Sisyphus mini: The polar-Delta_Ultimaker-gantry Thing

Hi everyone, my apologies for the weird headline...

Digital_Dentist introduced me ( us ) to a cool machine he wants to DIY CoreXY-style.
Sisyphus Kickstarter campaign

I thought of building a smaller, cheaper and easier to build desktop version.
It is based on bipolar-modded 28BYJ stepper, because it fit's the bill and has plenty of steps/turn ( ~4096).
That's important, because I want to build a 2D polar-Delta mechanic, which guides the magnet. The motor shaft will only turn 120° at most.



I hope the picture tells it all, but feel free to ask details.
I want to use Arduino UNO and CNC shield, because it has a small footprint and is cheap.

Problem is, I have no idea how to implement this kinematic into GRBL or any other FW that fits a 328P MCU.
Anyone having better controller in mind or is willing to cooperate in any way? We could call it: RepRap-Christmas project *wink*

I also have intentions to replace the sand with some transparent fluid ( honey-like consistence ) and just let the steelball carve some, slowly disappearing, traces while we could also watch the hypnotic moves of the mechanic.

Edited 3 time(s). Last edit at 06/24/2018 02:51AM by o_lampe.

The only way i think of doing it is by using sketch up with a Spirograph plugin and sketchucam to generate the gcode for GRBL but this is only good for x y coordinates.

Bcnc also has a Spirograph generator built in.

Perhaps you can convert the xy coordinates to delta style with the same maths as marlin uses to convert.

edit,

Thinking about it GRBL is only XYZ, might be easier to hack marlin and a ramps board at least it has delta built in

Edited 1 time(s). Last edit at 06/24/2018 04:39AM by adambrum.

Interesting points adambrum,
I thought of writing some basic routines and add random numbers in firmware to generate various patterns.
I didn't know there's a Spirograph-plugin. That would make things much easier. I wonder if there's one for Inkscape, too?

I'm not sure if the delta kinematic math fits here. The steppers move left/right and work with polar coordinates.
Generally I agree about Marlin. At least we could take a look how they implemented different kinematics. Then try to sqeeze that into a UNO.

Look up sandify. It's a program for generating patterns and gcode for them. The gcode is for a corexy mechanism, but you may be able to modify it for whatever you call your mechanism.

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Ultra MegaMax Dominator 3D printer: [drmrehorst.blogspot.com]

Sandify is very interesting! Thanks DD
It doesn't matter which printer kinematics you have, just like a slicer it doesn't care. I haven't found a way to set bed center to 0,0, but that's a minor issue.

Not to bash (I like the idea, actually have plans to make something similar in the future as a glass top coffee table), just a few things to note.
Those are some big levers on the motors, when the ball is further away from the motor I imagine the tiny steppers you plan to use will struggle. Having used them before, I actually have trouble believing they can handle the lever/guide things if they are even remotely "big". That being said, happy to be proved wrong.
Secondly, the system is over constrained, you have three constraints in a 2D plane. Aside from redundancy issues you'll probably end up with the motors fighting each other at some point and they will strip their gears, this I can say from experience.

I suggest something like the hang printer with three cables/wires attached to the magnet that get spooled onto the three motors. Aside from lowering the cost of the build, it also simplifies the kinematics a little from the microcontroller's point of view since it uses squares/square roots instead of trig functions. This is especially important since you plan to use an Uno which has even less grunt than a mega. I'd be happy to help you with the inverse/forward kinematics. Another little bonus is it puts a constant load on the motors rather than having a variable lever length changing the load on the motors.

Good points Trakyan.
I tried to envision the mechanic with only two steppers in the first place, but I saw problems with accuracy and torque at certain areas. Then I thought: a third motor would compensate that, since the three motors will bundle their torque and result in even forces and accuracy.

The whole calculation should be done in integer. The UNO has 16MHz clock, like the Mega. Maybe we run short in terms of RAM, but the machine wouldn't need all the fancy stuff like a 3dPrinter. And we can go slow, so no risk to see stuttering.

edit/ Mega/Ramps wouldn't be much longer than the CNC shield. We could use it as a starting point and shrink it down later.

Edited 1 time(s). Last edit at 06/26/2018 12:47AM by o_lampe.

In terms of accuracy you'll only be as good as your weakest link, but I think you're right about three motors helping with torque. I still see torque being an issue but the only way to know is testing.

EDIT: I'm not sure if its about the clock speed, but from what I've heard trig is more computationally intensive then squares/squareroots.

Edited 1 time(s). Last edit at 06/26/2018 05:07AM by Trakyan.

Vector-math is what we need here. IMHO,that's mainly squares/roots but can include sin/cos ( as lookuptable? )
I'd like to figure out the math for the polar Delta and compare it to normal Delta algorhythms. Maybe it's easy to rewrite Marlin

The configuration you've got is entirely polar, it requires just trig functions (inverse trig for the inverse kinematics, which is what you want). Delta printers use no trig functions, instead they use squares/square roots.
The two equations you'll want to solve are more or less atan((x-x0)/(y-y0)) for your polar version, where x-x0 and y-y0 are the difference between your desired x/y position and the x/y position of your motor.
r^2=(x-x0)^2+(y-y0)^2 is what you'll need for the string driven version I suggested. It's a 2D version of the inverse kinematics delta printers use. r is the length of the string that needs to be off the spool for that motor.

@Trakyan
Can you draw a pic of the 2D string driven system? I have no idea how I'd route the lines.
In the back of my head I think, there's a fourth motor on the hangprinter to tighten the three lines?
I'm also afraid, the output bearing of the BYJ motor won't like high side loads from string tension. That would require a second gear with propper bearing.

To make things easier, I think I'll build a square version with 4 motors. That would be a classic ultimaker gantry with cartesian kinematics. Easy to use GRBL ( or Teacup ) and CNC shield. ( one driver for two parallel motors ).
The gantry will be made from small smooth rods ( 4mm dia? ) and run on Teflon bushings.

The string driven version would have 3 motors, each positioned 120 degrees apart, each one has a spool of string which goes to the effector. The hangprinter does have a fourth motor, but that because it needs something to keep the other 3 strings in tension. Here the effector is held against the table/they are all in one plane and the three lines are sufficient to keep things in tension. With strings in general you need at least your number of axis+1 strings in order to fully constrain things since strings don't work in compression. The string driven mechanism would limit your effector movement to the triangle formed by the motors, though. A fourth motor would turn your work envelope into a square, etc.

I would draw a picture but I'm afraid I'm no good at drawing pretty things, it's why I use openscad . Essentially it looks the same as your picture but with strings coming off the motors and to the effector instead of the guides.

One reason I particularly like the string idea is I think the sound of ball bearings on a smooth rod will ruin the intended effect of a zen garden table. The string would be quiet in comparison. That being said, you can in theory build a rail-less cartesian system that just relies on the belt/string tension between the carriages to guide the motion. Motion will be relatively sloppy but it will also be cheap and quiet.

... depending on speeds and acceleration the string-driven 2D-setup can be done with two motors and a counter-spring

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Viktor
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Aufruf zum Projekt "Müll-freie Meere" - [reprap.org] -- Deutsche Facebook-Gruppe - [www.facebook.com]

Call for the project "garbage-free seas" - [reprap.org]

True, since the extra string to fully constrain things is only really there to keep the others in tension, it can be replaced by a spring. A constant force spring would be ideal, they have a constant force and usually have a relatively long stroke (plenty for anything desktop sized). Best part is you can get them for cheap by gutting a tape measure, just be careful when doing so.

Edited 1 time(s). Last edit at 06/28/2018 10:26PM by Trakyan.

Tape measure...or design it from PETG and implement it in the motor frame design.
My concern about the strings_only approach is: the toolhead might tilt too much. We had to build the 'mover' pretty large which would reduce the playground.

How about this one? Cartesian and spring loaded cable drive



Hmmm, just noticed it's not Cartesian, because of the anchor points on the mover.

So here's an alternative.



Both cable driven versions reduce the playground area to a triangle shape. Or the motors/spring anchor point would have to move further outside.
Me not like...

I still think a smooth rod/teflon bearing gantry would be better. Can be cable driven and spring loaded, too.
Running out of time to make a third sketch
CU later

Edited 3 time(s). Last edit at 06/29/2018 12:43AM by o_lampe.

... here a nice sample for "kinetic art" with light - [www.instagram.com]

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Viktor
--------
Aufruf zum Projekt "Müll-freie Meere" - [reprap.org] -- Deutsche Facebook-Gruppe - [www.facebook.com]

Call for the project "garbage-free seas" - [reprap.org]

Cool!
Reminds me off deepsea jellyfish.

@o_lampe, neither of those are cartesian. I don't know what to call it but it uses pythagoras. Also, near as I can tell, using two springs does nothing but slightly shrink your work envelope.

If you want a square working area just replace one of the springs in the dual spring diagram with a third motor.

if you want a round work envelope then really only your original solution will work out of whats suggested so far. You could also have a gantry spanning the diameter as a linear axis, and then have that gantry rotate about the circle center. Like how some polar printers work but with the x gantry revolving around the bed instead of the bed turning.

I thought of other rotary gantry designs as well, but they would require closed loop cables ( belts ) and it got complicady trying to use stationary motors only.
It seems to me DD was right by using a CoreXY kinematic for his project. I want to make one, where the idler wheels also act as linear guides, stay tuned...

Oh, my.. it's almost as time consuming to paint a '3D' drawing as it would be using a CAD tool...



As you might guess, the idler pulleys for the CoreXY mechanic also act as guide rollers. The X-axis has to be stiff enough to deal with the cable tension, otherwise the guide rollers will loose contact to the smooth rods. I'm glad it doesn't have to be precise like a 3D printer...

WOW, what a brain fart!!
The rollers can't be idlers, except the cable would slide on the rollers. Or the idlers would have a bearing inside the rollers....Hmmm

Edited 3 time(s). Last edit at 07/01/2018 03:41AM by o_lampe.

you could try an etch a sketch like setup and replace the crossing bars with some tensioned strings. Yes, the motion would be sloppy, but let me assure you that's a 'motion smoothing' feature for extra zen-ness :p

I made a short weight lifting test with a 100mm long lever, pressfit on the 28BYJ. Although the driver-current was set pretty low ( Vref 125mV@A4988 ), the motor didn't stop at all, but the output gear slipped. IDK if that's a bad batch I got, or a 'safety feature', but the force required to make the lever slip is pretty low.
Don't get me wrong, the lever is tight around the flat sides of the output shaft. It's something inside the gearbox slipping.

As a sidenote, I noticed that the gears have significant backlash. The idea to use a spring to replace the third motor makes even more sense now. It would eliminate this backlash, too.

I've ordered a few V-grooved bearings and a PTFE tube. We'll see soon if the slip is a problem or not.

It's the fact its a extremely cheap component, not a safety feature. A safety feature would be the motor stalling before anything gets damaged. In my experience that slipping will lead to broken gear teeth if it hasn't already, the gears in those motors have pretty weak teeth in my experience. It's not a bad batch, that's just the specs of the motor, they're all like that.

I don't think backlash will be an issue, you're not going to need high precision and there will be a lot of slop/lag between the magnet on the effector and the steel ball it drags around. I think your bigger issue is the lack of torque, have a look at the speeds 3d printers that use these motors run at. This machine will be table sized if I understand correctly (bigger, heavier than the 3d printers that use these motors), and the drag from the magnet dragging the ball through sand is more force on the effector than what a 3d printer sees. If it moves at all, it will be very slow. Why not use nema 17s? Buying two nemas instead of two byjs wont make a big difference to the overall cost.

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myself
I thought of building a smaller, cheaper and easier to build desktop version.

With desktop version I meant a small one that fits on a desktop The 100mm levers were already lifesize if I'd go that route.

Ahh, I was picturing a coffee table sized zen garden.

I can't use the roller as idler, but I found a way to use the roller shaft as idler shaft. A compromise, that makes the X.ends pretty compact.
I chose two different sized v-groove bearings ( V603 and V624 ), but V624 would work for both jobs.
The carbon rods are nested in the V-groove, but don't touch it.
The 3rd. roller might be useless. The cable tension will hold the X-gantry together.

What would be the best sheet-material for the bottom of the sandbox?
I made some tests with 2mm thick glass and the magnet holds the ball pretty good.
But I'm afraid, the sound of sand grinding on glass could be pretty disturbing.
Another option would be a thin sheet of aluminum. When the magnet moves slow, the 'Eddy-currents' won't have an effect I guess.

Is there any sheet material, that could dampen the sound instead of amplifying it?

I wonder how it will look on a large model? After a while I’ll do the calculation, I need something like that, but much more, although I still think that this will not work for me.

Best regards,
Liam