Hlidskjalf, Dual CoreXY

Hi.
Seeked out this forum to help with my first 3d printer design.
Hlidskjalf is a dual CoreXY 3d printer with CNC capabilities: [www.thingiverse.com]
The print heads are twin Toranado extruders: [www.thingiverse.com]

Some info:

24VDC 1000W PSU
.5 N-m steppers belted 2:1
MGN12 linear guides with H blocks
1605 anti-backlash ball screws
RADDSv1.5, RAPS128, Arduino Due with 7" Panel Due

Soon to begin wiring and testing with a single head using Repetier.
What I need help with is software implementing dual head support, and later linking X-carraiges for full out CNC.
Probably a good month away from powering up, so thought now is a good time to start fishing these waters.
Will barter for code.

Tom West
AKA Prot0typ1cal

Edited 1 time(s). Last edit at 01/11/2017 06:26PM by prot0typ1cal.

I've not seen a dual CoreXY before. Do the two carriages move in sync or independently? If independently, what are the kinematic equations for the 3 motors involved in moving each carriage to a desired XY position?

---

Large delta printer [miscsolutions.wordpress.com], E3D tool changer, Robotdigg SCARA printer, Crane Quad and Ormerod

Disclosure: I design Duet electronics and work on RepRapFirmware, [duet3d.com].

Looks like they move independently, the belts for one run along the top of the X axis while the belts for the second run along the bottom.

Thanks for the interest

dc42, X-Carriages move independently, though obviously share the Y-Gantry.
Each Carriage is belted to two motors to operate in a CoreXY fashion. Total of 4 motors.

Correct Widespreaddeadhead, only the lower run, right head, is belted ATM so it will work in the standard CoreXY config for testing. Will need to develop software to implement the left head.

Both CoreXY runs are belted 2:1 to their steppers for increased torque and positioning accuracy. Based on the power curve of the steppers, torque does not drop off until over 100 mm/sec travel speeds.
Eventually will be joining both X-Carriages with a milling head, to explain the over-kill with linear guides, multiple trucks and 1605 ball screws. The CNC set-up will operate as a standard CoreXY with two A&B motors rather than one.

It's proven that the CoreXY is isotropic with XY forces, only we know that the mass for the Y-Gantry with the X-Carriage is greater than the X-Carriage alone.
By "doubling up", one head will be in X equilibrium while the other head moves in X. This adds two more motors to move the Y-Gantry during prints, so even at 45 degree moves greater torque is available to overcome Y inertia.
Theory is that all four steppers will synch to achieve the desired motion. There's no supporting firmware currently, and my mechanical mind log jams when confronted with syntax.

Edited 2 time(s). Last edit at 01/12/2017 12:13PM by prot0typ1cal.

I'm interested in dual carriage CoreXY and I am prepared to look at extending RepRapFirmware to support it on Duet electronics (we already support dual X carriages on Cartesian printers). However, if you have 4 motors (excluding Z) then there should be 4 degrees of freedom. But I see only 3: X1, X2 and Y. So it seems to me that there is a danger that the two pairs of motors will fight to control the Y axis if they are not perfectly synchronized. Am I right?

Edited 1 time(s). Last edit at 01/12/2017 03:34PM by dc42.

---

Large delta printer [miscsolutions.wordpress.com], E3D tool changer, Robotdigg SCARA printer, Crane Quad and Ormerod

Disclosure: I design Duet electronics and work on RepRapFirmware, [duet3d.com].

Appreciate your offer on firmware. Absolutely accept.

Regarding 4 degrees of freedom, in a CoreXY both motors control the Y. In my case 4. As I understand it, there is no degrees of freedom in a CoreXY, adding another head should make very little change in the kinematics. Mathimatically it will be like running two CoreXY simutaneously, only they will both have the same Y targets all the time.

On the plus side, there's 2.4 meters of belt per run. Even though I'm using the steel wire variety, there should be plenty of give resulting in minor flucuations of tension as the steppers synch. So a few steps +/- should not cause a fight.

From a software side, it may be able to idle the second set of AB motors while the first homes, then home the second AB on X with all motors powered. Large gantry milling machines perform homing operations during power up the same way when axis are driven by multiple drives. May have to create a dump circuit to prevent the idle steppers from generating current and/or actively braking motion with holding torque if receiving power (which they shouldn't). Then again, being stepper motors, as long as they are all powered up simultaneously, there is no absolute positioning to create motion conflict if the output pulses they receive are calculated correctly and are consistent (no lost steps).

The dual CoreXY mitigates the asymmetrical mass issue of the single CoreXY, plus unleashes the potential for independent heads and CNC milling in a system currently incapable of such a feat. Obviously a dual CoreXY could be made lighter to perform only as a 3D printer. Hope this experiment opens the doors for others to build their own dual CoreXY rigs.

It seems to me that you could use one less motor to control 2 heads independently, whilst still controlling XY. Check out the CorEXY for ideas. I think you could easily use a similar belt run to control the 2nd tool.

Other than that, I am loving your machine. Linear rail and ballscrews in all the right places

Quote
prot0typ1cal
Appreciate your offer on firmware. Absolutely accept.

Regarding 4 degrees of freedom, in a CoreXY both motors control the Y. In my case 4. As I understand it, there is no degrees of freedom in a CoreXY, adding another head should make very little change in the kinematics. Mathimatically it will be like running two CoreXY simutaneously, only they will both have the same Y targets all the time.

On the plus side, there's 2.4 meters of belt per run. Even though I'm using the steel wire variety, there should be plenty of give resulting in minor flucuations of tension as the steppers synch. So a few steps +/- should not cause a fight.

From a software side, it may be able to idle the second set of AB motors while the first homes, then home the second AB on X with all motors powered. Large gantry milling machines perform homing operations during power up the same way when axis are driven by multiple drives. May have to create a dump circuit to prevent the idle steppers from generating current and/or actively braking motion with holding torque if receiving power (which they shouldn't). Then again, being stepper motors, as long as they are all powered up simultaneously, there is no absolute positioning to create motion conflict if the output pulses they receive are calculated correctly and are consistent (no lost steps).

The dual CoreXY mitigates the asymmetrical mass issue of the single CoreXY, plus unleashes the potential for independent heads and CNC milling in a system currently incapable of such a feat. Obviously a dual CoreXY could be made lighter to perform only as a 3D printer. Hope this experiment opens the doors for others to build their own dual CoreXY rigs.

For CoreXY we calculate the motor movements like this:

float Move::MotorFactor(size_t drive, const float directionVector[]) const
{
	switch(drive)
	{
	case X_AXIS:
		switch(coreXYMode)
		{
		case 1:			// CoreXY
			return (directionVector[X_AXIS] * axisFactors[X_AXIS]) + (directionVector[Y_AXIS] * axisFactors[Y_AXIS]);
		...
		}
		break;

	case Y_AXIS:
		switch(coreXYMode)
		{
		case 1:			// CoreXY
			return (directionVector[Y_AXIS] * axisFactors[Y_AXIS]) - (directionVector[X_AXIS] * axisFactors[X_AXIS]);
		...
		}
		break;
	...
	}
	...
}

For your machine, I think we need this:

float Move::MotorFactor(size_t drive, const float directionVector[]) const
{
	switch(drive)
	{
	case X_AXIS:
		switch(coreXYMode)
		{
		case 4:			// CoreXYU
			return (directionVector[X_AXIS] * axisFactors[X_AXIS]) + (directionVector[Y_AXIS] * axisFactors[Y_AXIS]);
		...
		}
		break;

	case Y1_AXIS:
		switch(coreXYMode)
		{
		case 4:			// CoreXYU
			return (directionVector[Y_AXIS] * axisFactors[Y_AXIS]) - (directionVector[X_AXIS] * axisFactors[X_AXIS]);
		...
		}
		break;

	case Y2_AXIS:
		switch(coreXYMode)
		{
		case 4:			// CoreXYU
			return (directionVector[Y_AXIS] * axisFactors[Y_AXIS]) - (directionVector[U_AXIS] * axisFactors[U_AXIS]);
		...
		}
		break;

	case U_AXIS:
		switch(coreXYMode)
		{
		case 4:			// CoreXYU
			return (directionVector[U_AXIS] * axisFactors[U_AXIS]) + (directionVector[Y_AXIS] * axisFactors[Y_AXIS]);
		...
		}
		break;
	...
	}
	...
}

We will need to add support for more independently-driven motors than axes (which we need to do to implement true bed levelling anyway), but other than that it looks straightforward. Homing in RRF is done in gcode files, so no firmware changes will be needed to support XYU homing, and any adjustment of motor currents during homing can be done in those files.

---

Large delta printer [miscsolutions.wordpress.com], E3D tool changer, Robotdigg SCARA printer, Crane Quad and Ormerod

Disclosure: I design Duet electronics and work on RepRapFirmware, [duet3d.com].

That makes sense, assigning U as the second X. You just invented CoreXYU !!!
See why you choose Y1 and Y2, rather than Y and V, as V would imply independent movement, Y1 and Y2 infers commonality, as used in multiple Z motor configs.
Have the RADDS with the extension board, for a total of 8 steppers. Planning to connect the extruders to the extension and use the main board for CoreXYU. Therefore outputs will be X, U, Y1, Y2, Z1, Z2, E1 and E2.

There's a few other twists that I'd like to implement on the IO side, including a 100 pulse/rev hand wheel and axis/step size selector for manual inputs. I have two limit switches per axis for homing and in the opposite direction to prevent over-travel in handle jog. Plus there's a Hall-e between the X-Carriages to detect collisions. Trying to figure out where to plug the Hall-e as all 6 +/- XYZ slots will be used. Gonna forego filament sensors at this time, though would like to add them later.

Fixing a minor issue with the twisted belts in the back, adding a second toothed idler as the belt wants to skip out on the toothed pulley. Since it's no load and only for straightening the run before it gets to the corner idler, a tangential 20T pulley on a brass shaft is sufficient. Will have them installed next week, just waiting for more filament from NewEgg, so I can print the new brackets on my Makerbot Rep2. Ran out of grey making Xmas presents

Then, start wiring

Edited 1 time(s). Last edit at 01/13/2017 12:14PM by prot0typ1cal.

Quote
Origamib
It seems to me that you could use one less motor to control 2 heads independently, whilst still controlling XY. Check out the CorEXY for ideas. I think you could easily use a similar belt run to control the 2nd tool.

Other than that, I am loving your machine. Linear rail and ballscrews in all the right places

Thanks for the praise
The "E" on the CoreEXY looks ineffectual as it's on a continuous belt. Without an anchor(s), looks like there's no impetus.
If you read my previous posts, you'll see there's a real need for 4 motors to counter the imbalanced masses of the Y and X carriages in a typical CoreXY, which most people tend to disregard.

Sure there's other solutions that will work, like a MarkOne loop for the second X so only one additional remotely mounted motor would be required.

CoreXYU is my solution (think I'm the first anyways). Not only do you get more Y-force to counter different inertial loads in the CoreXY configuration, also get two independent print heads. Booya !!!

Just throwing this pic out there, please tell me if it makes sense:

Edited 2 time(s). Last edit at 01/15/2017 06:21PM by prot0typ1cal.

It makes sense to me, but you need to add the drive system constraint delta A - delta B = delta C minus delta D.

Edited 1 time(s). Last edit at 01/15/2017 03:27AM by dc42.

---

Large delta printer [miscsolutions.wordpress.com], E3D tool changer, Robotdigg SCARA printer, Crane Quad and Ormerod

Disclosure: I design Duet electronics and work on RepRapFirmware, [duet3d.com].

Out of curiosity, what are you planning to have it mill? I doubt that the frame is rigid enough for metal work, so I'm guessing plastic/wood, or engraving?

Quote
dc42
It makes sense to me, but you need to add the drive system constraint delta A - delta B = delta C minus delta D.

Done, also fixed the delta C and delta D vectors, they were on the wrong side of the loop :p

Quote
anvoice
Out of curiosity, what are you planning to have it mill? I doubt that the frame is rigid enough for metal work, so I'm guessing plastic/wood, or engraving?

With high speed machining, I'm hoping to do some aluminium. No full width cuts, typically only 10-20% cutter width and 1/8" diameter cutter max, and depths of only .05-.10 mm deep at 50mm/sec or less.

Not done with the frame yet. Theres 8x more hidden button heads that will attach inside each Z side column. M5 tapped into the end of the 20x20 and 20x60. with the button head in the mating slot. Will need to drill clearance holes for the hex wrench in the right places.

In addition, there's going to be a plywood "U" on top, bolted to the frame. Plus, plywood side and back panels for even more rigidity. Also need to build a box for the electronics inside the frame's base, just haven't gotten that far yet

Nice, looking forward to seeing how it will turn out. Looks like a solid machine.

Been a month between jobs, so haven't the resources to work on Hlidskjalf.
As soon as time/money permits will continue Have too much invested to quit now dangit!

This is sweet, just for the record.

Following this on Thingiverse and here. Would love to swap out 2 of my 200mmx200mm printers for one of these!

+1 for this idea its a great looking machine and innovative too.

---

Simon Khoury

Co-founder of [www.precisionpiezo.co.uk] Accurate, repeatable, versatile Z-Probes
Published:Inventions

Thanks
Still a WIP. Got some quality crimpers coming from Japan to finish the wiring.
Slow but steady progress...

Keen to know how this is going? I plan to rebuild my corexy at some point and a dual x carriage design is definitely on the cards. What do you see as the advantages of going with two "corexy" mechanisms, rather than one with a second more conventional x rail mounted on it, with a motor stacked on the axis?

---

Simon Khoury

Co-founder of [www.precisionpiezo.co.uk] Accurate, repeatable, versatile Z-Probes
Published:Inventions

DjDemonD,

Well...let's break it down to math.

CoreXY equations of motion:

dX = ( dA+dB )/2, dY = ( dA-dB )/2
dA = dX+dY, dB = dX-dY

CoreXYU equations of motion:

dY = (( dA-dB )+( dC-dD ))/4, dA-dB=dC-dD
dX = ( dA+dB )/2, dA = dX+dY, dB = dX-dY
dU = ( dC+dD )/2, dC = dU+dY, dD = dU-dY

Given the following (using Hlidskjalf's masses as reference build):

X-Carriage = .30 kg
Y-Gantry = 2.20 kg
Torque per stepper = .54 N-m (.54 kg-m²/s² )
Vi = 0, initial velocity
Vf = .10 m/s, final velocity (100 mm/sec), at 45 or 135 Vf = 70.7mm/s for X (or U) and Y.

12.73mm = pitch diameter of 20T GT2 pulley (40mm/rev)
N-m = F x r
.54 kg-m²/s² = F x .006365m
F = 84.84 kg-m/s² ea. Stepper

25.46mm = pitch diameter of 40T GT2 pulley (80mm/rev)
belted 2:1, 20T pulley must drive at 2x RPM
Effectively doubling the Force! Even at 100 mm/s steppers turn at only 150 RPM.
F = 169.68 kg-m/s² ea. stepper

Ignoring inertia of steppers, belts and pulleys...

Equations for motion dynamics:

F=ma
Vf = at + Vi

Conditions for CoreXY:

1, accelerating X carriage only. (X only move)

dX = ( dA+dB )/2, therefore both A and B must accelerate to 100mm/s (.10m/s), load for each is halved (mass is divided by 2).

F=ma
169.68 kg-m/s² = .15kg(a)
1131.2 m/s² = a

Vf = at + Vi
.10 m/s = 1131.2 m/s² (t) + 0
= .00009 seconds

2, accelerating Y with X carriage stationary. (Y only move)

dY = ( dA-dB )/2, like an X only move, both A and B must accelerate to 100mm/s (.10m/s). Load is increased by gantry mass, still shared by both.

F=ma
169.68 kg-m/s² = 1.25 kg(a)
135.74 m/s² = a

Vf = at + Vi
.10 m/s = 135.74 m/s² (t) + 0
= .00074 seconds

3, accelerating in X and in Y. (45 or 135 degree move, only one stepper provides force))
Load is gantry plus carriage weight. However, we are moving at the sin of 45, velocity in each the X and Y is only .0707 m/s.

F=ma
169.68 kg-m/s² = 2.50 kg(a)
67.87 m/s² = a

Vf = at + Vi
.0707 m/s = 67.87 m/s² (t) + 0
= .00104 seconds

Obviously, even without the math, it takes longer to accelerate more mass.

Now for something completely different...
Hlidskjalf uses 4 motors to drive two X-carriages.

Conditions for CoreXYU:

1, accelerating one X-carriage only, Y stationary. (X or U only move) Again, two steppers share the load.
Not suprising, the time is the same as the CoreXY.

F=ma
169.68 kg-m/s² = .15kg(a)
1131.2 m/s² = a

Vf = at + Vi
.10 m/s = 1131.2 m/s² (t) + 0
= .00009 seconds

2, accelerating Y-gantry with both X-carriages stationary. (Y only move)
This is where it gets interesting.

For CoreXYU dY = (( dA-dB )+( dC-dD ))/4
All 4 steppers share in the load, 2.80 kg total for 2x 0.3kg carriages and the 2.20kg gantry, effectiively 0.7 kg per stepper.

F=ma
169.68 kg-m/s² = 0.7 kg(a)
242.4 m/s² = a

Vf = at + Vi
.10 m/s = 242.4 m/s² (t) + 0
= .00041 seconds for CoreXYU, compared to .00074 seconds for CoreXY with only 2 steppers. 1.8x times faster for CoreXYU.

2, accelerating Y-gantry and one X-carriage in X or U. (45 or 135 degree move)
Because we're only moving one carriage, two steppers are working on the Y and stationary carriage, plus the Y component of the second carriage moving at 45/135 degrees.
Third stepper translates in X (or U) of the 45/135 degree carriage and its Y component, while the last stepper remains motionless.

This is where the algebra gets wack, as we must look at the sum of the 3 active steppers and how each contribute to the motion.
3 steppers, each with a force of 169.68 kg-m/s² = 509.04 kg-m/s²
All mass is in motion = 2.80kg

F=ma
509.04 kg-m/s² = 2.80kg(a)
181.8 m/s² = a

Vf = at + Vi
.0707 m/s = 181.8 m/s² (t) + 0
= .00039 seconds for CoreXYU, compared to .00104 seconds for CoreXY. CoreXYU is almost 2.7x faster, even with the additional 0.3kg mass.

Now you don't need to believe that, so I'll break it down into the X and Y components acting alone.
Only 2x steppers moving the Y gantry:

F=ma
339.36 kg-m/s² = 2.80kg(a)
121.2 m/s² = a

Vf = at + Vi
.0707 m/s = 121.2 m/s² (t) + 0
= .00058 seconds

Third stepper acting alone on a single carriage:

F=ma
169.68 kg-m/s² = 0.3 kg(a)
565.6 m/s² = a

Vf = at + Vi
.0707 m/s = 565.6 m/s² (t) + 0
= .00013 seconds, hmm... that leaves time to help the Y which will have already reached .0158 m/s driven by 2x steppers.

Vf = 121.2 m/s² (.00013 seconds) = .0158 m/s

Now all 3 steppers are in full force on the Y,

509.04 kg-m/s² = 2.80kg(a)
181.8 m/s² = a

Vf = at + Vi
.0707 m/s = 181.8 m/s² (t) + .0158 m/s
.0549 m/s = 181.8 m/s² (t)
= .00030 seconds to finish Y acceleration

So if we assume the above, the total acceleration time will be .00013 + .00030 = .00043 seconds, which is still better than the .00104 for CoreXY.
However, force from the 3rd stepper will act on both the gantry and carriage simultaneously, not selectively on both axis.
So the third stepper will "help" the two moving the Y, while it moves the single carriage, hence the previous .00039 second, which is only a .00004 second gain.

Conclusion

CoreXYU has more force (steppers) available for any given move, providing better accel/deceleration times.
If you were to add an idex style second X carriage to the gantry, it will only add mass in the standard CoreXY equation.

Edited 2 time(s). Last edit at 05/24/2017 01:11PM by prot0typ1cal.

I'm going to be honest and say physics was not my speciality but it is clearly yours, so I will accept the calculations (impressive work).

Do you know the equations of motion I would need for my proposed scheme? A and B motors would have to control Y position for the 2nd carriage when it was active? Otherwise its standard corexy for the 1st carriage. Maybe thats the wrong question, its just a case of the firmware driving it differently when the second extruder is active.

However there is a trade off between complexity and the end result. I love the idea of your machine its pushing the boundaries which is very commendable, but perhaps I'm looking to achieve the same/similar result quicker and cheaper? I agree it will perform less well, but I'd argue that it would be marginally less, as my current A and B motors are well within their ability to move the corexy mechanism I have now, adding a carriage and (possibly) just a nema 14 motor to the mechanism to move the 2nd x carriage, will result in a lower performance machine but still a dual x carriage corexy.

Edited 1 time(s). Last edit at 05/24/2017 01:34PM by DjDemonD.

---

Simon Khoury

Co-founder of [www.precisionpiezo.co.uk] Accurate, repeatable, versatile Z-Probes
Published:Inventions

I think the firmware will be the only real hurdle, as a hybrid idex/coreXY isn't currently a provided configuration. DC42 could probably help you out if you were to use RADDS.
You will also need to work out belt routing, while the two tiered CoreXY to make the CoreXYU was actually pretty easy and added symmetry to the design and use common components.

Another item I didn't provide the math for is that I intend to use Hlidskjalf as a CNC, where the X and U carriages are ganged together with a connecting plate and a spindle added.
I'll have 4 steppers working in synch, and for 45/135 moves, 2 steppers will be active.
True, I could have built using nema 23's, however belting the 17's at 2:1 ratio give me higher resolution and higher torque without exceeding RPMs where torque drops.
For CNC work, power and precision are important. Having 4 belt ends attached to the CNC carriage, and attaching to both above and below the gantry extra stability.
I'm excited about finally getting Hlidskjalf together and running, as it's been almost a year in development. I have all final tools and materials required on hand, just need to do it.

Odin give me the strength to complete it, as I've already spent my wealth.

Carry on, can't wait to see it in action. These things are expensive, but very satisfying when they work. What sort of money have you ploughed into it, if its not too crude a question?

---

Simon Khoury

Co-founder of [www.precisionpiezo.co.uk] Accurate, repeatable, versatile Z-Probes
Published:Inventions

So far... over 2 grand (American).

Considering the closest printer is the BCN3D, which is over $3k with shipping, and only a 210 mm x 297 mm x 210 mm print volume.
[www.bcn3dtechnologies.com]

Hlidskjalf build volume is 340 mm sq x 400 mm tall, though Z might drop to 370 mm to accommodate a front panel.
Goal was only a 340 mm cube (13.37" cube), so all is good.

Nice, my kossel Xl cost me around £1000 but prints better than a commercial machine double that price. For that I could print 300mm circular x 450mm. Not that I've ever tried it.

---

Simon Khoury

Co-founder of [www.precisionpiezo.co.uk] Accurate, repeatable, versatile Z-Probes
Published:Inventions

Hi prot0typ1cal,
Your project looks very impressive as well as innovative. I’m currently building a printer with the same kinetics as Hlidskjalf. It’s a pure 3d-printer and have no ambitions of doubling a as CNC machine so it might be a bit less complex.
I posted a request for firmware support over at the duet forum for this style of printer and from Davids response I do believe it could be implemented in a not too distant future. I’m impressed with the community and support provided for the duet.

I’m currently designing the bed. It will be a driven with 3 steppers and at the end of the print I want it to drop the front 45deg (or as far as the build volume allows after the print) for easy access and removal of print.
Build volume will be 500x500 and maybe 800 in z. I’ll use zesty nimbles for extruders to keep the mass down. I’m planning on full enclosure to be able to keep o temperature of 70°C and have placed the electronics and steppers at the bottom of the printer to keep them cool. Outer dimensions without top enclosure are 750x750x1200mm.
I did record a quick xy movement test at [youtu.be]

Even through you probably started your project first you better speed up the implementation or I might be the first (as far as I know) to complete a corexyu/corexy-idx printer.
Please keep us informed of your progress!

Thanks for the heads up Lars.
The race is on !