the force only reducing to 10 Newtons and still5 Newtons when the ball was sitting on the edge of the cup. This was nearly 2mm out of the centre of the cup and nearly 4mm sideways. (@Redemptioner, is this what you were saying?)

When I replaced the iron cup with a Delrin one and doubled up on the magnets I get a clean disconnect at 12N of force. BTW, I thing the magnets with a countersunk hole are similar to the iron cup I tried - although possibly not as bad.

Re: Underslung Delta Effector
May 22, 2019 06:27AM

Yes, you will have other problems with bigger impact at 1 G accelerations. Most likely your belts will be too springy/elastic or stepper motors will have small holding torque at the microstep used. The prints will have serious ringing on the corners because of that. Anyway you can find out at what accelerations your joints start to "rattle" if you increase acceleration and speed slowly enough and make sure the printing is not slowed down by e.g. minimum layer time.

It is probable that many delta users use small accelerations because of long narrow glass core belts(*) and their impact on the ringing in print corners. Magnetic joints may be of smaller issue in such a case at least from the point of vie of a possible disconnection. But magnetic joints are heavier and that increases ringing as well.

(*) Narrow belts are cheap and easy to source. They are easy to use. Glass core is recommended for longevity. But from the elasticity point of view it is one of the worst options.

I think a lot of magnetic joint users would appreciate some table with these columns:
  • name of producer and name of the magnetic joint diagonal rods
  • static holding force of the magnetic joint
  • weight of the diagonal rods
  • weight of a carriage
  • weight of the platform
  • whether flying extruder was used and if yes then what was the length of the bowden and weight of the extruder
  • acceleration and speed at which magnetic joints start to "rattle" or will disconnect
  • belts used: kind and length (this is important because the more elastic the belts are the less acceleration is actually transferred to your magnetic joints; if your belts are ellastic enough and magnetic joints strong enough then you may not be able to get them to "rattle" or even disconnect)
Re: Underslung Delta Effector
May 22, 2019 06:58AM
add your first picture) It depends on the weights and how much elastic the "rest of device" is. And specially what is the maximum speed when motor pulling "rest of device" stops accelerating. It still can reconnect in general. It just may be less likely to happen.

add your second picture) No real opinion on it without building a simulation.
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