"Ola", the RepOlaRap.

I purchased all the hardware and non-RP parts for a Mendel. Initially, I had planned on, like others, to build the RP parts with wood. However, after spending a few days redesigning and prototyping alternate versions of the X carriage (at version 3 and still not completely happy with it), I’ve decided that payoff is not worth the time and effort for me.

Instead, I’ve decided to pursue an old idea I had about using a polar XY stage (and possibly a semi-polar Z stage – haven’t decided yet.) I’ve named the design “Ola”, a play on Re[pOlaR]ap.

I should be soon starting work building a prototype, but before I went forward, I wanted to see if anyone else had attempted this type of robot, see any obvious flaws in my plans, or have any comments in general. It seems the design should cost less, and be easier and quicker to build without any RP parts -- Some MDF and careful use of a handsaw, coping saw and hand drill should be adequate.

My current design consists of a build stage, a disk ~14cm in radius and ~15mm thick, sitting on a radial arm platform, a disk ~21cm in radius and ~15mm thick. The build stage is offset from the pivot arm at ~7cm radius relative to the radial arm center (the Z-axis moves the tool along the line orthogonal to the ~7cm radius circle too.) Two bearing carriages will separate each platform -- ~4mm thick; combined with about twenty 5mm steel balls each (and countertop laminate), this should give reasonable stability with thrust bearings and gravity to compress the stages together. My plan is to use a stepper belt driven mechanism to drive each stage, and to use a (relatively low resolution) encoder to maintain repeatable absolute and homing positions. I'll try to put a blender model up later, to make it easier to visualize.

My plan is to compute the inverse kinematics on the host computer, and send cubic splines to approximate required motions. Cubic splines can be computed stepwise using only integer addition, so I’m confident the current Arduino based electronics should be more than capable of handling the embedded computations; I’m also pretty sure the cubic splines should allow for enough reduced communication and accuracy to prevent a communications bottleneck between host and firmware.

This physical architecture, with .1mm resolution for the outer rim on the build stage and the circle with ~7cm radius on the radial arm disk, and proper size for the motor pulley, should give reasonable speed and resolution for the majority of the build platform area: the radial position constrain both -- E.G, at 5cm radius the build axis produces a circular 5mm/sec speed with .03mm resolution. At 10cm, it will be twice that. Some build areas do become problematic -- as you approach the center, the build platform resolution approaches 1/inf while speed approaches 0 (It becomes an incline for the .1mm resolution radial arm motion.) If necessary, it seems proper model positioning and/or “holes” can avoid these areas.

This results in a 2D donut shaped build area, about ~600 cm^2. It can build a square with a hole at 20cm x 20cm. It can build a rectangle with a hole at 24cm x 14cm. It can build circular shapes to the limits of the outer build platform rim (28cm diameter ~= 11 inches). I believe this should allow all RP parts of a Mendel to be built, as well as possibly RPing many of it's own parts (the bearing carriages, for example.) It avoids many parts required by Mendel X+Y axis: no studding, only 2 thrust bearings (instead of 20x 628's), no bearing bars, no highly detailed carraige parts, etc.

What do you all think? Any problems with the idea that you can see?

It sounds interesting. "Polar" RepRaps and RepStraps have been proposed before, but I don't remember if there's enough meat in the resultant discussion, kibbitzing, and analysis to do a search for.

One pesky issue is squareness. Because it's pretty easy to use a 1-2-3 block or straight edge and an electronic continuity-type edge finder or other random machinists tool to check squareness and linearity of a move. ("Make a line. Now a right angle, and another line. ... good to .005 inches!") And if there's error, it's easyish to diagnose and fix.

Now imagine discovering that your polar machine makes 87 degree angles, and prints cubes that aren't square. Now imagine troubleshooting. ... Bleeeeeeeergh. Once more, with feeling. Bleeeeeergh.

Now imagine you've got it working, with a nice writeup, and people are making them, and they're trying to get theirs square, and you need to write up squareness, and explain what a cubic spline is to a CS student who sleep-waked through calculus in order to get at the fun stuff like compiler design. Bleeeeeergh.

You run into similar problems with delta robots, stewart platforms, and so on. Cartesian robots are simple, even if they're not as elegant as designs which make more efficient and elegant use of materials and components.

Viktor has some thoughts on delta robots. He went delta, got frustrated, picked up a cartesian machine, (either a mill-Strap or a Cartesian pick-and-place-strap right now, I don't remember), and is jousting at that windmill again. I think we all will eventually, for the post mendel, and post-post designs. Because its cool.

So go for it, but be warned. And pick up a used sherline or taig to use as a testbed. Once you have polar working well, sell or keep the taig, incurring ~$50 shipping costs, in the former case, but you'll have had a working machine all that time, whereas a pure polar research project with no cartesian repstrap handy could be a death march, with no fun, and with no fun machine.

Now that you are warned and advised, I encourage you to go polar, and document/sketch/note at
[objects.reprap.org]
or
[objects.reprap.org]
and in this forum thread. Cause I want to see the drawings. Cause it sounds cool.

Edited 1 time(s). Last edit at 01/07/2010 06:56PM by SebastienBailard.

Thanks for the comment. I've filled out an initial draft of my plans for the structural components on the Wiki link; I also uploaded the image to demonstrate the structure there.

Do you know the general approach for measuring the tolerances you describe for general use turntable polar robots? I'm not sure how common the model I've use is in other applications. Anyone know?

I believe only 3 variables for the X Y polar stage need precise measurements to compute the exact polar coordinate of any 2D point in the model space for the the build platform: the radius of the radial arm pivot to build platform pivot, the radius of the radial arm pivot to the extruder head, and the exact radial arm angle for which the extruder head reaches it's maximal build platform radius. I think these can be measured by measuring exact distances between dots or lines?

Nope. I don't know that stuff. Conceptually, you could bolt the 123 block or angle plate onto your build platform, use the touchprobish stuff, and code a script that tries to follow the edges of the 123 block, feeding good and bad points back into the computer from the probe back into the arduino.

Or a pen and graph paper.

Then use the dataset with your control 'matrices', e.g.
[en.wikibooks.org]
I think, maybe.

Then something like back-propagating the errors to find out what iffy (off square bits) of your mechanisms are.
[en.wikipedia.org]

I'm a physicist, and I'd guess that's how an engineer would do it, but I enjoy hearing the real version. Physicists don't learn about complicated stuff like trusses and machine components, they learn about simple stuff like hydrogen atoms and planets.

A machinist would think about it for a little bit and then make a good Cartesian version that just worked.

I'm probably making it too hard. You could polar-raster across the big flat top of the 123 block in order to figure out how off-axis one platform was.

I haven't made any study of this stuff, I'm just generalizing from bits I've picked up.

Sounds good. I'll see what I can come up with when I get to the stage of having to measure how on or off the axis is. How likely will measuring straightness using a straight-edge and measuring the diagonals of a "rectangle" for squareness be? In theory an inaccurate machine can print parts for a more accurate child, correct? (Either mendel, or perhaps a second generation RepOlaRap!)

BTW: I've already got the forward and reverse kinematics working in software - the forward kinematics are extremely easy:
x = cos(e) + a*cos(e+s)
y = sin(e) + a*sin(e+s)

Inverse kinematics are a bit more complex, but still pretty easy to do in host software, though these formulas have to be tweaked a bit to handle special cases when motion crosses a branch cut on the acos and atan functions:
e = atan2( y, x ) - acos( ( xx + yy + 1 - aa ) / ( 2 * sqrt( xx + yy ) ) )
s = acos( ( xx + yy - aa - 1 ) / ( 2 * a )

'a' is a constant defining the ratios of the build platform radius and tool head radius, relative to the base/radial arm pivot. x and y are coordinates within the model space and would need scaling to achieve linear metrics (probably where the 123 block may need to come into play?)

In any case, I appreciate the comments. You have the excuse that you're a physist ; mine is that I'm a mathematician. If one had to increase milk production, an engineer would come up with a sensible solution like the purchase and installation of a milking machine; The mathematician would offer the advice to use spherical cows.

now the really fun part is plotting constant-speed movement along arbitrary lines, especially when the line being extruded comes close to the center point

Indeed. The area near the center gets really tricky. Initially, I simply plan to ignore that part and pretend it's not there. Not a problem if you never visit it. Hehe.

In the picture I posted to the wiki area (http://objects.reprap.org/wiki/RepOlaRap) for a simulated square, you can see the speed varies slightly even with 5mm splines. I may need to evaluate alternatives to cubic splines or some simple firmware capable transform that make them more suitable and accurate for constant linear motion.

As to my progress, I've started. I've ordered the 5mm steel balls ($8 per 100 -- should be more than enough.) Cut out build platform, and radial upper and lower platforms. It's quite heavy (~4kg or so) and I'm thinking now that perhaps 10mm platforms might be sturdy enough. I'll forge forward with the 15mm stuff for now. I simulated motion using some of my sons marbles and some cardboard bearing races, and it is extremely easy to spin by hand. The inertia might slow things down a little, but that can be managed, I think (It should be faster than cheap threaded rod, I think.)

How are you driving the wheels? Rubber belt around a wheel and drive wheel on a stepper?

Looking at your drawings I think that a RepOlaRap will be byfar the most interesting RepStrap to watch while its printing.
I can imagine the hypnotizing effect it will have on those watching it working.
It will look like a peice of animated modern art that has a true function in life.

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Bodge It [reprap.org]
=======================================

---

BIQ Sanguinololu SD LCD board	BIQ Stepcon	BIQ Opto Endstop
BIQ Heater Block PCB	BIQ Extruder Peek clamp replacement	BIQ Huxley Seedling
BIQ Sanguinololu mounting	BIQ standalone Sanguinololu or Ramps mounting	Print It Stick It Cut it

My rep strap: [repstrapbertha.blogspot.com]

Buy the bits from B&Q pipestrap [diyrepstrap.blogspot.com]
How to Build a Darwin without any Rep Rap Parts [repstrapdarwin.blogspot.com]
Web Site [www.takeaway3dtech.com]

>> How are you driving the wheels? Rubber belt around a wheel and drive wheel on a stepper?

Yep. Same stuff as Mendel I think -- Belt guides and encoders to keep it honest as backlash and slip happens. If I can print plastic on it, I should be able to make gears? They would huge though 26cm-28cm diameter for the little one; PLA best material for objects of this size, right? How were we gonna skin that fish again?

I'll post some photos to the rep-rappers blog once the steel balls arrive, and I've constructed the races and assembled everything together. The current stuff looks nice, but it's quite inert. MDF - MDF contact with tightened thrust bearing doesn't allow for much movement.

Oh, and speaking of encoders -- any good or bad experience with reflective LED/photo-transistors used on ink jet printed encoders? What is the minimum width for the light/dark strips and still have reliable detection? I currently plan on a ~27cm diameter encoder wheel, with dual ~3mm stripe tracks giving 512 steps per revolution. Can I go smaller (1024 @ 1.5mm or 2048 @ 0.75mm) and still get reliable encoder output?

- My current toolset is a scroll saw, power hand drill + bits, and assorted tools one would expect in a toolbox (wrenches, screwdrivers, etc.). Could replace scroll saw with coping saw with patience and slow careful cutting.

- I depend on a printer to print out templates that I glue to the MDF to cut it out.

I'd suggest making a jig. Drill through the center of the the piece of MDF, put a bolt through it, and sping it arount the bolt, cutting with the saw. Maybe.

Oh, and speaking of encoders -- any good or bad experience with reflective LED/photo-transistors used on ink jet printed encoders? What is the minimum width for the light/dark strips and still have reliable detection? I currently plan on a ~27cm diameter encoder wheel, with dual ~3mm stripe tracks giving 512 steps per revolution. Can I go smaller (1024 @ 1.5mm or 2048 @ 0.75mm) and still get reliable encoder output?

Take a look at these, which are cheap:
AEDR Reflective Optical Encoder Modules - $7.25
[usdigital.com]

The fine ones (212 lines / inch) are 8 lines / mm, or 1 line @ .125 mm, which will be fine, assuming the reflectivity works.

If inkjet and generic paper doesn't work, try coated papers, laser printer, and transparency film. (Note: transparency film for inkjets does not work in laser printer or photocopiers. It instead melts to make a nice set of ornamental frills around your rollers and in your fuser. Be sure to use laser printer transparencies in laser printers.)

The AEDR encodure modules look awesome.. Wowser! Even the course ones are better than the tolerance I was planning on for my first prototype. I'll plan on using two of these then for the XY polar stages. Thanks a bunch.

Something for future research too... use a cheap DC motor with these bad boys. No more steppers needed if a PID controller can be created to run fast enough on a arduino .. sheesh .. makes me wish I had the prototype already so I could play with this kind of stuff make it better and cheaper already..

one other small suggestion: try to find an efficient positioning algorithm that uses only motions in one direction of the radial axis (means clock wise or counter-clock wise). Why? it would then be easy to achive arbitrary precision, because you could simple take any gearbox out there and will never have the problem called "backlash".

Unless I'm mistaken, for arbitrary linear segments, the RepolaRap could only get away with this on the build platform; The radial arm platform must reverse direction whenever the line being printed becomes tangent to any circle with center at the build platform pivot. Also, only the build platform will have true cyclic motion, able to spin in one direction as long as desired. The power and communications wires to the inner motor and encoder will limit the rotational freedom on the radial arm platform; I'll probably limit its rotation to 180 degrees total for my prototype; mathematically, this allows reaching any reachable point on the build area.

Fortunately, the encoder mounts directly onto each platform. Backlash will not fool the feedback loop, so even with lots of backlash and minor vibration, the problem should be solvable in firmware/software. My initial plans were to measure backlash and use that to compute actual position when reversing directions. Now I that my encoder may very well have higher resolution than my stepper motor, I may just forget that plan and drive the stepper using a very simple feedback loop tied to the encoder and timeslice target position -- I.E, My steppers will actually be servos.

Backlash is not easily compensated for on an additive machine. When you change directions you get a dead band where the axis does not move, but the extruder will continue, so you will get a blob. You could turn the extruder off and on again but the extra stops and starts will not do your build quality any good.

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[www.hydraraptor.blogspot.com]

Just look at the excellent rack and pinion design from Forest.

I'm sure this could be re jigged to make segments of gear teeth for your drive system. This should/would eliminate any backlash problems.

---

Bodge It [reprap.org]
=======================================

---

BIQ Sanguinololu SD LCD board	BIQ Stepcon	BIQ Opto Endstop
BIQ Heater Block PCB	BIQ Extruder Peek clamp replacement	BIQ Huxley Seedling
BIQ Sanguinololu mounting	BIQ standalone Sanguinololu or Ramps mounting	Print It Stick It Cut it

My rep strap: [repstrapbertha.blogspot.com]

Buy the bits from B&Q pipestrap [diyrepstrap.blogspot.com]
How to Build a Darwin without any Rep Rap Parts [repstrapdarwin.blogspot.com]
Web Site [www.takeaway3dtech.com]

Yes. They look very nice. I had already planned on using his good work if I get to the point of a second generation RepolaRap.

Just saw your post with the stepper mounted looks good.

Will you stick a thin layer of rubber sheeting around the platform to give the belt better grip or stick more belt around the platform to make it like a big gear drive?

---

Bodge It [reprap.org]
=======================================

---

BIQ Sanguinololu SD LCD board	BIQ Stepcon	BIQ Opto Endstop
BIQ Heater Block PCB	BIQ Extruder Peek clamp replacement	BIQ Huxley Seedling
BIQ Sanguinololu mounting	BIQ standalone Sanguinololu or Ramps mounting	Print It Stick It Cut it

My rep strap: [repstrapbertha.blogspot.com]

Buy the bits from B&Q pipestrap [diyrepstrap.blogspot.com]
How to Build a Darwin without any Rep Rap Parts [repstrapdarwin.blogspot.com]
Web Site [www.takeaway3dtech.com]

BodgeIt Wrote:
-------------------------------------------------------
> Will you stick a thin layer of rubber sheeting
> around the platform to give the belt better grip
> or stick more belt around the platform to make it
> like a big gear drive?

I haven't made any plans yet. Your ideas might work. If it is a problem, I see four approaches to address it... did I miss any?

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- Increase coefficient of friction between belt and platform
* your 'rubber sheet' idea
* use with contact sheet sticky spray
* tack thin strips of sandpaper to circumference

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- Increase force between belt and platform
* add tension roller
* add pinch rollers

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- Add 'teeth' to give a greater angle of direct force
* your belt idea (even though teeth would not mesh completely)
* add several segments of belt
* use some kind of jig and sawblade to cut out gaps for teeth.

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- Ignore or work around the problem
* test out and see how much slip there is.. if it's minimal, encoder feedback should allow minor occasional corrections.
* use the encoder to detect actual position, and run a PID control to the stepper (start the siren if it hasn't been able to move it for a second or two.)
* use software to always adjust accelleration to never exceeds thresholds based on measured static friction coefficient.

This might be jibberish, but i had an idea that might fix the center hole problem.

Say you built two polar platforms like you had, that worked together over one build space, where the ouside of one circle would intersect the center of the other, so that when the machine enters unstable ground with one, the other is extremely accurate. I think this would solve the square problem also.

Not jibberish at all. It is actually the ideal RepolaRap configuration.

Just a note though.. it will be the position of the extruder, not the platforms, that determine the problematic locations. The issue you note about the disks lining up just determine the maximal model space area.

In any case, you're right that you'll have very great freedom along one line, even at or near the degenerate points; The degenerate points at the outer rim has greatest freedom in the 'orbit' direction around the model space. The degenerate points at the center have greatest freedom in the direction of current travel (it can't 'turn' very easily).

Once I see how fast the steppers can drive the platforms, I'll have a better idea about how limiting those areas will be and whether they'll need to be excluded or included for printable objects.

sounds good. between repolarap and the delta bots, im not sure if ill be going mcwire --> mendel anymore.

any update on this?

Nothing more to report as of yet, at least since mounting the motor. I have an FTDI cable on order, along with some LED/photo resistors that I'm going to try before doing the $8 encoder route.

I'll see what I can do about using my arduino mega I have, see if I can at least spin the platform. I'm still a little concerned about weight and speed to spin it.

I hope it's helpful.

I wish we had more RepRap servo documentation and development.

Because it's a useful technology and it's a waypoint for RepRap robotics projects.

Update on this: The build platform works great.

I was able to drive it at about 6 RPM, and switch directions very quickly. 6RPM is about 8cm per sec at the outer rim, and proportional to distance from the center (I.E, 4cm at 7cm radius.)

If I can figure out how to post a video, I'll add a blog entry.

Just a quick progress update, I received a package last night, and today.

The first package contained the 4 pulleys I ordered to replace the one I stripped. I figured since shipping was going to be $7, I might as well get my moneys worth, as the pulley was only $7. The other 3 will find homes, I am sure. The steppers are mounted. I've attached a 4 line screw junction on the radial arm platform, and wired the top motor to that. I have a ~40 cm long 4 wire CAT3 phone cable (AWG 24 - after studying the ohm/ft readings, it should be fine in open air) for that motor, terminating in an RJ25 plug. I've also modified two MakerBot stepper motor controllers by adding wires to the underside and terminating into an RJ25 jack. (The plugs were $10 for 25, the plugs about $23 for 10) I may eventually swap out the cables with a bit larger, twisted pair, stranded lines if these end up being too noisy or heat up too much.

The second package frightens me a bit.. SMD high intensity red LEDs and Red/Infrared photo-transistors. I'm not sure what insanity possessed me to order these, but I suppose I'll try to figure out if and how to turn them into a usable encoder. I believe Forrest was able to use conventional (tiny) wires on a magnetic hall effect SMD device, so I do have some hope that I can get something testable. Anyone have any hints, tips, or thoughts for the best way to create a prototype encoder from these tiny devices?

If it works, the encoder for a 3 photo-transistor detector (2 quadrature lines + 1 digital reader to detect absolute position at regular intervals) would come in for about $1-$2 per (really tiny) board; I bought 10 LEDs and 50 photo transistors (<$10); Oh, the package also had the FTDI cable needed to connect to the RepRap motherboard.

No pictures at this stage, I want to get both motors working so I can make fun rose curve pencil drawings.