Triperon Motion

[Adamfilip]

Curious of Duet supports Triperon Motion (Dual and Single Rail)

https://www.youtube.com/watch?v=D3Fpy2_MyYg

https://www.youtube.com/watch?v=oBBhVcemVHc

[droftarts]

@Adamfilip A regular Tripteron maps it’s axes exactly the same as a Cartesian machine. These Tripteron variants can be described in a kinematic matrix as a variation of a Cartesian printer, as there are three linear motor axes that control X, Y and Z positioning that have a 1:1 relationship:
X moves have the 'X' and 'Y' motor moving in opposite directions, 'Z' not moving;
Y moves have all three motors moving in the same direction;
Z moves have the 'Z' motor moving, with 'X' and 'Y' stationary.
So...
X = 1, -1, 0
Y = 1, 1, 1
Z = 0, 0, 1
You can then feed this into M669 command, something like:

M669 K0 X1:-1:0 Y1:1:1 Z0:0:1

I think that would work.

Ian

[fma]

@droftarts, have a look at the vidéos above, these are not classic tripteron kinematics... Much more complicated, and as Delta, non linear...

[droftarts]

@fma I did watch the videos (and I’d seen them before). A regular tripteron maps exactly like a Cartesian. If you look at what I wrote, it’s specific for these versions (at least the single and double horizontal rail versions, maybe not @Apsu version). I’ve edited my post to make that clear.

Ian

[o_lampe]

The second monorail video seems pretty straight forward.

X= 1,1,1
Y= -1,0,1
Z= 0,-1,0

But it has some design flaws, like the limitted Z-height.
And offcourse it has the same design-kinks, any Tripteron has. (I have wasted a lot of filament and Carbon tubes to build one...)

//edit I recently learned more about how the kinematic matris is built. I'm not sure, if the above code is still valid, but it's a starting point. Just have to sort out XYZ axis.
Right now I've put the Z-axis in the middle, same place as it was in the video...

X= 1,1,1
Y= -1,1,0
Z= 0,0,-1

Maybe that's more realistic.

[droftarts]

@fma said in Triperon Motion:

Much more complicated, and as Delta, non linear...

I don’t think it’s a delta movement. If the angle of the Tripteron effector is 45 degrees, a horizontal movement is translated into a 1:1 movement in the corresponding axis. However, I don’t know for sure; @apsu or @oliof would be the ones to ask!

Ian

[fma]

Yes, it requires very rigid joints, hard to achieve with 3D printed parts, I guess?

[oliof]

I have implemented Colinear Tripteron kinematics for RepRapFirmware but am waiting for a better mechanicsal build than mine before continuing. You can find my fork at https://github.com/oliof/RepRapFirmware/tree/colinear-tripteron.

It has not been merged back to recent versions, but the changes are well-contained within their own kinematics implementation.

[o_lampe]

@fma Right, designing these joints and then print them are two different shoes...

[oliof]

@fma joint design is one of the main challenges. Wider joints than on @Apsu s 2016 design will help with the backlash I encountered in https://forum.duet3d.com/topic/16588/colinear-tripteron-progress ... but I am currently doing other stuff.

Best,
Harald

[Apsu]

@droftarts said in Triperon Motion:

I don’t think it’s a delta movement. If the angle of the Tripteron effector is 45 degrees, a horizontal movement is translated into a 1:1 movement in the corresponding axis. However, I don’t know for sure; @apsu or @oliof would be the ones to ask!

You are indeed correct that it is not delta movement. It is completely linear, and described by a linear matrix/system of linear equations. All Tripterons are (including my 2016 Delteron/Colinear design), and as such are uniquely different from SCARAs or Deltas.

And lastly, just to say it, the orthogonal Tripteron layout is also Cartesian.

[Apsu]

@o_lampe said in Triperon Motion:

@fma Right, designing these joints and then print them are two different shoes...

Sure, but these machines do work. It's not like they haven't been built and we're just guessing. Questions about specific rigidity/resonance targets are a separate thing, but one of the benefits of parallel kinematic systems is that they are redundantly constrained (not overconstrained). Meaning the rigidity and dynamic behavior isn't just a question of individual joints but the system as a whole.

Or to think of it another way, the whole is stiffer than the sum of its parts

[droftarts]

@Apsu thanks for the info. Is there a link to how the joints are currently designed? I’d think something like a motorcycle/bicycle head race (tapered roller bearing) would be ideal.

Ian

[Apsu]

@droftarts https://i.imgur.com/o2IsTWH.png is the original joint I settled on in my 2016 build. Double-shear, dual-back-to-back preloaded radial bearings (608), with steel washers used for compressing plastic between metal, and separating inner from outer bearing races.

Tapered rollers or angular contact sets have been suggested before, and I think they're a fine idea, but I think larger bearings (like the 6806s in Seward's latest videos) and using square tube (printed or otherwise) is a much bigger improvement over my old 2020 arm idea. Extrusion does not resist torsion force very well due to the small core diameter, and there's a large number of elbow angles where the force on one or more of the arm segments is largely torsional.

My most recent Tripteron prototype (https://www.youtube.com/watch?v=7LAmA4Q6-o4) build is using 2040 segments with single-shear joints, radial bearings on each end 40mm apart, and a thrust bearing inbetween. It's decently stiff, but I still think single-shear needs much larger bearings to improve the surface area over which the joint halves interact (stiffening the lever arm of the interface).

Seward's current joints in the video mockups are pairs of 6806s in single-shear with bolted in caps to secure them together, and it's a very reasonable approach. I also believe you could use a 6806 and 608 in combination with a similar setup and it'd be fine. The biggest question overall here is honestly joint 'wrist' geometry/cross-section, and the material/cross-section of the arm segments given their torsional and bending forces. Everyone focuses in on the joint itself but these other two points are much bigger in my experience. And I built dozens of these things to test

Anyhow, that's my $0.02

[fcwilt]

Interesting stuff.

What is the raison d'etre for such machines?

Thanks.

Frederick

[Apsu]

@fcwilt said in Triperon Motion:

What is the raison d'etre for such machines?

There are very few machine designs -- for printers or otherwise -- that are linked in parallel, in 3 or more axes, and also linear kinematic mechanisms. Of those, the multipteron family are the simplest.

The general benefit of parallel machines is high dynamic stiffness without needing to move one actuator with another (serial linkage), which can compound the error of one axis with the other due to the coupling. The side effect is you can build a 3D printer with a fixed bed and all fixed motors.

[fcwilt]

@Apsu said in Triperon Motion:

The general benefit of parallel machines is high dynamic stiffness without needing to move one actuator with another (serial linkage), which can compound the error of one axis with the other due to the coupling. The side effect is you can build a 3D printer with a fixed bed and all fixed motors.

Thanks.

Is it hard to get the "slop" out of the joints?

I understand your comment about serial linkage but it would seem, from an "outsiders" point of view, you've traded one engineering challenge for another.

Frederick

[Apsu]

@fcwilt Joint slop is quite easy to take out with one of these types of arrangements, as preloading radial bearings is exactly the method used for doing so in machinery. There are many articles and data sheets discussing taking slop out of radial bearings by preloading, as well as different preload approaches (and when you might want to use angular contact or tapered rollers, etc) out there in the wild. Like https://www.nationalprecision.com/info-library/technical-data/bearing-preload/ or https://www.skf.com/binaries/pub12/Images/0901d1968065f1f4-Bearing-preload_tcm_12-299896.pdf for example.

Back to back and face to face are both very common setups for wheels and shafts, from bicycles to engines to skateboards. Getting the joints stiff is pretty easy. Designing the housings and connections and arms to handle the large lever and twisting forces is the real challenge.

[fcwilt]

@Apsu

Thanks.

They do look like they could be a fun and challenging project.

Frederick

[o_lampe]

If you need another excuse to build a monorail Tripteron, imagine you have four of them surrounding the printbed.